Viscous Fingering in Deformable Systems

NASA Astrophysics Data System (ADS)

Guan, Jian Hui; MacMinn, Chris

2017-11-01

Viscous fingering is a classical hydrodynamic instability that occurs when an invading fluid is injected into a porous medium or a Hele-Shaw cell that contains a more viscous defending fluid. Recent work has shown that viscous fingering in a Hele-Shaw cell is supressed when the flow cell is deformable. However, the mechanism of suppression relies on a net volumetric expansion of the flow area. Here, we study flow in a novel Hele-Shaw cell consisting of a rigid bottom plate and a flexible top plate that deforms in a way that is volume-conserving. In other words, fluid injection into the flow cell leads to a local expansion of the flow area (outward displacement of the flexible surface) that must be coupled to non-local contraction (inward displacement of the flexible surface). We explore the impact of this volumetric confinement on steady viscous flow and on viscous fingering. We would like to thank EPSRC for the funding for this work.

Viscous dipping, application to the capture of fluids in living organisms

NASA Astrophysics Data System (ADS)

Lechantre, Amandine; Michez, Denis; Damman, Pascal

Some insects, birds and mammals use flower nectar as their energy resources. For this purpose, they developed specific skills to ingest viscous fluids. Depending on the sugar content, i.e., the viscosity, different strategies are observed in vivo. Indeed, butterflies use simple suction for low viscosity nectars; hummingbirds have a tongue made from two thin flexible sheets that bend to form a tube when immersed in a fluid; other animals exhibit in contrast complex papillary structures. We focus on this last method generally used for very viscous nectars. More specifically, bees and bats possess a tongue decorated with microstructures that, according to biologists, would be optimized for fluid capture by viscous dipping. In this talk, we will discuss this assumption by comparing physical models of viscous dipping to in vivo measurements. To mimic the tongue morphology, we used various rod shapes obtained by 3D printing. The influence of the type and size of lateral microstructures was then investigated and used to build a global framework describing viscous dipping for structured rods/tongues.

Phase change material storage heater

DOEpatents

Goswami, D. Yogi; Hsieh, Chung K.; Jotshi, Chand K.; Klausner, James F.

1997-01-01

A storage heater for storing heat and for heating a fluid, such as water, has an enclosure defining a chamber therein. The chamber has a lower portion and an upper portion with a heating element being disposed within the enclosure. A tube through which the fluid flows has an inlet and an outlet, both being disposed outside of the enclosure, and has a portion interconnecting the inlet and the outlet that passes through the enclosure. A densely packed bed of phase change material pellets is disposed within the enclosure and is surrounded by a viscous liquid, such as propylene glycol. The viscous liquid is in thermal communication with the heating element, the phase change material pellets, and the tube and transfers heat from the heating element to the pellets and from the pellets to the tube. The viscous fluid has a viscosity so that the frictional pressure drop of the fluid in contact with the phase change material pellets substantially reduces vertical thermal convection in the fluid. As the fluid flows through the tube heat is transferred from the viscous liquid to the fluid flowing through the tube, thereby heating the fluid.

Planar, free oscillations of a cylindrical fluid filament

NASA Astrophysics Data System (ADS)

Dasgupta, Ratul; Farsoiya, Palas Kumar

2017-11-01

A viscous cylindrical fluid filament of infinite axial extent is immersed in another viscous fluid at rest. We perturb the circular cross section of the filament with an azimuthal Fourier mode (exp(imθ) with wavenumber m real). Under/over damped free oscillations occur due to surface tension and we study these theoretically and through DNS. In the invisicd, irrotational approximation the dispersion relation for these oscillations was first obtained by Rayleigh (Proc. Roy. Soc. Lond., 29, 71, 1879) ignoring the inertia of the ambient fluid. Fyfe et al.. (J. Comp. Phys., 76, 349-384, 1988) subsequently included the inertia of the ambient fluid to the dispersion relation. We study the viscous correction to this relation, including viscosity of both the fluids. Unlike the inviscid dispersion relation which is an algebraic equation, the viscous dispersion relation turns out to be a transcendental equation. We study the roots of this equation on the complex frequency plane. In addition to the discrete spectrum, the viscous problem also has a continuous spectrum. The solution to the initial value problem which includes both, will be presented. Comparisons of analytical results with DNS results obtained from an in house developed VOF code, will be discussed.

Salinity effects during immiscible displacement in porous media: electrokinetic stabilization of viscous fingering

NASA Astrophysics Data System (ADS)

Mirzadeh, Mohammad; Bazant, Martin

2017-11-01

Interfacial instabilities are ubiquitous in Fluid Mechanics and have been one of the main the subjects of pattern formation. However, these instabilities could lead to inefficiencies which are undesired in many applications. For instance, viscous fingering results in residual trapping of oil during secondary recovery when a low-viscosity fluid, e.g. water, is used for injection. In their seminal work, Saffman and Taylor showed that the onset of this instability is controlled by the viscosity ratio of the two fluids. However, other physiochemical processes could enhance or suppress viscous fingering. Here we consider the role of salinity effects on the front stability. Our recent theory suggests that viscous fingering could be controlled, and even suppressed, by appropriately injecting electric currents. However, even in the absence of any external currents, strong electrokinetic coupling (present in small pores when the electric double layers overlap) can reduce viscous fingering by increasing the ``effective viscosity'' of the injected fluid. These findings suggest that it might be possible to improve extraction efficiencies by appropriately controlling the salt concentration of the injected fluid.

Linear Rayleigh-Taylor instability in an accelerated Newtonian fluid with finite width

NASA Astrophysics Data System (ADS)

Piriz, S. A.; Piriz, A. R.; Tahir, N. A.

2018-04-01

The linear theory of Rayleigh-Taylor instability is developed for the case of a viscous fluid layer accelerated by a semi-infinite viscous fluid, considering that the top interface is a free surface. Effects of the surface tensions at both interfaces are taken into account. When viscous effects dominate on surface tensions, an interplay of two mechanisms determines opposite behaviors of the instability growth rate with the thickness of the heavy layer for an Atwood number AT=1 and for sufficiently small values of AT. In the former case, viscosity is a less effective stabilizing mechanism for the thinnest layers. However, the finite thickness of the heavy layer enhances its viscous effects that, in general, prevail on the viscous effects of the semi-infinite medium.

Fingering dynamics on the adsorbed solute with influence of less viscous and strong sample solvent.

PubMed

Rana, Chinar; Mishra, Manoranjan

2014-12-07

Viscous fingering is a hydrodynamic instability that sets in when a low viscous fluid displaces a high viscous fluid and creates complex patterns in porous media flows. Fundamental facets of the displacement process, such as the solute concentration distribution, spreading length, and the solute mixing, depend strongly on the type of pattern created by the unstable interface of the underlying fluids. In the present study, the frontal interface of the sample shows viscous fingering and the strong solvent causes the retention of the solute to depend on the solvent concentration. This work presents a computational investigation to explore the effect of the underlying physico-chemical phenomena, (i.e., the combined effects of solvent strength, retention, and viscous fingering) on the dynamics of the adsorbed solute. A linear adsorption isotherm has been assumed between the mobile and stationary phases of the solute. We carried out the numerical simulations by considering a rectangular Hele-Shaw cell as an analog to 2D-porous media containing a three component system (displacing fluid, sample solvent, solute) to map out the evolution of the solute concentration. We observed that viscous fingering at the frontal interface of the strong sample solvent intensifies the band broadening of the solute zone. Also notable increase in the spreading dynamics of the solute has been observed for less viscous and strong sample solvent as compared to the high viscous sample slices or in the pure dispersive case. On the contrary, the solute gets intensively mixed at early times for more viscous sample in comparison to less viscous one. The results of the simulations are in qualitative agreement with the behavior observed in the liquid chromatography column experiments.

Deformation of interface in a partially miscible system during favorable displacement

NASA Astrophysics Data System (ADS)

Suzuki, Ryuta; Nagatsu, Yuichiro; Mishra, Manoranjan; Ban, Takahiko

2017-11-01

The Saffman-Taylor instability triggers a well-known viscous fingering (VF, called unfavorable displacement), occurring when a less viscous fluid displaces a more viscous one in porous media or in a Hele-Shaw cell because the boundary of the two fluids becomes hydrodynamically unstable. In the reverse situation (called favorable displacement) in which a more viscous fluid displaces a less viscous one, no instabilities occur due to hydrodynamically stable system. It has been reported that the favorable displacements become unstable by several physicochemical effects. So far, studies of both displacements have focused on fluids that are either fully miscible or immiscible. However, little attention has been paid to displacements in partially miscible system. Here, we have discovered that a partial miscibility triggers fingering instability in a favorable displacement without any chemical reactions. The occurrence of this new instability is induced by not hydrodynamic effects but a thermodynamic effect that is so-called Korteweg effect in which convection is induced during phase separation process in a partially miscible system.

Controlling Viscous Fingering Using Time-Dependent Strategies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stone, Howard; Zheng, Zhong; Kim, Hyoungsoo

Control and stabilization of viscous fingering of immiscible fluids impacts a wide variety of pressure-driven multiphase flows. Here, we report theoretical and experimental results on time-dependent control strategy by manipulating the gap thickness b(t) in a lifting Hele-Shaw cell in the power-law form b(t) = b 1t 1/7. Experimental results show good quantitative agreement with the predictions of linear stability analysis. Furthermore, by choosing the value of a single time-independent control parameter we can either totally suppress the viscous fingering instability or maintain a series of non-splitting viscous fingers during the fluid displacement process. Besides the gap thickness of amore » Hele-Shaw cell, in principle, time-dependent control strategies can also be placed on the injection rate, viscosity of the displaced fluid, and interfacial tensions between the two fluids.« less

Controlling Viscous Fingering Using Time-Dependent Strategies

DOE PAGES

Stone, Howard; Zheng, Zhong; Kim, Hyoungsoo

2015-10-20

Control and stabilization of viscous fingering of immiscible fluids impacts a wide variety of pressure-driven multiphase flows. Here, we report theoretical and experimental results on time-dependent control strategy by manipulating the gap thickness b(t) in a lifting Hele-Shaw cell in the power-law form b(t) = b 1t 1/7. Experimental results show good quantitative agreement with the predictions of linear stability analysis. Furthermore, by choosing the value of a single time-independent control parameter we can either totally suppress the viscous fingering instability or maintain a series of non-splitting viscous fingers during the fluid displacement process. Besides the gap thickness of amore » Hele-Shaw cell, in principle, time-dependent control strategies can also be placed on the injection rate, viscosity of the displaced fluid, and interfacial tensions between the two fluids.« less

Development of high gradient magnetic separation system for removing the metallic wear debris to be present in highly viscous fluid

NASA Astrophysics Data System (ADS)

Hayashi, S.; Mishima, F.; Akiyama, Y.; Nishijima, S.

2010-11-01

In the industrial plants processing highly viscous fluid such as foods or industrial materials, there is an issue of contamination by metallic wear debris originating from pipe of manufacturing line. It is necessary to remove the metallic wear debris in highly viscous fluid, since these debris causes quality loss. In this study, we developed a high gradient magnetic separation system by using superconducting magnet to remove the metallic wear debris. The particle trajectory simulation and the magnetic separation experiment were conducted with polyvinyl alcohol as a model material. As a result, ca. 100% and 92.2% of the separation efficiency was achieved respectively for the highly viscous fluid of 1 Pa s and 6 Pa s in viscosity, with 14 and 30 mesh magnetic filters.

Initial eccentricity and constituent quark number scaling of elliptic flow in ideal and viscous dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chaudhuri, A. K.

2010-04-15

In the Israel-Stewart theory of dissipative hydrodynamics, the scaling properties of elliptic flow in Au+Au collisions are studied. The initial energy density of the fluid was fixed to reproduce STAR data on phi-meson multiplicity in 0-5% Au+Au collisions such that, irrespective of fluid viscosity, entropy at the freeze-out is similar in ideal or in viscous evolution. The initial eccentricity or constituent quark number scaling is only approximate in ideal or minimally viscous (eta/s=1/4pi) fluid. Eccentricity scaling becomes nearly exact in more viscous fluid (eta/s>=0.12). However, in more viscous fluid, constituent quark number scaled elliptic flow for mesons and baryons splitsmore » into separate scaling functions. Simulated flows also do not exhibit 'universal scaling'; that is, elliptic flow scaled by the constituent quark number and charged particles v{sub 2} is not a single function of transverse kinetic energy scaled by the quark number. From a study of the violation of universal scaling, we obtain an estimate of quark-gluon plasma viscosity, eta/s=0.12+-0.03. The error is statistical only. The systematic error in eta/s could be as large.« less

Natural convection in annular cone: Influence of radius ratio

NASA Astrophysics Data System (ADS)

Ahmed, N. J. Salman; Kamangar, Sarfaraz; Al-Rashed, Abdullah A. A. A.; Govindaraju, Kalimuthu; Khan, T. M. Yunus

2018-05-01

The viscous dissipation in the fluid flow refers to the transformation of the kinetic energy to the internal energy due to the viscosity of the fluid. The current work investigates the effect of viscous dissipation and radius ratio on the heat transfer characteristics and fluid flow behavior in an annular cone embedded with the porous medium. It is observed that the viscous dissipation effect leads to the decrease in the heat transfer rate from the external wall of the cone to the inner region of the geometry.

Effect of viscous dissipation and radiation in an annular cone

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahmed, N. J. Salman; Kamangar, Sarfaraz; Khan, T. M. Yunus, E-mail: yunus.tatagar@gmail.com

The viscous dissipation is an effect due to which heat is generated inside the medium. The presence of radiation further complicates the heat transfer behavior inside porous medium. The present paper discusses the combined effect of viscous dissipation and radiation inside a porous medium confined in an annular cone with inner radius r{sub i}. The viscous dissipation and radiation terms are included in the energy equation thereby solving the coupled momentum and energy equations with the help of finite element method. The results are presented in terms of isothermal and streamline indicating the thermal and fluid flow behavior of porousmore » medium. It is found that the combination of viscous dissipation and radiation parameter and the cone angle has significant effect on the heat transfer and fluid flow behavior inside the porous medium. The fluid velocity is found to increase with the increase in Raleigh number.« less

Stability of a dragged viscous thread: Onset of ``stitching'' in a fluid-mechanical ``sewing machine''

NASA Astrophysics Data System (ADS)

Ribe, Neil M.; Lister, John R.; Chiu-Webster, Sunny

2006-12-01

A thin thread of viscous fluid that falls on a moving belt acts like a fluid-mechanical "sewing machine," exhibiting a rich variety of "stitch" patterns including meanders, translated coiling, slanted loops, braiding, figures-of-eight, W-patterns, side kicks, and period-doubled patterns. Using a numerical linear stability analysis, we determine the critical belt speed and oscillation frequency of the first bifurcation, at which a steady dragged viscous thread becomes unstable to transverse oscillations or "meandering." The predictions of the stability analysis agree closely with the experimental measurements of Chiu-Webster and Lister [J. Fluid Mech. 569, 89 (2006)]. Moreover, the critical belt speed and onset frequency for meandering are nearly identical to the contact-point migration speed and angular frequency, respectively, of steady coiling of a viscous thread on a stationary surface, implying a remarkable degree of dynamical similarity between the two phenomena.

Periodic folding of viscous sheets

NASA Astrophysics Data System (ADS)

Ribe, Neil M.

2003-09-01

The periodic folding of a sheet of viscous fluid falling upon a rigid surface is a common fluid mechanical instability that occurs in contexts ranging from food processing to geophysics. Asymptotic thin-layer equations for the combined stretching-bending deformation of a two-dimensional sheet are solved numerically to determine the folding frequency as a function of the sheet’s initial thickness, the pouring speed, the height of fall, and the fluid properties. As the buoyancy increases, the system bifurcates from “forced” folding driven kinematically by fluid extrusion to “free” folding in which viscous resistance to bending is balanced by buoyancy. The systematics of the numerically predicted folding frequency are in good agreement with laboratory experiments.

Dynamics of an elastic sphere containing a thin creeping region and immersed in an acoustic region for similar viscous-elastic and acoustic time- and length-scales

NASA Astrophysics Data System (ADS)

Gat, Amir; Friedman, Yonathan

2017-11-01

The characteristic time of low-Reynolds number fluid-structure interaction scales linearly with the ratio of fluid viscosity to solid Young's modulus. For sufficiently large values of Young's modulus, both time- and length-scales of the viscous-elastic dynamics may be similar to acoustic time- and length-scales. However, the requirement of dominant viscous effects limits the validity of such regimes to micro-configurations. We here study the dynamics of an acoustic plane wave impinging on the surface of a layered sphere, immersed within an inviscid fluid, and composed of an inner elastic sphere, a creeping fluid layer and an external elastic shell. We focus on configurations with similar viscous-elastic and acoustic time- and length-scales, where the viscous-elastic speed of interaction between the creeping layer and the elastic regions is similar to the speed of sound. By expanding the linearized spherical Reynolds equation into the relevant spectral series solution for the hyperbolic elastic regions, a global stiffness matrix of the layered elastic sphere was obtained. This work relates viscous-elastic dynamics to acoustic scattering and may pave the way to the design of novel meta-materials with unique acoustic properties. ISF 818/13.

Crossover from capillary fingering to viscous fingering in a rough fracture

NASA Astrophysics Data System (ADS)

Hu, R.; Chen, Y.; Wu, D. S.

2017-12-01

Controlled by the competition between capillary and viscous forces, the displacement patterns of one fluid displacing another more viscous one exhibit capillary fingering, viscous fingering, and the crossover between the two. Although extensive studies have investigated viscous and capillary fingerings in porous and fractured media, a few studies focused on the crossover in rough fractures, and how viscous and capillary forces affect the crossover remains unclear. Using a transparent fracture visualization system, we studied how the competition impacts the crossover in a horizontal rough fracture. Drainage experiments of water displacing oil were conducted at seven flow rates (capillary number log10Ca ranging from -7.07 to -3.07) and four viscosity ratios (M = 1/1000, 1/500, 1/100 and 1/50). We consistently observed lower invading fluid saturations in the crossover zone. In addition, we proposed a phase diagram for the displacement patterns in a rough fracture that is consistent with similar studies in porous media. Based on real-time imaging and statistical analysis of the invasion morphology, we showed that the competition between the capillary and viscous forces is responsible for the saturation reduction in the crossover zone. In this zone, finger propagation toward the outlet (characteristic of viscous fingering) as well as void-filling in the transverse and backward directions (characteristic of capillary fingering), are both suppressed. Therefore, the invading fluid tends to occupy larger apertures with higher characteristic front velocity, promoting void-filling toward the outlet with thinner finger growth and resulting in a larger volume of defending fluid left behind.

Investigation of shock waves in the relativistic Riemann problem: A comparison of viscous fluid dynamics to kinetic theory

NASA Astrophysics Data System (ADS)

Bouras, I.; Molnár, E.; Niemi, H.; Xu, Z.; El, A.; Fochler, O.; Greiner, C.; Rischke, D. H.

2010-08-01

We solve the relativistic Riemann problem in viscous matter using the relativistic Boltzmann equation and the relativistic causal dissipative fluid-dynamical approach of Israel and Stewart. Comparisons between these two approaches clarify and point out the regime of validity of second-order fluid dynamics in relativistic shock phenomena. The transition from ideal to viscous shocks is demonstrated by varying the shear viscosity to entropy density ratio η/s. We also find that a good agreement between these two approaches requires a Knudsen number Kn<1/2.

Investigation of shock waves in the relativistic Riemann problem: A comparison of viscous fluid dynamics to kinetic theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bouras, I.; El, A.; Fochler, O.

2010-08-15

We solve the relativistic Riemann problem in viscous matter using the relativistic Boltzmann equation and the relativistic causal dissipative fluid-dynamical approach of Israel and Stewart. Comparisons between these two approaches clarify and point out the regime of validity of second-order fluid dynamics in relativistic shock phenomena. The transition from ideal to viscous shocks is demonstrated by varying the shear viscosity to entropy density ratio {eta}/s. We also find that a good agreement between these two approaches requires a Knudsen number Kn<1/2.

Cochlear perfusion with a viscous fluid.

PubMed

Wang, Yi; Olson, Elizabeth S

2016-07-01

The flow of viscous fluid in the cochlea induces shear forces, which could provide benefit in clinical practice, for example to guide cochlear implant insertion or produce static pressure to the cochlear partition or wall. From a research standpoint, studying the effects of a viscous fluid in the cochlea provides data for better understanding cochlear fluid mechanics. However, cochlear perfusion with a viscous fluid may damage the cochlea. In this work we studied the physiological and anatomical effects of perfusing the cochlea with a viscous fluid. Gerbil cochleae were perfused at a rate of 2.4 μL/min with artificial perilymph (AP) and sodium hyaluronate (Healon, HA) in four different concentrations (0.0625%, 0.125%, 0.25%, 0.5%). The different HA concentrations were applied either sequentially in the same cochlea or individually in different cochleae. The perfusion fluid entered from the round window and was withdrawn from basal scala vestibuli, in order to perfuse the entire perilymphatic space. Compound action potentials (CAP) were measured after each perfusion. After perfusion with increasing concentrations of HA in the order of increasing viscosity, the CAP thresholds generally increased. The threshold elevation after AP and 0.0625% HA perfusion was small or almost zero, and the 0.125% HA was a borderline case, while the higher concentrations significantly elevated CAP thresholds. Histology of the cochleae perfused with the 0.0625% HA showed an intact Reissner's membrane (RM), while in cochleae perfused with 0.125% and 0.25% HA RM was torn. Thus, the CAP threshold elevation was likely due to the broken RM, likely caused by the shear stress produced by the flow of the viscous fluid. Our results and analysis indicate that the cochlea can sustain, without a significant CAP threshold shift, up to a 1.5 Pa shear stress. Beside these finding, in the 0.125% and 0.25% HA perfusion cases, a temporary CAP threshold shift was observed, perhaps due to the presence and then clearance of viscous fluid within the cochlea, or to a temporary position shift of the Organ of Corti. After 0.5% HA perfusion, a short latency positive peak (P0) appeared in the CAP waveform. This P0 might be due to a change in the cochlea's traveling-wave pattern, or distortion in the cochlear microphonic. Copyright © 2016 Elsevier B.V. All rights reserved.

Cochlear perfusion with a viscous fluid

PubMed Central

Wang, Yi; Olson, Elizabeth S.

2016-01-01

The flow of viscous fluid in the cochlea induces shear forces, which could provide benefit in clinical practice, for example to guide cochlear implant insertion or produce static pressure to the cochlear partition or wall. From a research standpoint, studying the effects of a viscous fluid in the cochlea provides data for better understanding cochlear fluid mechanics. However, cochlear perfusion with a viscous fluid may damage the cochlea. In this work we studied the physiological and anatomical effects of perfusing the cochlea with a viscous fluid. Gerbil cochleae were perfused at a rate of 2.4 μL/min with artificial perilymph (AP) and sodium hyaluronate (Healon, HA) in four different concentrations (0.0625%, 0.125%, 0.25%, 0.5%). The different HA concentrations were applied either sequentially in the same cochlea or individually in different cochleae. The perfusion fluid entered from the round window and was withdrawnfrom basal scala vestibuli, in order to perfuse the entire perilymphatic space. Compound action potentials (CAP) were measured after each perfusion. After perfusion with increasing concentrations of HA in the order of increasing viscosity, the CAP thresholds generally increased. The threshold elevation after AP and 0.0625% HA perfusion was small or almost zero, and the 0.125% HA was a borderline case, while the higher concentrations significantly elevated CAP thresholds. Histology of the cochleae perfused with the 0.0625% HA showed an intact Reissner’s membrane, while in cochleae perfused with 0.125% and 0.25% HA Reissner’s membrane (RM) was torn. Thus, the CAP threshold elevation was likely due to the broken of RM, which likely caused by the shear stress produced by the flow of the viscous fluid. Our results and analysis indicate that the cochlea can sustain, without a significant CAP threshold shift, up to a 1.5 Pa shear stress. Beside these finding, in the 0.125% and 0.25% HA perfusion cases, a temporary CAP threshold shift was observed, perhaps due to the presence and then clearance of viscous fluid within the cochlea, or to a temporary position shift of the Organ of Corti. After 0.5% HA perfusion, a short latency positive peak (P0) appeared in the CAP wavefrom. This P0 might be due to a change in the cochlea’s traveling-wave pattern, or distortion in the cochlear microphonic. PMID:27220484

Self-similarity and scaling transitions during rupture of thin free films of Newtonian fluids

NASA Astrophysics Data System (ADS)

Thete, Sumeet Suresh; Anthony, Christopher; Doshi, Pankaj; Harris, Michael T.; Basaran, Osman A.

2016-09-01

Rupture of thin liquid films is crucial in many industrial applications and nature such as foam stability in oil-gas separation units, coating flows, polymer processing, and tear films in the eye. In some of these situations, a liquid film may have two free surfaces (referred to here as a free film or a sheet) as opposed to a film deposited on a solid substrate that has one free surface. The rupture of such a free film or a sheet of a Newtonian fluid is analyzed under the competing influences of inertia, viscous stress, van der Waals pressure, and capillary pressure by solving a system of spatially one-dimensional evolution equations for film thickness and lateral velocity. The dynamics close to the space-time singularity where the film ruptures is asymptotically self-similar and, therefore, the problem is also analyzed by reducing the transient partial differential evolution equations to a corresponding set of ordinary differential equations in similarity space. For sheets with negligible inertia, it is shown that the dominant balance of forces involves solely viscous and van der Waals forces, with capillary force remaining negligible throughout the thinning process in a viscous regime. On the other hand, for a sheet of an inviscid fluid for which the effect of viscosity is negligible, it is shown that the dominant balance of forces is between inertial, capillary, and van der Waals forces as the film evolves towards rupture in an inertial regime. Real fluids, however, have finite viscosity. Hence, for real fluids, it is further shown that the viscous and the inertial regimes are only transitory and can only describe the initial thinning dynamics of highly viscous and slightly viscous sheets, respectively. Moreover, regardless of the fluid's viscosity, it is shown that for sheets that initially thin in either of these two regimes, their dynamics transition to a late stage or final inertial-viscous regime in which inertial, viscous, and van der Waals forces balance each other while capillary force remains negligible, in accordance with the results of Vaynblat, Lister, and Witelski.

Efficient Simulation of Compressible, Viscous Fluids using Multi-rate Time Integration

NASA Astrophysics Data System (ADS)

Mikida, Cory; Kloeckner, Andreas; Bodony, Daniel

2017-11-01

In the numerical simulation of problems of compressible, viscous fluids with single-rate time integrators, the global timestep used is limited to that of the finest mesh point or fastest physical process. This talk discusses the application of multi-rate Adams-Bashforth (MRAB) integrators to an overset mesh framework to solve compressible viscous fluid problems of varying scale with improved efficiency, with emphasis on the strategy of timescale separation and the application of the resulting numerical method to two sample problems: subsonic viscous flow over a cylinder and a viscous jet in crossflow. The results presented indicate the numerical efficacy of MRAB integrators, outline a number of outstanding code challenges, demonstrate the expected reduction in time enabled by MRAB, and emphasize the need for proper load balancing through spatial decomposition in order for parallel runs to achieve the predicted time-saving benefit. This material is based in part upon work supported by the Department of Energy, National Nuclear Security Administration, under Award Number DE-NA0002374.

On a class of exact solutions of the equations of motion of a viscous fluid

NASA Technical Reports Server (NTRS)

Yatseyev, V I

1953-01-01

The general solution is obtained of the equations of motion of a viscous fluid in which the velocity field is inversely proportional to the distance from a certain point. Some particular cases of such motion are investigated.

A constitutive relation for the viscous flow of an oriented fiber assembly

NASA Technical Reports Server (NTRS)

Pipes, R. B.; Hearle, J. W. S.; Beaussart, A. J.; Sastry, A. M.; Okine, R. K.

1991-01-01

A constitutive relation for an equivalent, homogeneous fluid is developed for the anisotropic viscous flow of an oriented assembly of discontinuous fibers suspended in a viscous fluid. The anisotropic viscous compliance matrix can be expressed in terms of three constants by assuming the equivalent fluid to be incompressible and the microstructure to have axial symmetry (transversely isotropic). By means of a micromechanics analysis, the three terms of the constitutive relation are expressed in terms of the viscosity of the matrix fluid, the fiber aspect ratio, and the fiber volume fraction. A comparison of the viscosity terms reveals that the elongational viscosity in the fiber direction varies as the square of the fiber aspect ratio and a complex function of the fiber volume fraction. Furthermore, the ratio of the axial elongational viscosity to the transverse elongational viscosity and both axial and transverse shear viscosities was shown to be 10 exp 4 - 10 exp 6 for fiber aspect ratio of 100-1000, except at extreme values of the fiber volume fraction.

On some problems in a theory of thermally and mechanically interacting continuous media. Ph.D. Thesis; [linearized theory of interacting mixture of elastic solid and viscous fluid

NASA Technical Reports Server (NTRS)

Lee, Y. M.

1971-01-01

Using a linearized theory of thermally and mechanically interacting mixture of linear elastic solid and viscous fluid, we derive a fundamental relation in an integral form called a reciprocity relation. This reciprocity relation relates the solution of one initial-boundary value problem with a given set of initial and boundary data to the solution of a second initial-boundary value problem corresponding to a different initial and boundary data for a given interacting mixture. From this general integral relation, reciprocity relations are derived for a heat-conducting linear elastic solid, and for a heat-conducting viscous fluid. An initial-boundary value problem is posed and solved for the mixture of linear elastic solid and viscous fluid. With the aid of the Laplace transform and the contour integration, a real integral representation for the displacement of the solid constituent is obtained as one of the principal results of the analysis.

Simulation of swimming strings immersed in a viscous fluid flow

NASA Astrophysics Data System (ADS)

Huang, Wei-Xi; Sung, Hyung Jin

2006-11-01

In nature, many phenomena involve interactions between flexible bodies and their surrounding viscous fluid, such as a swimming fish or a flapping flag. The intrinsic dynamics is complicate and not well understood. A flexible string can be regarded as a one-dimensional flag model. Many similarities can be found between the flapping string and swimming fish, although different wake speed results in a drag force for the flapping string and a propulsion force for the swimming fish. In the present study, we propose a mathematical formulation for swimming strings immersed in a viscous fluid flow. Fluid motion is governed by the Navier-Stokes equations and a momentum forcing is added in order to bring the fluid to move at the same velocity with the immersed surface. A flexible inextensible string model is described by another set of equations with an additional momentum forcing which is a result of the fluid viscosity and the pressure difference across the string. The momentum forcing is calculated by a feedback loop. Simulations of several numerical examples are carried out, including a hanging string which starts moving under gravity without ambient fluid, a swinging string immersed in a quiescent viscous fluid, a string swimming within a uniform surrounding flow, and flow over two side-by-side strings. The numerical results agree well with the theoretical analysis and previous experimental observations. Further simulation of a swimming fish is under consideration.

Viscous entrainment on hairy surfaces

NASA Astrophysics Data System (ADS)

Nasto, Alice; Brun, P.-T.; Hosoi, A. E.

2018-02-01

Nectar-drinking bats and honeybees have tongues covered with hairlike structures, enhancing their ability to take up viscous nectar by dipping. Using a combination of model experiments and theory, we explore the physical mechanisms that govern viscous entrainment in a hairy texture. Hairy surfaces are fabricated using laser cut molds and casting samples with polydimethylsiloxane (PDMS) elastomer. We model the liquid trapped within the texture using a Darcy-Brinkmann-like approach and derive the drainage flow solution. The amount of fluid that is entrained is dependent on the viscosity of the fluid, the density of the hairs, and the withdrawal speed. Both experiments and theory reveal an optimal hair density to maximize fluid uptake.

Coiling of viscous jets

NASA Astrophysics Data System (ADS)

Ribe, Neil M.

2004-11-01

A stream of viscous fluid falling from a sufficient height onto a surface forms a series of regular coils. I use a numerical model for a deformable fluid thread to predict the coiling frequency as a function of the thread's radius, the flow rate, the fall height, and the fluid viscosity. Three distinct modes of coiling can occur: viscous (e.g. toothpaste), gravitational (honey falling from a moderate height) and inertial (honey falling from a great height). When inertia is significant, three states of steady coiling with different frequencies can exist over a range of fall heights. The numerically predicted coiling frequencies agree well with experimental measurements in the inertial coiling regime.

Mechanics of Hydraulic Fractures

NASA Astrophysics Data System (ADS)

Detournay, Emmanuel

2016-01-01

Hydraulic fractures represent a particular class of tensile fractures that propagate in solid media under pre-existing compressive stresses as a result of internal pressurization by an injected viscous fluid. The main application of engineered hydraulic fractures is the stimulation of oil and gas wells to increase production. Several physical processes affect the propagation of these fractures, including the flow of viscous fluid, creation of solid surfaces, and leak-off of fracturing fluid. The interplay and the competition between these processes lead to multiple length scales and timescales in the system, which reveal the shifting influence of the far-field stress, viscous dissipation, fracture energy, and leak-off as the fracture propagates.

On the motion of viscous fluids in the presence of diffusion

NASA Astrophysics Data System (ADS)

Secchi, Paolo

1988-01-01

The flow of a viscous incompressible two-component fluid with Fick's-law diffusion is investigated analytically. The existence of a unique global solution for small values of the diffusion coefficient (lambda) is proved for two-dimensional flow. The two- and three-dimensional solutions are also shown to converge toward the solutions of the Navier-Stokes equations for inhomogeneous fluids as lambda approaches zero.

Spiral pattern in a radial displacement involving a reaction-producing gel.

PubMed

Nagatsu, Yuichiro; Hayashi, Atsushi; Ban, Mitsumasa; Kato, Yoshihito; Tada, Yutaka

2008-08-01

We have shown experimentally that the pattern created by the displacement of a more viscous fluid by a less viscous one in a radial Hele-Shaw cell develops not radially but spirally when a more viscous sodium polyacrylate solution is displaced by a less viscous trivalent iron ion (Fe3+) solution with a sufficiently high concentration of Fe3+ . Another experiment revealed that an instantaneous chemical reaction takes place between the two fluids, and at high Fe3+ concentrations it produces a film of the gel at the contact plane. The gel film is proposed to be responsible for the spiral pattern.

Spiral pattern in a radial displacement involving a reaction-producing gel

NASA Astrophysics Data System (ADS)

Nagatsu, Yuichiro; Hayashi, Atsushi; Ban, Mitsumasa; Kato, Yoshihito; Tada, Yutaka

2008-08-01

We have shown experimentally that the pattern created by the displacement of a more viscous fluid by a less viscous one in a radial Hele-Shaw cell develops not radially but spirally when a more viscous sodium polyacrylate solution is displaced by a less viscous trivalent iron ion (Fe3+) solution with a sufficiently high concentration of Fe3+ . Another experiment revealed that an instantaneous chemical reaction takes place between the two fluids, and at high Fe3+ concentrations it produces a film of the gel at the contact plane. The gel film is proposed to be responsible for the spiral pattern.

Spiral pattern in a radial displacement in a Hele-Shaw cell

NASA Astrophysics Data System (ADS)

Ban, Mitsumasa; Nagatsu, Yuichiro; Hayashi, Atsushi; Kato, Yoshihiro; Tada, Yutaka

2008-11-01

When a reactive and miscible less-viscous liquid displaces a more-viscous liquid in a Hele-Shaw cell, reactive miscible viscous fingering takes place. We have experimentally shown that the pattern created by the displacement of a more-viscous fluid by a less-viscous one in a radial Hele-Shaw cell develops not radially but spirally when a more-viscous sodium polyacrylate solution is displaced by a less-viscous trivalent iron ion (Fe^3+) solution with a sufficiently high concentration of Fe^3+. Another experiment in order to investigate the mechanism of spiral pattern formation revealed that an instantaneous chemical reaction takes place between the two fluids and at high Fe^3+ concentrations it produces a film of the gel at the contact plane. The gel is formed by three-dimensional network structures between the polyacrylate solution and the trivalent iron ion (Fe^3+) solution. We have proposed a physical model that the gel's film is responsible for the form of the spiral pattern.

Tidal disruption of viscous bodies

NASA Technical Reports Server (NTRS)

Sridhar, S.; Tremaine, S.

1992-01-01

Tidal disruptions are investigated in viscous-fluid planetesimals whose radius is small relative to the distance of closest (parabolic-orbit) approach to a planet. The planetesimal surface is in these conditions always ellipsoidal, facilitating treatment by coupled ODEs which are solvable with high accuracy. While the disrupted planetesimals evolve into needlelike ellipsoids, their density does not decrease. The validity of viscous fluid treatment holds for solid (ice or rock) planetesimals in cases where tidal stresses are greater than material strength, but integrity is maintained by self-gravity.

Complex large-scale convection of a viscous incompressible fluid with heat exchange according to Newton's law

NASA Astrophysics Data System (ADS)

Gorshkov, A. V.; Prosviryakov, E. Yu.

2017-12-01

The paper considers the construction of analytical solutions to the Oberbeck-Boussinesq system. This system describes layered Bénard-Marangoni convective flows of an incompressible viscous fluid. The third-kind boundary condition, i. e. Newton's heat transfer law, is used on the boundaries of a fluid layer. The obtained solution is analyzed. It is demonstrated that there is a fluid layer thickness with tangential stresses vanishing simultaneously, this being equivalent to the existence of tensile and compressive stresses.

Scrutinization of thermal radiation, viscous dissipation and Joule heating effects on Marangoni convective two-phase flow of Casson fluid with fluid-particle suspension

NASA Astrophysics Data System (ADS)

Mahanthesh, B.; Gireesha, B. J.

2018-03-01

The impact of Marangoni convection on dusty Casson fluid boundary layer flow with Joule heating and viscous dissipation aspects is addressed. The surface tension is assumed to vary linearly with temperature. Physical aspects of magnetohydrodynamics and thermal radiation are also accounted. The governing problem is modelled under boundary layer approximations for fluid phase and dust particle phase and then Runge-Kutta-Fehlberg method based numeric solutions are established. The momentum and heat transport mechanisms are focused on the result of distinct governing parameters. The Nusselt number is also calculated. It is established that the rate of heat transfer can be enhanced by suspending dust particles in the base fluid. The temperature field of fluid phase and temperature of dust phase are quite reverse for thermal dust parameter. The radiative heat, viscous dissipation and Joule heating aspects are constructive for thermal fields of fluid and dust phases. The velocity of dusty Casson fluid dominates the velocity of dusty fluid while this trend is opposite in the case of temperature. Moreover qualitative behaviour of fluid phase and dust phase temperature/velocity are similar.

Nonmonotonic magnetoresistance of a two-dimensional viscous electron-hole fluid in a confined geometry

NASA Astrophysics Data System (ADS)

Alekseev, P. S.; Dmitriev, A. P.; Gornyi, I. V.; Kachorovskii, V. Yu.; Narozhny, B. N.; Titov, M.

2018-02-01

Ultrapure conductors may exhibit hydrodynamic transport where the collective motion of charge carriers resembles the flow of a viscous fluid. In a confined geometry (e.g., in ultra-high-quality nanostructures), the electronic fluid assumes a Poiseuille-type flow. Applying an external magnetic field tends to diminish viscous effects leading to large negative magnetoresistance. In two-component systems near charge neutrality, the hydrodynamic flow of charge carriers is strongly affected by the mutual friction between the two constituents. At low fields, the magnetoresistance is negative, however, at high fields the interplay between electron-hole scattering, recombination, and viscosity results in a dramatic change of the flow profile: the magnetoresistance changes its sign and eventually becomes linear in very high fields. This nonmonotonic magnetoresistance can be used as a fingerprint to detect viscous flow in two-component conducting systems.

An improved weakly compressible SPH method for simulating free surface flows of viscous and viscoelastic fluids

NASA Astrophysics Data System (ADS)

Xu, Xiaoyang; Deng, Xiao-Long

2016-04-01

In this paper, an improved weakly compressible smoothed particle hydrodynamics (SPH) method is proposed to simulate transient free surface flows of viscous and viscoelastic fluids. The improved SPH algorithm includes the implementation of (i) the mixed symmetric correction of kernel gradient to improve the accuracy and stability of traditional SPH method and (ii) the Rusanov flux in the continuity equation for improving the computation of pressure distributions in the dynamics of liquids. To assess the effectiveness of the improved SPH algorithm, a number of numerical examples including the stretching of an initially circular water drop, dam breaking flow against a vertical wall, the impact of viscous and viscoelastic fluid drop with a rigid wall, and the extrudate swell of viscoelastic fluid have been presented and compared with available numerical and experimental data in literature. The convergent behavior of the improved SPH algorithm has also been studied by using different number of particles. All numerical results demonstrate that the improved SPH algorithm proposed here is capable of modeling free surface flows of viscous and viscoelastic fluids accurately and stably, and even more important, also computing an accurate and little oscillatory pressure field.

Computational modelling of the flow of viscous fluids in carbon nanotubes

NASA Astrophysics Data System (ADS)

Khosravian, N.; Rafii-Tabar, H.

2007-11-01

Carbon nanotubes will have extensive application in all areas of nano-technology, and in particular in the field of nano-fluidics, wherein they can be used for molecular separation, nano-scale filtering and as nano-pipes for conveying fluids. In the field of nano-medicine, nanotubes can be functionalized with various types of receptors to act as bio-sensors for the detection and elimination of cancer cells, or be used as bypasses and even neural connections. Modelling fluid flow inside nanotubes is a very challenging problem, since there is a complex interplay between the motion of the fluid and the stability of the walls. A critical issue in the design of nano-fluidic devices is the induced vibration of the walls, due to the fluid flow, which can promote structural instability. It has been established that the resonant frequencies depend on the flow velocity. We have studied, for the first time, the flow of viscous fluids through multi-walled carbon nanotubes, using the Euler-Bernoulli classical beam theory to model the nanotube as a continuum structure. Our aim has been to compute the effect of the fluid flow on the structural stability of the nanotubes, without having to consider the details of the fluid-walls interaction. The variations of the resonant frequencies with the flow velocity are obtained for both unembedded nanotubes, and when they are embedded in an elastic medium. It is found that a nanotube conveying a viscous fluid is more stable against vibration-induced buckling than a nanotube conveying a non-viscous fluid, and that the aspect ratio plays the same role in both cases.

Stability of miscible core?annular flows with viscosity stratification

NASA Astrophysics Data System (ADS)

Selvam, B.; Merk, S.; Govindarajan, Rama; Meiburg, E.

The linear stability of variable viscosity, miscible core-annular flows is investigated. Consistent with pipe flow of a single fluid, the flow is stable at any Reynolds number when the magnitude of the viscosity ratio is less than a critical value. This is in contrast to the immiscible case without interfacial tension, which is unstable at any viscosity ratio. Beyond the critical value of the viscosity ratio, the flow can be unstable even when the more viscous fluid is in the core. This is in contrast to plane channel flows with finite interface thickness, which are always stabilized relative to single fluid flow when the less viscous fluid is in contact with the wall. If the more viscous fluid occupies the core, the axisymmetric mode usually dominates over the corkscrew mode. It is demonstrated that, for a less viscous core, the corkscrew mode is inviscidly unstable, whereas the axisymmetric mode is unstable for small Reynolds numbers at high Schmidt numbers. For the parameters under consideration, the switchover occurs at an intermediate Schmidt number of about 500. The occurrence of inviscid instability for the corkscrew mode is shown to be consistent with the Rayleigh criterion for pipe flows. In some parameter ranges, the miscible flow is seen to be more unstable than its immiscible counterpart, and the physical reasons for this behaviour are discussed.A detailed parametric study shows that increasing the interface thickness has a uniformly stabilizing effect. The flow is least stable when the interface between the two fluids is located at approximately 0.6 times the tube radius. Unlike for channel flow, there is no sudden change in the stability with radial location of the interface. The instability originates mainly in the less viscous fluid, close to the interface.

Pore Fluid Extraction by Reactive Solitary Waves in 3-D

NASA Astrophysics Data System (ADS)

Omlin, Samuel; Malvoisin, Benjamin; Podladchikov, Yury Y.

2017-09-01

In the lower crust, viscous compaction is known to produce solitary porosity and fluid pressure waves. Metamorphic (de)volatilization reactions can also induce porosity changes in response to the propagating fluid pressure anomalies. Here we present results from high-resolution simulations using Graphic Processing Unit parallel processing with a model that includes both viscous (de)compaction and reaction-induced porosity changes. Reactive porosity waves propagate in a manner similar to viscous porosity waves, but through a different mechanism involving fluid release and trap in the solid by reaction. These waves self-generate from red noise or an ellipsoidal porosity anomaly with the same characteristic size and abandon their source region to propagate at constant velocity. Two waves traveling at different velocities pass through each other in a soliton-like fashion. Reactive porosity waves thus provide an additional mechanism for fluid extraction at shallow depths with implications for ore formation, diagenesis, metamorphic veins formation, and fluid extraction from subduction zones.

Bianchi Type VI1 Viscous Fluid Cosmological Model in Wesson´s Theory of Gravitation

NASA Astrophysics Data System (ADS)

Khadekar, G. S.; Avachar, G. R.

2007-03-01

Field equations of a scale invariant theory of gravitation proposed by Wesson [1, 2] are obtained in the presence of viscous fluid with the aid of Bianchi type VIh space-time with the time dependent gauge function (Dirac gauge). It is found that Bianchi type VIh (h = 1) space-time with viscous fluid is feasible in this theory, whereas Bianchi type VIh (h = -1, 0) space-times are not feasible in this theory, even in the presence of viscosity. For the feasible case, by assuming a relation connecting viscosity and metric coefficient, we have obtained a nonsingular-radiating model. We have discussed some physical and kinematical properties of the models.

Compressible viscous flows generated by oscillating flexible cylinders

NASA Astrophysics Data System (ADS)

Van Eysden, Cornelis A.; Sader, John E.

2009-01-01

The fluid dynamics of oscillating elastic beams underpin the operation of many modern technological devices ranging from micromechanical sensors to the atomic force microscope. While viscous effects are widely acknowledged to have a strong influence on these dynamics, fluid compressibility is commonly neglected. Here, we theoretically study the three-dimensional flow fields that are generated by the motion of flexible cylinders immersed in viscous compressible fluids and discuss the implications of compressibility in practice. We consider cylinders of circular cross section and flat blades of zero thickness that are executing flexural and torsional oscillations of arbitrary wave number. Exact analytical solutions are derived for these flow fields and their resulting hydrodynamic loads.

A Theoretical and Experimental Study for a Developing Flow in a Thin Fluid Gap

NASA Astrophysics Data System (ADS)

Wu, Qianhong; Lang, Ji; Jen, Kei-Peng; Nathan, Rungun; Vucbmss Team

2016-11-01

In this paper, we report a novel theoretical and experimental approach to examine a fast developing flow in a thin fluid gap. Although the phenomena are widely observed in industrial applications and biological systems, there is a lack of analytical approach that captures the instantaneous fluid response to a sudden impact. An experimental setup was developed that contains a piston instrumented with a laser displacement sensor and a pressure transducer. A sudden impact was imposed on the piston, creating a fast compaction on the thin fluid gap underneath. The motion of the piston was captured by the laser displacement sensor, and the fluid pressure build-up and relaxation was recorded by the pressure transducer. For this dynamic process, a novel analytical approach was developed. It starts with the inviscid limit when the viscous fluid effect has no time to appear. This short process is followed by a developing flow, in which the inviscid core flow region decreases and the viscous wall region increases until the entire fluid gap is filled with viscous fluid flow. A boundary layer integral method is used during the process. Lastly, the flow is completely viscous dominant featured by a typical squeeze flow in a thin gap. Excellent agreement between the theory and the experiment was achieved. The study presented herein, filling the gap in the literature, will have broad impact in industrial and biomedical applications. This research was supported by the National Science Foundation under Award #1511096.

Exact solution for the layered convection of a viscous incompressible fluid at specified temperature gradients and tangential forces on the free boundary

NASA Astrophysics Data System (ADS)

Burmasheva, N. V.; Prosviryakov, E. Yu.

2017-12-01

A new exact analytical solution of a system of thermal convection equations in the Boussinesq approximation describing layered flows in an incompressible viscous fluid is obtained. A fluid flow in an infinite layer is considered. Convection in the fluid is induced by tangential stresses specified on the upper non-deformable boundary. At the fixed lower boundary, the no-slip condition is satisfied. Temperature corrections are given on the both boundaries of the fluid layer. The possibility of physical field stratification is investigated.

Application of wave mechanics theory to fluid dynamics problems: Boundary layer on a circular cylinder including turbulence

NASA Technical Reports Server (NTRS)

Krzywoblocki, M. Z. V.

1974-01-01

The application of the elements of quantum (wave) mechanics to some special problems in the field of macroscopic fluid dynamics is discussed. Emphasis is placed on the flow of a viscous, incompressible fluid around a circular cylinder. The following subjects are considered: (1) the flow of a nonviscous fluid around a circular cylinder, (2) the restrictions imposed the stream function by the number of dimensions of space, and (3) the flow past three dimensional bodies in a viscous fluid, particularly past a circular cylinder in the symmetrical case.

Viscous effects on the Rayleigh-Taylor instability with background temperature gradient

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gerashchenko, Sergiy; Livescu, Daniel

Here we studied the growth rate of the compressible Rayleigh-Taylor instability in the presence of a background temperature gradient, Θ, using a normal mode analysis. The effect of Θ variation is examined for three interface types corresponding to the combinations of the viscous properties of the fluids (inviscid-inviscid, viscous-viscous, and viscous-inviscid) at different Atwood numbers, At, and when at least one of the fluids' viscosity is non-zero, as a function of the Grashof number. For the general case, the resulting ordinary differential equations are solved numerically; however, dispersion relations for the growth rate are presented for several limiting cases. Anmore » analytical solution is found for the inviscid-inviscid interface and the corresponding dispersion equation for the growth rate is obtained in the limit of large Θ. For the viscous-inviscid case, a dispersion relation is derived in the incompressible limit and Θ=0. Compared to Θ=0 case, the role of Θ<0 (hotter light fluid) is destabilizing and becomes stabilizing when Θ>0 (colder light fluid). The most pronounced effect of Θ ≠ 0 is found at low At and/or at large perturbation wavelengths relative to the domain size for all interface types. On the other hand, at small perturbation wavelengths relative to the domain size, the growth rate for the Θ<0 case exceeds the infinite domain incompressible constant density result. The results are applied to two practical examples, using sets of parameters relevant to Inertial Confinement Fusion coasting stage and solar corona plumes. The role of viscosity on the growth rate reduction is discussed together with highlighting the range of wavenumbers most affected by viscosity. The viscous effects further increase in the presence of background temperature gradient, when the viscosity is temperature dependent.« less

Viscous effects on the Rayleigh-Taylor instability with background temperature gradient

DOE PAGES

Gerashchenko, Sergiy; Livescu, Daniel

2016-07-28

Here we studied the growth rate of the compressible Rayleigh-Taylor instability in the presence of a background temperature gradient, Θ, using a normal mode analysis. The effect of Θ variation is examined for three interface types corresponding to the combinations of the viscous properties of the fluids (inviscid-inviscid, viscous-viscous, and viscous-inviscid) at different Atwood numbers, At, and when at least one of the fluids' viscosity is non-zero, as a function of the Grashof number. For the general case, the resulting ordinary differential equations are solved numerically; however, dispersion relations for the growth rate are presented for several limiting cases. Anmore » analytical solution is found for the inviscid-inviscid interface and the corresponding dispersion equation for the growth rate is obtained in the limit of large Θ. For the viscous-inviscid case, a dispersion relation is derived in the incompressible limit and Θ=0. Compared to Θ=0 case, the role of Θ<0 (hotter light fluid) is destabilizing and becomes stabilizing when Θ>0 (colder light fluid). The most pronounced effect of Θ ≠ 0 is found at low At and/or at large perturbation wavelengths relative to the domain size for all interface types. On the other hand, at small perturbation wavelengths relative to the domain size, the growth rate for the Θ<0 case exceeds the infinite domain incompressible constant density result. The results are applied to two practical examples, using sets of parameters relevant to Inertial Confinement Fusion coasting stage and solar corona plumes. The role of viscosity on the growth rate reduction is discussed together with highlighting the range of wavenumbers most affected by viscosity. The viscous effects further increase in the presence of background temperature gradient, when the viscosity is temperature dependent.« less

Bacterial accumulation in viscosity gradients

NASA Astrophysics Data System (ADS)

Waisbord, Nicolas; Guasto, Jeffrey

2016-11-01

Cell motility is greatly modified by fluid rheology. In particular, the physical environments in which cells function, are often characterized by gradients of viscous biopolymers, such as mucus and extracellular matrix, which impact processes ranging from reproduction to digestion to biofilm formation. To understand how spatial heterogeneity of fluid rheology affects the motility and transport of swimming cells, we use hydrogel microfluidic devices to generate viscosity gradients in a simple, polymeric, Newtonian fluid. Using video microscopy, we characterize the random walk motility patterns of model bacteria (Bacillus subtilis), showing that both wild-type ('run-and-tumble') cells and smooth-swimming mutants accumulate in the viscous region of the fluid. Through statistical analysis of individual cell trajectories and body kinematics in both homogeneous and heterogeneous viscous environments, we discriminate passive, physical effects from active sensing processes to explain the observed cell accumulation at the ensemble level.

Pin stack array for thermoacoustic energy conversion

DOEpatents

Keolian, Robert M.; Swift, Gregory W.

1995-01-01

A thermoacoustic stack for connecting two heat exchangers in a thermoacoustic energy converter provides a convex fluid-solid interface in a plane perpendicular to an axis for acoustic oscillation of fluid between the two heat exchangers. The convex surfaces increase the ratio of the fluid volume in the effective thermoacoustic volume that is displaced from the convex surface to the fluid volume that is adjacent the surface within which viscous energy losses occur. Increasing the volume ratio results in an increase in the ratio of transferred thermal energy to viscous energy losses, with a concomitant increase in operating efficiency of the thermoacoustic converter. The convex surfaces may be easily provided by a pin array having elements arranged parallel to the direction of acoustic oscillations and with effective radial dimensions much smaller than the thicknesses of the viscous energy loss and thermoacoustic energy transfer volumes.

Including fluid shear viscosity in a structural acoustic finite element model using a scalar fluid representation

PubMed Central

Cheng, Lei; Li, Yizeng; Grosh, Karl

2013-01-01

An approximate boundary condition is developed in this paper to model fluid shear viscosity at boundaries of coupled fluid-structure system. The effect of shear viscosity is approximated by a correction term to the inviscid boundary condition, written in terms of second order in-plane derivatives of pressure. Both thin and thick viscous boundary layer approximations are formulated; the latter subsumes the former. These approximations are used to develop a variational formation, upon which a viscous finite element method (FEM) model is based, requiring only minor modifications to the boundary integral contributions of an existing inviscid FEM model. Since this FEM formulation has only one degree of freedom for pressure, it holds a great computational advantage over the conventional viscous FEM formulation which requires discretization of the full set of linearized Navier-Stokes equations. The results from thick viscous boundary layer approximation are found to be in good agreement with the prediction from a Navier-Stokes model. When applicable, thin viscous boundary layer approximation also gives accurate results with computational simplicity compared to the thick boundary layer formulation. Direct comparison of simulation results using the boundary layer approximations and a full, linearized Navier-Stokes model are made and used to evaluate the accuracy of the approximate technique. Guidelines are given for the parameter ranges over which the accurate application of the thick and thin boundary approximations can be used for a fluid-structure interaction problem. PMID:23729844

Including fluid shear viscosity in a structural acoustic finite element model using a scalar fluid representation.

PubMed

Cheng, Lei; Li, Yizeng; Grosh, Karl

2013-08-15

An approximate boundary condition is developed in this paper to model fluid shear viscosity at boundaries of coupled fluid-structure system. The effect of shear viscosity is approximated by a correction term to the inviscid boundary condition, written in terms of second order in-plane derivatives of pressure. Both thin and thick viscous boundary layer approximations are formulated; the latter subsumes the former. These approximations are used to develop a variational formation, upon which a viscous finite element method (FEM) model is based, requiring only minor modifications to the boundary integral contributions of an existing inviscid FEM model. Since this FEM formulation has only one degree of freedom for pressure, it holds a great computational advantage over the conventional viscous FEM formulation which requires discretization of the full set of linearized Navier-Stokes equations. The results from thick viscous boundary layer approximation are found to be in good agreement with the prediction from a Navier-Stokes model. When applicable, thin viscous boundary layer approximation also gives accurate results with computational simplicity compared to the thick boundary layer formulation. Direct comparison of simulation results using the boundary layer approximations and a full, linearized Navier-Stokes model are made and used to evaluate the accuracy of the approximate technique. Guidelines are given for the parameter ranges over which the accurate application of the thick and thin boundary approximations can be used for a fluid-structure interaction problem.

Modeling of viscoelastic properties of nonpermeable porous rocks saturated with highly viscous fluid at seismic frequencies at the core scale

NASA Astrophysics Data System (ADS)

Wang, Zizhen; Schmitt, Douglas R.; Wang, Ruihe

2017-08-01

A core scale modeling method for viscoelastic properties of rocks saturated with viscous fluid at low frequencies is developed based on the stress-strain method. The elastic moduli dispersion of viscous fluid is described by the Maxwell's spring-dash pot model. Based on this modeling method, we numerically test the effects of frequency, fluid viscosity, porosity, pore size, and pore aspect ratio on the storage moduli and the stress-strain phase lag of saturated rocks. And we also compared the modeling results to the Hashin-Shtrikman bounds and the coherent potential approximation (CPA). The dynamic moduli calculated from the modeling are lower than the predictions of CPA, and both of these fall between the Hashin-Shtrikman bounds. The modeling results indicate that the frequency and the fluid viscosity have similar effects on the dynamic moduli dispersion of fully saturated rocks. We observed the Debye peak in the phase lag variation with the change of frequency and viscosity. The pore structure parameters, such as porosity, pore size, and aspect ratio affect the rock frame stiffness and result in different viscoelastic behaviors of the saturated rocks. The stress-strain phase lags are larger with smaller stiffness contrasts between the rock frame and the pore fluid. The viscoelastic properties of saturated rocks are more sensitive to aspect ratio compared to other pore structure parameters. The results suggest that significant seismic dispersion (at about 50-200 Hz) might be expected for both compressional and shear waves passing through rocks saturated with highly viscous fluids.