Showing papers on "Velocity gradient published in 2003"

Evaluating the law of the wall in two-dimensional fully developed turbulent channel flows

Abstract: This article is concerned with the mean velocity distributions of two-dimensional fully developed turbulent plane-channel flows. To yield reliable information, the authors performed detailed hot-wire measurements for more than 12 Reynolds numbers. The experimental investigations covered a wide range of the Reynolds numbers up to Reτ≈5×103, where Reτ is based on the wall friction velocity and the channel half-height. From the distribution of the mean velocity gradient (dU+/dy+)=f(y+) the entire flow field was analyzed, resulting in a logarithmic region for the mean velocity profile in the inertial sublayer, extending almost up to the center of the channel at higher Reynolds numbers. The analysis of the experimental results yield a value of the von Karman constant, κ, close to 0.37(≈1/e) independent of the Reynolds number and the additive constant B=3.70, which is close to 10/e, i.e., U+=e ln y++10/e=(1/0.37)ln y++3.70.

A hybrid RANS/LES simulation of turbulent channel flow

Abstract: Hybrid models combining large eddy simulation (LES) with Reynolds-averaged Navier–Stokes (RANS) simulation are expected to be useful for wall modeling in the LES of high Reynolds number flows. Some hybrid simulations of turbulent channel flow have a common defect; the mean velocity profile has a mismatch between the RANS and LES regions due to a steep velocity gradient at the interface. This mismatch is reproduced and examined using a simple hybrid model; the Smagorinsky model is switched to a RANS model increasing the filter width. It is suggested that a rapid spatial variation in the eddy viscosity is responsible for an underestimate of the grid-scale shear stress and for the steep velocity gradient. To reduce the mean velocity mismatch a new scheme is proposed; additional filtering is introduced to define two kinds of velocity components at the interface between the two regions. The two components are used to remove inconsistency in the velocity equations due to a rapid variation in the filter width. Using the new scheme, simulations of channel flow are carried out with the simple hybrid model. It is shown that the grid-scale shear stress becomes large enough and most of the mean velocity mismatch is removed. Simulations for higher Reynolds numbers are carried out with the k–e model and the one-equation subgrid-scale model. Although it is necessary to improve the turbulence models and the treatment of the buffer region, the new scheme is shown to be effective for reducing the mismatch and to be useful for developing better hybrid simulations.

Evaluation of viscous dissipation in liquid flow in microchannels

Abstract: Different phenomena have been observed in various works indicating that the mechanisms of flow and heat transfer in microchannels are still not understood clearly. There is little experimental data and theoretical analysis available in the literature to elucidate the mechanisms. It is reasonable to assume that, as the dimensions of flow channels approach the micro-level, viscous dissipation could be too significant to be neglected due to a high velocity gradient in the channel. However, no evidence and analysis was presented to verify such an explanation. Therefore, in this paper, the effects of viscous dissipation in microchannel flows are analyzed and examined theoretically. A criterion to draw the limit of the significance of the viscous dissipation effects in the microchannel flows is suggested based on the present analysis.

Velocity-Gradient Dynamics in Turbulence: Effect of Viscosity and Forcing

Abstract: The restricted Euler equation is a promising but incomplete model for velocity-gradient dynamics in turbulent flows While it captures many of the geometric features of the vorticity vector and the strain rate tensor, viscous and anisotropic pressure Hessian effects are not accounted for satisfactorily Inadequate viscous-effect modeling causes velocity gradients to diverge in finite time, rendering the restricted Euler model unsuitable for practical applications We perform a Lagrangian frame analysis to comprehend fully the physics of the viscous relaxation time scale and propose a variable time-scale model that can adequately account for deformation history Most importantly, the finite-time singularity (divergence of velocity gradients) problem is fully resolved with the present model We also model the effects of forcing that is used in numerical simulations to sustain stationary isotropic turbulence Detailed comparison of the new model with DNS data reveals good agreement

Texture Evolution in Severe Plastic Deformation by Equal Channel Angular Extrusion

Abstract: The majority of the techniques of severe plastic deformation calls for simple shear deformation mode. This is why a special interest is given in this paper to textures that develop in simple shear. The evolution of texture in Equal Channel Angular Extrusion (ECAE) is also discussed in detail. The classical “simple shear model” of ECAE is examined as well as a new, more precise flow field which uses an analytical flow function. The proposed function is inspired from finite element calculations. The velocity gradient that follows from the analysis is incorporated into the self consistent viscoplastic polycrystal code. The evolution of deformation texture is predicted up to two passes in the A-route ECAE deformation of copper polycrystal when the extrusion angle is 90°.

Unsteady free convection flow over an infinite vertical porous plate due to the combined effects of thermal and mass diffusion, magnetic field and Hall currents

Abstract: The unsteady free convection flow over an infinite vertical porous plate, which moves with time-dependent velocity in an ambient fluid, has been studied. The effects of the magnetic field and Hall current are included in the analysis. The buoyancy forces arise due to both the thermal and mass diffusion. The partial differential equations governing the flow have been solved numerically using both the implicit finite difference scheme and the difference-differential method. For the steady case, analytical solutions have also been obtained. The effect of time variation on the skin friction, heat transfer and mass transfer is very significant. Suction increases the skin friction coefficient in the primary flow, and also the Nusselt and Sherwood numbers, but the skin friction coefficient in the secondary flow is reduced. The effect of injection is opposite to that of suction. The buoyancy force, injection and the Hall parameter induce an overshoot in the velocity profiles in the primary flow which changes the velocity gradient from a negative to a positive value, but the magnetic field and suction reduce this velocity overshoot.

Cellular neural network to detect spurious vectors in PIV data

Abstract: This paper proposes an artificial neural network (ANN) method to effectively detect spurious velocity vectors in a velocity field measured by particle image velocimetry (PIV). The neural network is a recurrent network referred to as a cellular neural network (CNN). The method is compared with the local-median method to remove measurement outliers. Both artificially generated velocity fields containing known errors and actual experimental data were used to study the performance of these methods. The influences of the velocity gradient and the error percentage are discussed. The CNN model was shown to be more efficient for removal of erroneous vectors.

An experimental investigation of the near-field flow development in coaxial jets

Abstract: The near-field region of a coaxial jet having inner to outer diameter ratio di/do=0.39 is investigated experimentally for four ratios of annular to central jet velocities of η=0.18, 0.48, 0.8, and 1.11. Measurements were acquired nonintrusively using molecular tagging velocimetry at downstream distances up to six inner jet diameters. High spatial-resolution profiles of mean axial velocity, axial turbulent intensity, skewness, kurtosis, radial gradients of mean velocity, and velocity gradient fluctuations are presented and discussed. In the near-exit region of the inner mixing layer, evidence suggests the existence of two trains of vortices shed from the inner jet wall for velocity ratios η>0.18. The results also indicate that for the flow configuration examined the length of the annular potential core is a function of the velocity ratio. Turbulence characteristics of the flow appear to be influenced by both the velocity ratio and absolute velocity of the annular jet. Integral length and Taylor microscales...

Non-isothermal dispersed phase of particles in turbulent flow

Abstract: In this paper we consider, for modelling and simulation, a non-isothermal turbulent flow laden with non-evaporating spherical particles which exchange heat with the surrounding fluid and do not collide with each other during the course of their journey under the influence of the stochastic fluid drag force. In the modelling part of this study, a closed kinetic or probability density function (p.d.f.) equation is derived which describes the distribution of position x, velocity v, and temperature θ of the particles in the flow domain at time t. The p.d.f. equation represents the transport of the ensemble-average (denoted by 〈 〉) phase-space density 〈W(x, v, θ, t)〉. The process of ensemble averaging generates unknown terms, namely the phase-space diffusion current j = βv〈u′W〉 and the phase-space heat current h = βθ〈t′W〉, which pose closure problems in the kinetic equation. Here, u′ and t′ are the fluctuating parts of the velocity and temperature, respectively, of the fluid in the vicinity of the particle, and βv and βθ are inverse of the time constants for the particle velocity and temperature, respectively. The closure problems are first solved for the case of homogeneous turbulence with uniform mean velocity and temperature for the fluid phase by using Kraichnan’s Lagrangian history direct interaction (LHDI) approximation method and then the method is generalized to the case of inhomogeneous flows. Another method, which is due to Van Kampen, is used to solve the closure problems, resulting in a closed kinetic equation identical to the equation obtained by the LHDI method. Then, the closed equation is shown to be compatible with the transformation constraint that is proposed by extending the concept of random Galilean transformation invariance to non-isothermal flows and is referred to as the ‘extended random Galilean transformation’ (ERGT). The macroscopic equations for the particle phase describing the time evolution of statistical properties related to particle velocity and temperature are derived by taking various moments of the closed kinetic equation. These equations are in the form of transport equations in the Eulerian framework, and are computed for the case of two-phase homogeneous shear turbulent flows with uniform temperature gradients. The predictions are compared with the direct numerical simulation (DNS) data which are generated as another part of this study. The predictions for the particle phase require statistical properties of the fluid phase which are taken from the DNS data. In DNS, the continuity, Navier–Stokes, and energy equations are solved for homogeneous turbulent flows with uniform mean velocity and temperature gradients. For the mean velocity gradient along the x2- (cross-stream) axis, three different cases in which the mean temperature gradient is along the x1-, x2-, and x3-axes, respectively, are simulated. The statistical properties related to the particle phase are obtained by computing the velocity and temperature of a large number of particles along their Lagrangian trajectories and then averaging over these trajectories. The comparisons between the model predictions and DNS results show very encouraging agreement.

Spatially averaged time-resolved particle-tracking velocimetry in microspace considering Brownian motion of submicron fluorescent particles

Abstract: A time-series measurement method is proposed to detect velocity fields in a microchannel taking into account Brownian motion of submicron tracer particles. The present study proposes spatially averaged time-resolved particle-tracking velocimetry (SAT–PTV), which can detect temporal variations of fluid flow and eliminate errors associated with Brownian motion without losing temporal resolution. Velocity vectors of tracer particles obtained by PTV are spatially averaged in each interrogation window of particle-image velocimetry, yielding full velocity field information with temporal resolution. Synthetic particle images, which include Brownian motion of submicron fluorescent particles in flow fields with linear velocity gradients, are generated to validate the ability of SAT–PTV to track particles. SAT–PTV correctly captures the velocity gradient profiles. The spatial resolution based on the size of the first interrogation window and the measurement depth of the microscope system is 6.7 μm×6.7 μm×1.9 μm, within which several vectors are averaged. SAT–PTV is shown to measure the velocity field of a pulsating flow generated by an electrokinetic pump.

Properties of Magnetic and Velocity Fields in and around Solar Pores

Abstract: We studied the magnetic and velocity fields of four pores situated close to the disk center and its surrounding regions. We find the following results from our analysis: The velocity inside the pore is very close to zero, whereas there is a strong and narrow downflow around the pore. The vertical velocity gradient observed at the edge of the pore is stronger than the velocity gradient seen in intergranular lanes. Immediately surrounding these narrow downflows, normal granular convection is observed. This observation is consistent with the theoretical picture of an isolated flux tube embedded in a quiet region surrounded by a downflow driven by radiative energy losses. Needle-like structures were seen around the pore, with the head of the needle showing an upflow. The needle tail ends in the downflow surrounding the pore. Assuming the flow is horizontal in the body of the needle, the needle-like structures would represent a possible signature of circular flow system surrounding the pore. The radial extent of this observed flow system (which likely feeds the downflow around the pore) is about 10''. A pore with relatively large fill fraction shows a small upflow in the center surrounded by the downflow, whereas a pore with small fill fraction shows downflows throughout the pore. The asymmetries of the observed Stokes V profiles and their temporal variations are studied. We find temporal variations of V-profile asymmetries observed within pores on timescales of 5 minutes.

Nonequilibrium Dynamics and Magnetoviscosity of Moderately Concentrated Magnetic Liquids: A dynamic Mean-field Study

Abstract: A mean-field Fokker-Planck equation approach to the dynamics of ferrofluids in the presence of a magnetic field and velocity gradients is proposed that incorporates magnetic dipole-dipole interactions of the colloidal particles. The model allows to study the combined effect of a magnetic field and dipolar interactions on the viscosity of the ferrofluid. It is found that dipolar interactions lead to additional non-Newtonian contributions to the stress tensor, which modify the behavior of the non-interacting system. The predictions of the present model are in qualitative agreement with experimental results, such as the enhancement as well as the different anisotropy of the magnetoviscous effect and the dependence on the symmetric velocity gradient.

Rigorous justification of the Kirchhoff law for junction of thin pipes filled with viscous fluid

Abstract: We study the junction of $m$ pipes that are either thin or long (i.e. they have small ratio between the cross-section and the length, denoted by $\varepsilon $). Pipes are filled with incompressible Newtonian fluid and the values of the pressure $p_i$ at the end of each pipe are prescribed. By rigorous asymptotic analysis, as $\varepsilon\to 0$, we justify the analog of the Kirchhoff law for computing the junction pressure. In interior of each pipe the effective flow is the Poiseuille flow governed by the pressure drop between the end of the pipe and the junction point. The pressure at the junction point is equal to a weighted mean value of the prescribed $p_i$-s (Kirchhoff law). In the vicinity of the junction there is an interior layer, with thickness $\varepsilon\, \mbox{; ; ; ; log}; ; ; ; (1/\varepsilon)$. To get a better approximation and to control the velocity gradient in vicinity of the junction, first order asymptotic approximation has to be corrected by solving the appropriate Leray problem. We prove the asymptotic error estimate for the approximation.

Linear stability analysis of flow of an Oldroyd-B fluid through a linear array of cylinders

Abstract: The linear stability of the flow of an Oldroyd-B fluid through a linear array of cylinders confined in a channel is analyzed by computing both the steady-state flows and the linear stability of these states by finite element analysis. The linear stability of two-dimensional base flows to three-dimensional perturbations is computed both by time integration of the linearized evolution equations for infinitesimal perturbations and by an iterative eigenvalue analysis based on the Arnoldi method. These flows are unstable to three-dimensional perturbations at a critical value of the Weissenberg number that is in very good agreement with the experimental observations by Liu [Viscoelastic Flow of Polymer Solutions around Arrays of Cylinders: Comparison of Experiment and Theory, Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge, MA, 1997] for flow of a polyisobutylene Boger fluid through a linear periodic array of cylinders. The wave number of the disturbance in the neutral or spanwise direction also is in good agreement with experimental measurements. For closely spaced cylinders, the mechanism for the calculated instability is similar to the mechanism proposed by Joo and Shaqfeh [J. Fluid Mech. 262 (1994) 27] for the non-axisymmetric instability observed in viscoelastic Couette flow, where perturbations to the shearing component of the velocity gradient interact with the polymer stresses in the base flow. However, when the cylinder spacing is increased, we discover a new mechanism for instability that involves the coupling between the elongational component of the velocity gradient and the streamwise normal stress in the base state. In addition, the most unstable disturbance in the Couette geometry is over-stable (leading to time-periodic states) whereas the instability calculated for closely spaced cylinders grows monotonically with time. This apparent inconsistency is resolved by the observation that in a complex flow, the evolution of the perturbations to the base flow can be transient in a Lagrangian frame of reference, while steady in an Eulerian frame.

An optical MEMS-based shear stress sensor for high reynolds number applications

Abstract: In an effort to extend wall shear stress measurements to high Reynolds number flows, a new MEMSbased optical shear stress sensor was fabricated and tested in the 2 feet wind tunnel at the California Institute of Technology for Reynolds numbers of up to 5.6 x 106. The description of this sensor and the test results are reported in this paper. The sensor, the Dual Velocity sensor, designed using recent developments in diffractive and integrated optics, was small enough to be embeddable in test models. The sensor measured the average flow velocity at two probe volumes located within the first 110 micrometers above the flush-mounted sensor surface. The velocity gradient at the wall was estimated by fitting the Spalding formula to the average velocity measurements, once mapped using the inner-law variables u+ and y+. The results obtained with the Dual Velocity sensor were in excellent agreement with measurements obtained in the same tunnel using other techniques such as the oil film interferometry technique and with another MEMS-based optical shear stress sensor, the Diverging Fringe Doppler sensor. All wall shear stress measurements were also in agreement with those calculated from boundary layer surveys obtained with a miniature LDV.

Experimental Investigation of Flow Regimes in an SMX Sulzer Static Mixer

Abstract: An experimental study of the flow pattern in the wall region of an SMX static mixer was performed by using electrochemical shear rate sensors. Electrochemical signals were related to the local shear stress and the fluctuating rate of the velocity gradient. Signal fluctuation analysis allowed one to define the flow regimes inside the static mixers. The laminar flow was characterized by a time-constant evolution of the velocity gradient, while the turbulent flow corresponded to the stabilization of the fluctuating rate of the velocity gradient for high values of pore Reynolds number, defined by considering the static mixer as a porous medium and by using a capillary model. The transition from a laminar flow to an intermediate flow occurred at a pore Reynolds number of about 200. The turbulent flow was observed at a pore Reynolds number of between 1500 and 3000.

Brownian dynamics simulations of polymer stretching and transport in a complex electroosmotic flow

Abstract: Brownian dynamics simulations are performed to study the stretching and transport of flexible polymers in complex electroosmotic flows. The flows are generated by prescribing a spatially periodic charge distribution on the walls of a parallel-plate channel and applying an electric field parallel to the direction of charge modulation. The polymer molecules are modeled as bead–spring chains and the model parameters are chosen to be representative of DNA. Simulations are performed for the cases of uncharged and charged polymers. For the uncharged case, it is found that the stagnation point in the center of the flow is not effective at stretching the polymers due to the fact that the flow has an inhomogeneous velocity gradient. It is observed that polymers tend to become trapped in the recirculation rolls near that stagnation point, and that the amount of stretching that does occur is directly proportional to the amount of time that the polymer spends near the stagnation point at the wall. For the charged case, it is found that the trapping persists below a critical charge density, but that above this threshold the polymer escapes from the rolls. Our observations suggest that while these complex flows may not be useful for stretching polymers far away from the channel walls, they may be useful for localizing the position of Brownian particles in microfluidic devices. In addition, they illustrate the rich dynamics that arise when polymers are placed in flows with inhomogeneous velocity gradients and when electroosmotic flow competes with electrophoresis.

Fourth-order statistical moments of the velocity gradient tensor in homogeneous, isotropic turbulence

Abstract: A compact expression of fourth-order statistical moments of the velocity gradient tensor in homogeneous, isotropic, incompressible turbulence is obtained as a function of its invariants and of generic components of the velocity gradient. This single, compact expression is in full agreement with the four different expressions previously obtained by Siggia as functions of the same invariants and of generic components of the vorticity vector and the strain tensor; however, some discrepancies arise with respect to a similar, single expression obtained by Phan-Thien and Antonia. The used algorithm may be easily extended to handle higher order statistical moments of the velocity gradient.

Large-scale anisotropy effect on small-scale statistics over rough wall turbulent boundary layers

Abstract: According to the local isotropy hypothesis presented by Kolmogorov, small-scale velocity fluctuations should be universal in any kind of turbulent flow when the Reynolds number is sufficiently large. This is one of the key assumptions in turbulence phenomena. At this stage, the question is not whether this assumption is correct or not, but rather how the local isotropy works as a good approximation depending on the nature of the large-scale anisotropy. In this paper, we report on how the large-scale anisotropy penetrates the small scales. Based on the experiments performed in the strong mean shear flow on the rough-wall boundary layer, we consider how the local isotropy is restored. The anisotropic parameter S* is defined as a ratio of the time scale caused by the mean velocity gradient and the Kolmogorov time scale. It is found that the local isotropy is achieved in the dissipation range even in S*≃0.1. On the other hand, there is no clear evidence of isotropy in the inertial range. Due to the strong mean shear, the second-order structure functions do not satisfy the exact power-law relation but they indicate the convex shape plotted in the logarithmic coordinate. Computing the local slope and the curvature of structure functions, we found they are a strong function of anisotropic parameter.

Effect of the orientation of the magnetic field on the flow of a magnetorheological fluid. I. Plane channel

Abstract: Shear flow and Poiseuille flow of magnetorheological fluids in a plane channel under an inclined magnetic field are studied. The proposed theoretical model is based on stability analysis of chain-like clusters of dipolar magnetic particles. Hydrodynamic and magnetic torque acting on aggregates balances each other such that some misalignment between orientations of chains and the field takes place. Two magnetic field directions symmetric relative to the velocity gradient influence the aggregate behavior in different ways. In one case, the aggregates tend to turn along the flow whereas in the other case, they tend to turn transverse to the flow. The predicted peak value of the yield stress arises for θ0=−π/4 (where θ0 is the clockwise angle between the velocity gradient and the direction of the field) and is 1.8 times the value for θ0=0. If we consider Poiseuille flow between two parallel plates, the velocity gradient, being positive on one side and negative on the other, the stress is no longer symmetric r...

The effect of serrated fins on the flow around a circular cylinder

Abstract: An experimental study is performed to investigate the characteristics of near wake flow behind a circular cylinder with serrated fins using a constant temperature anemometer and flow visualization. Various vortex shedding modes are observed. Fin height and pitch are closely related to the vortex shedding frequency after a certain transient Reynolds number. The through-velocity across the fins decreases with increasing fin height and decreasing fin pitch. Vortex shedding is affected strongly by the velocity distribution just on top of the finned tube. The weaker gradient of velocity distribution is shown as increasing the freestream velocity and the fin height, while decreasing the fin pitch. The weaker velocity gradient delays the entrainment flow and weakens its strength. As a result of this phenomenon, vortex shedding is decreased. The effective diameter is defined as a virtual circular cylinder diameter taking into account the volume of fins, while the hydraulic diameter is proposed to cover the effect of friction by the fin surfaces. The Strouhal number based upon the effective diameters seems to correlate well with that of a circular cylinder without fins. After a certain transient Reynolds number, the trend of the Strouhal number can be estimated by checking the ratio of effective diameter to inner diameter. The normalized velocity and turbulent intensity distributions with the hydraulic diameter exhibit the best correlation with the circular cylinder’s data.

Seismic velocity, anisotropy, and fluid pressure in the Barbados accretionary wedge from an offset vertical seismic profile with seabed sources

Abstract: [1] The state of compaction and fluid pressure in the Barbados accretionary wedge near its toe, at Ocean Drilling Program Site 949, were investigated by modeling travel times of seismic waves from ocean bottom shots to a borehole geophone array. The model, constrained by a three-dimensional seismic survey and well logs, shows (1) a velocity gradient of about 1–1.25 s−1 in the uppermost 180–230 m of the wedge; (2) a zone of variable, but no net change in, velocity between 230 and 350 m depth; (3) a low-velocity zone 40–50 m thick just above the decollement at 391 m; and (4) a displacement of the low-velocity zone by thrust faults. Pore fluid pressure sections derived from P wave velocity show that the upper half of the wedge is normally pressured while the lower half is overpressured. The ∼160 m thick, underconsolidated basal zone shows anisotropy, which increases downward. The lowest 40–50 m has velocity varying (1) azimuthally (3%), being fastest in the direction of plate convergence, and (2) in the vertical plane (2–5%), horizontal faster than vertical. After correction for the effect of anisotropy in the derivation of effective stress from seismic velocity the calculated pore fluid pressure ratio λ does not exceed 0.9 and in the lowest 40–50 m of the basal zone, is between 0.71 and 0.82, with λ* [(fluid pressure − hydrostatic)/(lithostatic pressure − hydrostatic)] between 0.5 and 0.65, in accordance with in situ measurements of fluid pressure in the decollement zone beneath. These indicate that the accretionary wedge is stronger and less overpressured than was previously supposed.

Development of erosive burning models for cfd predictions of solid rocket motor internal environments

Abstract: Four erosive burning models, equations (11) to (14). are developed in this work by using a power law relationship to correlate (1) the erosive burning ratio and the local velocity gradient at propellant surfaces; (2) the erosive burning ratio and the velocity gradient divided by centerline velocity; (3) the erosive burning difference and the local velocity gradient at propellant surfaces; and (4) the erosive burning difference and the velocity gradient divided by centerline velocity. These models depend on the local velocity gradient at the propellant surface (or the velocity gradient divided by centerline velocity) only and, unlike other empirical models, are independent of the motor size. It was argued that, since the erosive burning is a local phenomenon occurring near the surface of the solid propellant, the erosive burning ratio should be independent of the bore diameter if it is correlated with some local flow parameters such as the velocity gradient at the propellant surface. This seems to be true considering the good results obtained by applying these models, which are developed from the small size 5 inch CP tandem motor testing, to CFD simulations of much bigger motors.

Computation of slip flow in microchannels using langmuir slip condition

Abstract: To analyze microscale slip flows, a new simulation method is proposed that combines the Navier-Stokes solution with a new slip model called the Langmuir slip condition. The proposed method is applied to a gaseous microchannel flow model. The Langmuir slip model can simulate the velocity slip effect at the wall that comes from rarefaction and the compressibility effect of the microscale gases. The Langmuir slip model solution is analogous to the results of the well-known Maxwell slip condition. As the Knudsen number becomes higher, the Maxwell slip condition decreases pressure nonlinearity, while the Langmuir slip condition increases it slightly. Increased nonlinearity is more compatible with experimental results. The Langmuir slip condition does not require a cumbersome process in either calculation of streamwise velocity gradient at the wall or calibration of empirical accommodation coefficient. The proposed method using the Langmuir slip condition is proved to be an efficient, practical, and accurate to...

Forces on Spherical Particles in Terms of Upstream Flow Characteristics

Abstract: The paper is devoted to the estimation of hydrodynamic forces induced by different flows around an isolated solid sphere. The goal of the study is to relate the stresses exerted by the flow around the particle to the upstream flow characteristics, in particular in terms of velocity gradient in the case of pure shear flow. Three-dimensional numerical simulations have been performed. Fluent® code has been used. The computational flow dynamics (CFD) code has been first validated in classical cases of (i) uniform flow around a fixed spherical particle at low and finite Reynolds numbers (1 to 300) and (ii) linear shear superimposed to a uniform flow past a fixed spherical particle at finite Reynolds numbers (10 to 100). After the validation step of the study, the CFD code has been applied to pure linear shear flow around a fixed spherical particle. The effect of free rotation of the sphere has been analysed. The magnitude of the forces exerted on each hemisphere of a spherical particle is derived in this paper compared to forces inducing floc breakup.

Dynamics of complex interfaces. I. Rheology, morphology, and diffusion

Abstract: In this paper, we investigate, on two levels of description, the isothermal coupling: (i) between rheology and morphology in immiscible blends (A/B) and (ii) among rheology, morphology, and diffusion in mixtures consisting of an immiscible blend (A/B) and one simple fluid, s. The interface separating the phases A and B is described, on the kinetic level by an area density distribution function and on the mesoscopic level by a scalar and a traceless symmetric second order tensor. The nonlinear formulations are derived using the general equation for nonequilibrium reversible and irreversible coupling formalism which ensures the consistency of dynamics with thermodynamics. In addition to the non-Fickian character of mass transport, the coupled three-dimensional governing equations explicitly show the effects of the external flow and diffusion on the size and shape of the interface. New expressions for the stress tensor emerge naturally in the models including the contributions of the diffusion fluxes and the isotropic (Laplace) and anisotropic deformations of the interface. Asymptotic solutions of the governing equations also show that the transport coefficients (diffusivity, etc.) are explicitly dependent on the interfacial tension and on the velocity gradient of the applied flow. The latter dependence renders the process of mass transfer highly anisotropic even in the absence of internal stresses created by the deformation of the interface. The diffusion-free models of Doi–Ohta and Lee–Park are recovered as particular cases.