Couette Flow Geometry Research Articles

Three-dimensional numerical investigation of a suspension flow in an eccentric Couette flow geometry

This paper investigates the influence of eccentricity on flow characteristics and particle migration in Couette geometries. The study involves numerical simulations using the recent frame-invariant model developed by Badia et al. [J. Non-Newtonian Fluid Mech. 309, 104904 (2022)]. The study begins with a two-dimensional analysis, focusing first on the Newtonian fluid in order to thoroughly characterize the specific properties of this flow configuration. Next, the impact of eccentricity on particle migration in an isodense suspension is examined by numerical simulations based on the experiments conducted by Subia et al. [J. Fluid Mech. 373, 193–219 (1998)]. Furthermore, the study is extended to include a full three-dimensional analysis of a dense suspension flow in an eccentric Couette geometry based on resuspension experiments conducted by Saint-Michel et al. [Phys. Fluids 31, 103301 (2019)] and D'Ambrosio et al.[J. Fluid Mech. 911, A22 (2021)]. The main objective of the latter study is to investigate the influence of eccentricity on the resuspension height and on the calculation of the particle normal stress in the vertical direction through the volume fraction profile analysis. Our results show that even minimal eccentricity can lead to significant changes compared to the centered case.

Grain size distribution in sheared polycrystals

Plastic deformation in solids induced by external stresses is of both fundamental and practical interest. Using both phase field crystal modeling and molecular dynamics simulations, we study the shear response of monocomponent polycrystalline solids. We subject mesocale polycrystalline samples to constant strain rates in a planar Couette flow geometry for studying its plastic flow, in particular its grain deformation dynamics. As opposed to equilibrium solids where grain dynamics is mainly driven by thermal diffusion, external stress/strain induce a much higher level of grain deformation activity in the form of grain rotation, coalescence, and breakage, mediated by dislocations. Despite this, the grain size distribution of this driven system shows only a weak power-law correction to its equilibrium log-normal behavior. We interpret the grain reorganization dynamics using a stochastic model.

Rheo-optical response of carbon nanotube suspensions

In this work, the rheo-optical response of multiwalled carbon nanotube (MWCNT) suspensions was analyzed. Dichroism was obtained using a polarization-modulation technique in parallel disks and for the first time for these particles in a Couette flow geometry. MWCNTs were dispersed in a Newtonian epoxy matrix, at different concentrations covering the dilute and semidilute regimes. Measurements of dichroism were performed as functions of shear rate and nanotube concentration. Surprisingly, the ultimate average orientation angle with respect to the flow direction was far from zero degree, even at high Peclet (Pe) numbers in very dilute suspensions. To explain this peculiar behavior, a new model for flexible rods, valid in the dilute regime, is proposed. It is based on the development of Strautins and Latz [Rheol. Acta 46, 1057–1064 (2007)] that considers flexible rods made of beads and connectors. We modified their bending potential that allows only straight rods at equilibrium with a harmonic cosine expression. This simple modification changes drastically the behavior of these flexible particles that exhibit a non-negligible orientation in the vorticity direction under steady state.

Rheological analysis of graphene oxide coated anisotropic PMMA microsphere based electrorheological fluid from Couette flow geometry

Based on flow curve of graphene oxide coated polymeric microsphere based electrorheological (ER) fluid, model independent yield stress and shear rate, γ˙(τ), were determined using a Tikhonov regularization technique developed to solve the inverse problem of the shear rate in Couette flow viscometry. The model independent yield stress data were compared with that extracted from yield stress fluid models of Bingham plastic and Cho-Choi-Jhon (CCJ) used to fit the γ˙(τ) data. The agreement between model independent and Bingham yield stress was excellent, while the CCJ model yield stresses are generally slightly higher.

Traveling hairpin-shaped fluid vortices in plane Couette flow

Traveling-wave solutions are discovered in plane Couette flow. They are obtained when the so-called steady hairpin vortex state found recently by Gibson [J. Fluid Mech. 638, 243 (2009)] and Itano and Generalis [Phys. Rev. Lett. 102, 114501 (2009)] is continued to sliding Couette flow geometry between two concentric cylinders by using the radius ratio as a homotopy parameter. It turns out that in the plane Couette flow geometry two traveling waves having the phase velocities with opposite signs are associated with their appearance from the steady hairpin vortex state, where the amplitude of the phase velocities increases gradually from zero as the Reynolds number is increased. The solutions obviously inherit the streaky structure of the hairpin vortex state, but shape preserving flow patterns propagate in the streamwise direction. Other striking features of the solution are asymmetric mean flow profiles and strong quasistreamwise vortices which occupy the vicinity of only the top or bottom moving boundary, depending on the sign of the phase velocity. Furthermore, we find that the pitchfork bifurcation associated with the appearance of the solution becomes imperfect when the flow is perturbed by a Poiseuille flow component.

T0501-1-3 白金上の水の動的接触角に対する温度の影響に関する分子動力学解析([T0501-1]マイクロ・ナノスケールの熱流体現象(1))

Microscopic contact angle at a moving contact line among water-vapor-platinum interfaces was investigated with molecular dynamics calculations. The extended simple point charge (SPC/E) model was used for the water molecules and the interactions between water and platinum plate were calculated with the potential model proposed by Zuh and Philpott(1994). The simulations were performed in a Couette flow geometry in which water slug were placed between two parallel plates of platinum. The simulation results show that the static contact angle decreased with the increment in the temperature. The dynamic contact angle, which depends on the wall velocity Vw, became less sensitive to Vw as the temperature was increased. The ordered structure of the water molecules was observed in the vicinity of the wall surface, and was disordered as the temperature was raised. This should be responsible for the lowering of the sensitivity of the dynamic contact angle in the high temperature condition.

T0501-2-3 ナノスケールステップにおける微視的接触角の分子動力学解析(マイクロ・ナノスケールの熱流体現象(2))

Microscopic contact angle on a moving contact line traveling over a step with a height of 0.3〜1.2 nm is investigated with molecular dynamics simulation. The simulations were made with a Couette flow geometry where two immiscible fluids are sheared between two parallel plates, one of which is equipped with step-structured surface. The contact lines strongly tend to be captured (pinned) at the edge of the convex step and the minimum contact angle observed at the moment of the depinning of the contact line is dependent on the height of the steps. An analytical model for the estimation of the relation between the minimum contact angle and the step height is developed. By taking account into the deviation between the normal and tangential components of the pressure distribution near the interface, the model reproduces well the increase of the minimum contact angle with the decrement in the step height.

Molecular dynamic simulations of viscosity of argon at high pressures

A new formulation of the boundary conditions in Couette flow geometry was used to enforce a no-slip condition at the boundaries. This condition was used employing two counter-moving boundaries to enforce the symmetry of the flow. Molecular dynamics (MD) simulations employing Lenard–Jones potential were performed to derive shear force, the gradient of the velocity, and consequently, the shear velocity. MD simulations were preformed for high pressures, up to 1 GPa, and low temperatures, up to 500 K, i.e. for the region dominated by the interaction potential. The obtained results were compared with the existing experimental data [E.W. Lemmon and R.T. Jacobsen, Viscosity and thermal conductivity equations for nitrogen, oxygen, argon, and air, Int. J. Thermophys. 25(1) (2004), pp. 21–69]. It is shown that MD results are in very good agreement with the experiments, having a difference not higher than 4% for all the considered results. From the analysis of these results, it also follows that the dominant portion of the error is due to insufficiently precise determination of the velocity gradient in MD simulations.

A Model for Estimating the Dynamic Contact Angle with Molecular Dynamics Simulation

The microscopic configuration of fluid interface near the wetting or dewetting front (i.e., moving contact line) is of significant interest in relation to many industrial processes. In this paper we report on molecular dynamics (MD) simulations conducted for investigation of the dependence of the microscopic contact angle θ on the speed of contact line relative to the solid surface, ΔV. Our simulations were made for a Couette flow geometry where two Lennard-Jones (LJ) liquids are sheared between two solid walls moving at a speed V in opposite directions. The two liquids are immiscible and have different wall-wetting properties. The liquid configuration remains unchanged with time, since ΔV=V at all the contact lines, for V below a certain critical value. The contact angle θ measured under such steady conditions varies monotonically with ΔV. Above the critical wall speed, however, the flow at the receding contact line, where the more wetting liquid of the two is being replaced by the less wetting one, starts becoming unsteady, as ΔV remains smaller than the critical wall speed. We show that the viscous and pressure forces measured from the MD simulation results can be reproduced by the Stokes flow model of Huh and Scriven (1971) using the MD-predicted value of θ at the given ΔV. It follows that, by the aid of Qian et al.'s formulation (2003) of the stress balance at the moving contact line, and by using the MD-predicted proportionality constant between the total wall-tangential force and ΔV, this model can reproduce the MD-predicted dependence of θ on ΔV. The model predictions, furthermore, give insight into the reason why the contact line flow becomes unsteady above the critical wall speed.

Thermal stability of shear‐induced precursor structures in isotactic polypropylene by rheo‐X‐ray techniques with couette flow geometry

AbstractCombined in situ rheo‐SAXS (small‐angle X‐ray scattering) and ‐WAXD (wide‐angle X‐ray diffraction) studies using couette flow geometry were carried out to probe thermal stabilty of shear‐induced oriented precursor structure in isotactic polypropylene (iPP) at around its normal melting point (162 °C). Although SAXS results corroborated the emerging consensus about the formation of “long‐living” metastable mesomorphic precursor structures in sheared iPP melts, these are the first quantitative measures of the limiting temperature at which no oriented structures survive. At the applied shear, rate = 60 s−1 and duration ts = 5 s, the oriented iPP structures survived a temperature of 185 °C for 1 h after shear, while no stable structures were detected at and above 195 °C. Following Keller's concepts of chain orientation in flow, it is proposed that the chains with highly oriented high molecular weight fraction are primarily responsible for their stability at high temperatures. Furthermore, the effects of flow condition, specifically the shear temperature, on the distributions of oriented and unoriented crystals were determined from rheo‐WAXD results. As expected, at a constant flow intensity (i.e., rate = 30 s−1 and duration, ts = 5 s), the oriented crystal fraction decreased with the increase in temperature above 155 °C, below which the oriented fraction decreased with the decrease in temperature. As a result, a crystallinty “phase” diagram, i.e., temperature versus crystal fraction ratio, exhibited a peculiar “hourglass” shape, similar to that found in many two‐phase polymer–polymer blends. This can be explained by the competition between the oriented and unoriented crystals in the available crystallizable species. Below the shear temperature (155 °C), the unoriented crystals crystallized so rapidly that they overwhelmed the crystallization of the oriented crystals, thus depleting a major portion of the crystallizable species and increasing their contribution in the final total crystalline phase. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3553–3570, 2006

Nonlinear shear and extensional flow dynamics of wormlike surfactant solutions

Nonlinear shear and extensional flow dynamics of a wormlike micellar solution based on erucyl bis(2-hydroxyethyl) methyl ammonium chloride (EHAC) are reported here. The influences of surfactant (EHAC) and salt (NH 4Cl) concentrations on the linear viscoelastic parameters are determined using small amplitude oscillatory shear experiments. The steady and time-dependent shear rheology is determined in a double gap Couette cell, and transient extensional flow measurements are performed in a capillary breakup extensional rheometer (CABER). In the nonlinear shear flow experiments, the micellar fluid samples show strong hysteretic behavior upon increasing and decreasing the imposed shear stress due to the development of shear-banding instabilities. The non-monotone flow curves of stress versus shear rate can be successfully modeled in a macroscopic sense by using the single-mode Giesekus constitutive equation. The temporal evolution of the flow structure of the surfactant solutions in the Couette flow geometry is analyzed by instantaneous shear rate measurements for various values of controlled shear stress, along with FFT analysis. The results indicate that the steady flow bifurcates to a global time-dependent state as soon as the shear-banding/hysteresis regime is reached. Increasing the salt–surfactant ratio or the temperature is found to stabilize the flow, and corresponds to decreasing values of anisotropy factor in the Giesekus model. Finally, we have investigated the dynamics of capillary breakup of the micellar fluid samples in uniaxial extensional flow. The filament thinning behavior of the micellar fluid samples is also accurately predicted by the Giesekus constitutive equation. Indeed quantitative agreement between the experimental and numerical results can be obtained providing that the relaxation time of the wormlike micellar solutions in extensional flows is a factor of three lower than in shear flows.

From shear-thickening and periodic flow behavior to rheo-chaos in nonlinear Maxwell-model fluids

The nonlinear Maxwell model equation for the stress tensor as introduced previously in [O. Hess and S. Hess, Physica A 207 (1994) 517] to treat the shear-thickening and shear-thinning behavior of fluids can also be applied for temperatures and densities where a substance shows a yield stress. The basic equations are discussed. Analytic and mainly numerical results are presented for the plane Couette flow geometry. Depending on the model parameters and on the imposed shear rate, a stationary state can be reached or not. In the second case periodic solutions of stick-slip like motions or irregular chaotic behavior is found. For some typical cases the shear stress, the first and second normal stress differences as well as the stress components which break the Couette symmetry are displayed as functions of time. Different types of time dependent solutions can be distinguished by the rheological phase portraits. Some remarks are made on the entropy production associated with the viscous flow and the stress relaxation.

Orientational phenomena in a plastic flow of a two-dimensional square crystal

Within the framework of irreversible thermodynamics, a nonlinear relaxation equation for the 4-rank alignment tensor is formulated for a two-dimensional square crystal subjected to the shear flow. An evolution equation governing the dynamics of the orientation of the crystal, analogous to the Ericksen–Leslie balance equation used in the theory of liquid crystals, is derived from the relaxation equation and analyzed for a Couette flow geometry. It is found that two solutions of the evolution equation are possible: (i) the crystal aligns at a specific angle or (ii) rotates in the shear plane (tumbling). The flow alignment angle is predicted to depend on the value of the shear rate. Furthermore, a generalized Fokker–Planck equation for the probability distribution function is formulated within the mean-field approximation. It is used to derive a scalar counterpart, expressed in terms of microscopic quantities, of the phenomenological evolution equation. The stationary solution is also investigated, based on the kinetic equation.

Monte Carlo method and the nonequilibrium structure and non-Newtonian viscosity of a sheared simple liquid

The Monte Carlo method is applied to study the nonequilibrium steady-state structure and non-Newtonian viscosity of a sheared simple liquid. The simulation is performed in-plane Couette flow geometry on the basis of the nonequilibrium statistical mechanical formalism provided by the nonequilibrium ensemble method. The results are compared with those by the nonequilibrium molecular-dynamics simulation results and also those by the integral equation method. The present Monte Carlo method is comparable in accuracy with the molecular-dynamics simulation method for the quantities compared.

Nonequilibrium statistical thermodynamics: Nonequilibrium grand ensemble method for sheared dilute gases

The nonequilibrium grand ensemble method previously reported is rigorously implemented for a nonequilibrium dilute gas mixture sheared in plane Couette flow geometry and analytic results are presented for the nonequilibrium thermodynamic quantities of the sheared gas. The calortropy is shown to contain all the constitutive information of the system. The notions of temperature and pressure for the nonequilibrium gas are examined on the basis of the calortropy calculated from the nonequilibrium grand partition function. The shear rate dependence of the nonlinear shear and first normal stress coefficients is calculated numerically and also by means of an iterative method. The first iterative solutions are found to give a qualitatively correct behavior for all Peclet numbers.

Rheological properties of thin liquid films by molecular dynamics simulations

In this paper we present the molecular dynamics simulations of thin fluids films sheared in Couette flow geometry between two structured plane walls. An NVT ensemble of atoms was chosen and simulation conducted in isothermal conditions. To keep the temperature at the required level a Gaussian thermostat was employed. This method was shown to be superior to the simple velocity rescaling method, especially at high shear rates. The Gaussian thermostat method gave results for viscosity in good agreement with the results of other researchers who used the reservoir method. The results for density and velocity profiles were obtained for a wide range of simulation parameters. The effects of shear rate and wall-fluid interaction strength were investigated in detail over a wide range of parameters. The material functions and normal stress differences were also obtained and the effects of shear rate and wall strength parameter on these properties were studied. The effect of film thickness on the viscosity was investigated and was compared with what we found for bulk fluid using the SLLOD algorithm. the existence of a non-Newtonian region with shear-thinning effect is found and examined for various films. The results suggest an increase in viscosity for thinner films in the Newtonian regime, though this is valid only for a limited range of wall-fluid interaction strength. A decrease in viscosity was also observed when the attraction force of the wall was increased.

STEADY AND TRANSIENT RESPONSES OF ELECTRORHEOLOGICAL SUSPENSION PASSING THROUGH A RECTANGULAR CHANNEL

The steady and transient responses of ER effect of ER fluids containing sulfonated polymer particles, passing through a rectangular channel between two fixed parallel electrodes, were investigated by ensuring pressure drops across the channel in which the flow established a Poiseuille flow geometry. Effects of the types and the strength of applied electric field and the mean flow velocity on the steady response were clarified, and compared with those in a Couette flow geometry using a rotary rheometer in order to investigate the dependence of ER effects on the flow geometry. As the mean flow velocity increased, the yield stress decreased exponentially under DC voltage, while, in the case of AC voltage, gradually increased and reached a peak level and decreased thereafter. Contrastively, the yield stress measured by the rotary rheometer decreased suddenly at low shear rate, and reached almost constant level. That is, the measured yield stress depends on the flow geometry and the type of applied electric field. The measured pressure response to a step input voltage can be approximated by a first order response, and the rising time constant of ER effect depend on the compositions of ER fluids and range from 5 to 40 msec.

Nanorheology of strongly confined oligomeric lubricants

Lubricant films confined in nanometric slit pores and subjected to shear flow are studied by non-equilibrium molecular dynamics in a planar Couette flow geometry. An inhomogeneous, layered density profile is developed near the confining surfaces and the shape of the velocity profile across the pore depends on the wall energetics. A nonlinear velocity profile is developed and both slippage located at the wall and inside the film (interlayer slip) are observed. The local slope of the velocity profile and the location of the slippage plane are determined by the adsorption energy of the wall. Shear-induced changes of the adsorbed chain conformations are discussed in relation with the molecular mechanism of slippage and the magnitude of the interlayer slip.

Extended irreversible thermodynamics, generalized hydrodynamics, kinetic theory, and rheology

The gist of extended irreversible thermodynamics and generalized hydrodynamics is presented within the context of rheology of complex molecules (e.g., polymers) in this paper. Then, the constitutive equation for stress developed for polyatomic fluids in a previous paper is applied to rheology of polymeric fluids. This constitutive equation is fully consistent with the thermodynamic laws. It is shown that the collision bracket integrals appearing in the constitutive equation can be recast in terms of friction tensors of beads and equilibrium force-force correlation functions if the momentum relaxation is much faster than the configuration relaxation and there exist such relaxation times. The force-force correlation functions reduce to those related to the mean square radius of gyration of the polymer if the Hookean model is taken for forces. By treating the recast collision bracket integrals in the constitutive equation as empirical parameters, we analyze some experimental data on shear rate and elongation rate dependence of polymeric melts and obtain excellent agreement with experiment. We show that the empirical parameters can be related to the zero shear rate viscosity and the ratio of the secondary to the primary normal stress coefficient. Therefore, for the plane Couette flow geometry considered in the paper, the constitutive equation is completely specified by the limiting material functions at zero shear rate and relaxation times.

Irreversible thermodynamic theory of shear-induced melting point depression

Extended irreversible thermodynamics is applied in this paper to study the effect of shear on two-phase equilibrium between a liquid and its solid. The theory predicts a lowering of the melting point of the solid when the liquid is sheared in a plane Couette flow geometry, regardless of whether the liquid is Newtonian or non-Newtonian. A model is used for the temperature dependence of viscosity to estimate the melting point depression which increases with the shear rate. In the case of an activation energy for viscosity sufficiently low compared with the thermal energy the melting point depression is proportional to the square of the Reynolds number. Although for a system different from the experimental ones, this Reynolds number dependence is reminiscent of that observed by Goldburg et al. on critical binary mixtures subjected to a random (turbulent) stirring.