evgeny asmolov - Academia.edu (original) (raw)

Papers by evgeny asmolov

Journal of Fluid Mechanics, 2001

The flow induced by a sphere which undergoes unsteady motion in a Newtonian fluid at small Reynol... more The flow induced by a sphere which undergoes unsteady motion in a Newtonian fluid at small Reynolds number is considered at distances large compared with sphere radius a. Previous solutions of the unsteady Oseen equations (Ockendon 1968; Lovalenti & Brady 1993b) for rectilinear motion are refined. Three-dimensional Fourier transforms of the disturbance field are integrated over Fourier space to derive new concise equations for the velocity field and history force in terms of single history integrals.Various slip-velocity profiles are classified by the ratio A of the particle relative displacement, z′p(t′) − z′p(τ′), to the diffusion length, l′D = 2[v(t′ − τ′)]1/2, where v is the kinematic viscosity of the fluid. Most previous studies are concerned with large-displacement motions for which the ratio is large in the long-time limit. It is shown using asymptotic calculations that the flow at any point at large distance z past a sphere for arbitrary large-displacement and non-reversing ...

Fluid Dynamics, Sep 2, 1989

Sedimentation and Sediment Transport, 2003

Coherent structures in the turbulent boundary layer were investigated under different stability c... more Coherent structures in the turbulent boundary layer were investigated under different stability conditions. Qualitative analyses of the flow field, spatial correlation coefficient field and pre-multiplied wind velocity spectrum showed that the dominant turbulent eddy structure changed from small-scale motions to large-and very-large-scale motions and then to thermal plumes as the stability changed from strong stable to neutral and then to strong unstable. A quantitative analysis of the size characteristics of the three-dimensional turbulent eddy structure based on the spatial correlation coefficient field showed that under near-neutral stability, the streamwise, wall-normal and spanwise extents remained constant at approximately 0.3δ, 0.1δ and 0.2δ (δ, boundary layer height), respectively, while for other conditions, the extent in each direction varied in a log-linear manner with stability; only the spanwise extent under stable conditions was also independent of stability. The peak wavenumber of the pre-multiplied wind velocity spectrum moves towards small values from stable conditions to neutral condition and then to unstable conditions; thus, for the wind velocity spectrum, another form is needed that takes account the effects of the stability condition.

High Performance Computing in Science and Engineering ‘14, 2014

Compared to macroscopic systems, fluids on the micro-and nanoscales have a larger surface-to-volu... more Compared to macroscopic systems, fluids on the micro-and nanoscales have a larger surface-to-volume ratio, thus the boundary condition becomes crucial in determining the fluid properties. No-slip boundary condition has been applied successfully to wide ranges of macroscopic phenomena, but its validity in microscopic scale is questionable. A more realistic description is that the flow exhibits slippage at the surface, which can be characterized by a Navier slip length. We present a tunable-slip method by implementing Navier boundary condition in particle-based computer simulations (Dissipative Particle Dynamics as an example). To demonstrate the validity and versatility of our method, we have investigated two model systems: (i) the flow past a patterned surface with alternating no-slip/partialslip stripes and (ii) the diffusion of a spherical colloidal particle.

Physical Review E, 2015

Aligned superhydrophobic surfaces with the same texture orientation reduce drag in the channel an... more Aligned superhydrophobic surfaces with the same texture orientation reduce drag in the channel and generate secondary flows transverse to the direction of the applied pressure gradient. Here we show that a transverse shear can be easily generated by using superhydrophobic channels with misaligned textured surfaces. We propose a general theoretical approach to quantify this transverse flow by introducing the concept of an effective shear tensor. To illustrate its use, we present approximate theoretical solutions and Dissipative Particle Dynamics simulations for striped superhydrophobic channels. Our results demonstrate that the transverse shear leads to complex flow patterns, which provide a new mechanism of a passive vertical mixing at the scale of a texture period. Depending on the value of Reynolds number two different scenarios occur. At relatively low Reynolds number the flow represents a transverse shear superimposed with two co-rotating vortices. For larger Reynolds number these vortices become isolated, by suppressing fluid transport in the transverse direction.

The linear stability of incompressible boundary-layer flow of dusty gas is considered. Eigenvalue... more The linear stability of incompressible boundary-layer flow of dusty gas is considered. Eigenvalue problem for modified Orr-Sommerfeld equation is solved numerically using two approaches: a) directly by orthonormalization method, and b) by perturbation method. Particles most effectively suppress the instability waves when the relaxation length of their velocity is near to the wavelength of Tollmien-Schlicting (TS) wave. In this case 4% of mass particle content may reduce the growth more than one third. There is a region in the stable part of the flow where one more discrete mode of TS wave is added and the region where the eigenvalue problem has no solution.

On the basis of the quantitative physical model of gas-assisted laser cutting of thick metal in a... more On the basis of the quantitative physical model of gas-assisted laser cutting of thick metal in air or oxygen the maximum cutting velocity and thickness are calculated. The effect of beam shape on cutting efficiency is considered. The theoretical results are in qualitative agreement with the experimental data at the carbon-dioxide-laser of 7...15 kW. It is shown that the cutting velocity can be increased substantially by means of beam shape and gas jet optimization.

ABSTRACT In a shear flow, a small sphere may experience a lift force due to fluid inertia. Most p... more ABSTRACT In a shear flow, a small sphere may experience a lift force due to fluid inertia. Most previous workers assumed that the particle was stationary so that they could treat the fluid motion as steady. In spite of this, the results of previous analyses have generally been applied to problems in which particles move in an unsteady fashion. This paper presents the results of singular perturbation calculations of the lift on a sphere in a linear shear flow. The velocity of the sphere oscillates sinusoidally in time. Although the problem is idealized, the results provide some physical understanding of the effects of unsteadiness and the frequency regime in which one may assume quasisteady conditions.

Non-Brownian particles migrate randomly across the streamlines of a carrier flow in sheared suspe... more Non-Brownian particles migrate randomly across the streamlines of a carrier flow in sheared suspensions at small Reynolds numbers. A random motion is very similar to that in turbulent flows but result not from a flow instability but from the hydrodynamic interactions of particles. It is characterized by the coefficient of particle self-diffusion Ds. Several mechanisms of diffusivity in dilute suspensions based on the interactions of two isolated particles were considered [1],[2]. The model of interactions of rough spheres [1] gives correct linear dependence of Ds on particle volume fraction o. However, the experimental value of the diffusivity [3] is an order of magnitude greater than the theoretical predictions. Another mechanism of the diffusivity was proposed [2] for a wall-bounded shear flow. Two particles do not pass each other in such a configuration but exchange their positions in the normal direction. Swapping trajectories result in a particle cross-stream migration.

Within the framework of the model of two interpenetrating continua, a horizontal laminar dilute-s... more Within the framework of the model of two interpenetrating continua, a horizontal laminar dilute-suspension flow in a vertical Hele-Shaw cell is investigated. Using the method of matched asymptotic expansions, an asymptotic model of the transverse migration of sedimenting particles is constructed. The particle migration in the horizontal section of the cell is caused by an inertial lateral force induced by the particle sedimentation and the shear flow of the carrier phase. A characteristic longitudinal length scale is determined, on which the particles migrate across the slot through a distance of the order of the slot half-width. The evolution of the particle number concentration and velocity fields along the channel is studied using the full Lagrangian method. Depending on the particle inertia parameter, different particle migration regimes (with and without crossing of the channel central plane by the particles) are detected. A critical value of the particle inertia parameter corresponding to the change in migration regime is found analytically. The possibility of intersection of the particle trajectories and the formation of singularities in the particle number concentration is demonstrated.

ABSTRACT Particle migration in a horizontal flow of dilute suspension through a vertical slot wit... more ABSTRACT Particle migration in a horizontal flow of dilute suspension through a vertical slot with porous walls is studied using the two-continua approach. The lateral migration is induced by two opposite effects: an inertial lift force due to particle settling and directed toward the slot centre-line, and a drag due to leak-off entraining particles toward the walls. An expression for the inertial lift on a settling particle in a horizontal channel flow found recently is generalized to the case of a low leak-off velocity. The evolution of an initial uniform particle concentration profile is studied within the full Lagrangian approach. Four migration regimes are found differing by the direction of particle migration and numbers of equilibrium positions. Conditions of the regime change and a critical value of dimensionless leak-off velocity for particle deposition on the walls are obtained analytically. Suspension flows with zones where the particle concentration is zero or increases infinitely, are studied numerically.

Soft Matter, 2013

Superhydrophobic one-dimensional surfaces reduce drag and generate transverse hydrodynamic phenom... more Superhydrophobic one-dimensional surfaces reduce drag and generate transverse hydrodynamic phenomena by combining hydrophobicity and roughness to trap gas bubbles in microscopic textures. Recent works in this area have focused on specific cases of superhydrophobic stripes. Here we provide some theoretical results to guide the optimization of the forward flow and transverse hydrodynamic phenomena in a parallel-plate channel with a superhydrophobic trapezoidal texture, varying on scales larger than the channel thickness. The permeability of such a thin channel is shown to be equivalent to that of a striped one with greater average slip. The maximization of a transverse flow normally requires largest possible slip at the gas areas, similarly to a striped channel. However, in case of trapezoidal textures with a very small fraction of the solid phase this maximum occurs at a finite slip at the gas areas. Exact numerical calculations show that our analysis, based on a lubrication theory, can also be applied for a larger gap. However, in this case it overestimates a permeability of the channel, and underestimates an anisotropy of the flow. Our results provide a framework for the rational design of superhydrophobic surfaces for microfluidic applications.

Physics of Fluids, 2002

The lateral migration of a small spherical particle translating within a vertical channel flow wi... more The lateral migration of a small spherical particle translating within a vertical channel flow with large channel Reynolds numbers Rc is investigated. The weak-shear case is studied when the ratio of the slip velocity to maximum velocity of the channel flow, Vs, is finite, while two other dimensionless groups, particle Reynolds number Rs and Rc−1, are asymptotically small. The disturbance flow at large distances from the sphere is governed by Oseen-like equations. The ratio of Oseen length to channel width is &egr;=ls/l=(Rc|Vs|)−1≪1, i.e., the Oseen region is only a small part of the channel while the major portion of the disturbance flow is inviscid. A solution of the governing equations is constructed in terms of two-dimensional Fourier transform of the disturbance field in a plane parallel to the channel walls. The ordinary differential equation for Fourier transform of lateral velocity Γz(k,z) is solved using the method of matched asymptotic expansions based on &egr;. Several domains in (k,z) space are distinguished that correspond to different regions in physical space: Oseen region, inviscid region, viscous wake, boundary, and critical layers. For the weak-shear case the dominant contribution to the lift gives not velocity disturbances within the Oseen region but the large-scale inviscid disturbances. For such disturbances both effects due to an inviscid interaction with the walls and the curvature of the undisturbed velocity profile should be taken into account. The particle equilibrium positions at the distances from the wall of the order of the channel width arise for both negative and positive slip velocities.

Physics of Fluids, 2008

The inertial migration of particles in a dilute suspension flow through the entry region of a pla... more The inertial migration of particles in a dilute suspension flow through the entry region of a plane channel ͑or a circular pipe͒ is considered. Within the two-fluid approach, an asymptotic one-way coupling model of the dilute suspension flow in the entry region of a channel is constructed. The carrier phase is a viscous incompressible Newtonian fluid, and the dispersed phase consists of identical noncolloidal rigid spheres. In the interphase momentum exchange, we take into account the drag force, the virtual mass force, the Archimedes force, and the inertial lift force with a correction factor due to the wall effect and an arbitrary particle slip velocity. The channel Reynolds number is high and the particle-to-fluid density ratio is of order unity or significantly larger unity. The solution is constructed using the matched asymptotic expansion method. The problem of finding the far-downstream cross-channel profile of particle number concentration is reduced to solving the equations of the two-phase boundary layer developing on the channel walls. The full Lagrangian approach is used to study the evolution of the cross-flow particle concentration profile. The inertial migration results in particle accumulation on two symmetric planes ͑an annulus͒ distanced from the walls, with a nonuniform concentration profile between the planes ͑inside the annulus͒ and particle-free layers near the walls. When the particle-to-fluid density ratio is of order unity, an additional local maximum of the particle concentration on inner planes ͑an inner annulus͒ is revealed. The inclusion of the corrected lift force makes it possible to resolve the nonintegrable singularity in the concentration profile on the wall, which persisted in all previously published solutions for the dilute suspension flow in a boundary layer. The numerical results are compared to the tubular pinch effect observed in experiments, and a qualitative analogy is found.

Physics of Fluids, 2009

The inertial lift force exerted on a small rigid sphere settling due to gravity in a horizontal c... more The inertial lift force exerted on a small rigid sphere settling due to gravity in a horizontal channel flow between vertical walls is investigated. The method of matched asymptotic expansions is used to obtain solutions for the disturbance flow on the length scales of the particle radius and the channel width ͑inner and outer regions, respectively͒. The channel Reynolds number is finite, while the particle Reynolds numbers that are based on the slip velocity and the mean shear rate are small. The inner flow is described by the linear Stokes equations. The outer problem is governed by the linear Oseen-like equations with the particle effect approximated by a point force. The outer equations are solved numerically using the two-dimensional Fourier transform of the disturbance velocity field. The lift coefficient is evaluated as a function of governing dimensionless parameters: the particle coordinate across the channel, the channel Reynolds number, and the slip parameter. The particle always migrates away from the walls, with an equilibrium position being on the channel centerline. Close to the walls, the lift coefficient is the same regardless of the slip velocity and the channel Reynolds number. At large channel Reynolds numbers, a local maximum of the migration velocity forms near the channel centerline due to a combined effect of the slip, the linear shear, and the curvature of the undisturbed velocity profile. The results obtained are extended to the case when the drag on a particle has components both parallel and perpendicular to the undisturbed flow. One of primary applications of the results is modeling of the cross-flow migration of settling particles during particle transport in a hydraulic fracture.

Physical Review E, 2008

Random migrations of non-Brownian neutrally buoyant particles in the flow of a dilute suspension ... more Random migrations of non-Brownian neutrally buoyant particles in the flow of a dilute suspension in a periodic Couette cell is simulated on the basis of a dipole model. A diffusivity is due to far-field collective hydrodynamic interactions. Large-scale fluctuations of particle concentration induce fluid velocity disturbances with a length scale comparable to the cell size. The calculated self-diffusivity coefficient is linear in particle volume content and agrees well with the experimental data.

Physical Review E, 2011

We analyze theoretically a high-speed drainage of liquid films squeezed between a hydrophilic sph... more We analyze theoretically a high-speed drainage of liquid films squeezed between a hydrophilic sphere and a textured super-hydrophobic plane, that contains trapped gas bubbles. A superhydrophobic wall is characterized by parameters L (texture characteristic length), b1 and b2 (local slip lengths at solid and gas areas), and φ1 and φ2 (fractions of solid and gas areas). Hydrodynamic properties of the plane are fully expressed in terms of the effective slip-length tensor with eigenvalues that depend on texture parameters and H (local separation). The effect of effective slip is predicted to decrease the force as compared with expected for two hydrophilic surfaces and described by the Taylor equation. The presence of additional length scales, L, b1 and b2, implies that a film drainage can be much richer than in case of a sphere moving towards a hydrophilic plane. For a large (compared to L) gap the reduction of the force is small, and for all textures the force is similar to expected when a sphere is moving towards a smooth hydrophilic plane that is shifted down from the super-hydrophobic wall. The value of this shift is equal to the average of the eigenvalues of the slip-length tensor. By analyzing striped super-hydrophobic surfaces, we then compute the correction to the Taylor equation for an arbitrary gap. We show that at thinner gap the force reduction becomes more pronounced, and that it depends strongly on the fraction of the gas area and local slip lengths. For small separations we derive an exact equation, which relates a correction for effective slip to texture parameters. Our analysis provides a framework for interpreting recent force measurements in the presence of super-hydrophobic surface.

Physical Review E, 2013

Understanding the influence of topographic heterogeneities on liquid flows has become an importan... more Understanding the influence of topographic heterogeneities on liquid flows has become an important issue with the development of microfluidic systems, and more generally for the manipulation of liquids at the small scale. Most studies of the boundary flow past such surfaces have concerned poorly wetting liquids for which the topography acts to generate superhydrophobic slip. Here we focus on topographically patterned but chemically homogeneous surfaces, and measure a drag force on a sphere approaching a plane decorated with lyophilic microscopic grooves. A significant decrease in the force compared with predicted even for a superhydrophobic surface is observed. To quantify the force we use the effective no-slip boundary condition, which is applied at the imaginary smooth homogeneous isotropic surface located at an intermediate position between top and bottom of grooves. We relate its location to a surface topology by a simple, but accurate analytical formula. Since groves represent the most anisotropic surface, our conclusions are valid for any texture, and suggest rules for the rational design of topographically patterned surfaces to generate desired drag.

Physical Review E, 2013

Anisotropic super-hydrophobic surfaces have the potential to greatly reduce drag and enhance mixi... more Anisotropic super-hydrophobic surfaces have the potential to greatly reduce drag and enhance mixing phenomena in microfluidic devices. Recent work has focused mostly on cases of superhydrophobic stripes. Here, we analyze a relevant situation of cosine variation of the local slip length. We derive approximate formulae for maximal (longitudinal) and minimal (transverse) directional effective slip lengths that are in good agreement with the exact numerical solution and lattice-Bolzmann simulations for any surface slip fraction. The cosine texture can provide a very large effective (forward) slip, but it was found to be less efficient in generating a transverse flow as compared to super-hydrophobic stripes.

Physical Review E, 2007

The evolution of large-scale fluctuations in a monodisperse dilute suspension sedimenting in a wa... more The evolution of large-scale fluctuations in a monodisperse dilute suspension sedimenting in a wall-bounded container is considered on the basis of a continuum model. The case when the velocity fluctuations are comparable with the Stokes settling velocity is studied. Small deformations of the sedimentation front is replaced by a flat interface with a surface force distribution. The front holds position ensuring the vertical fluid velocity across the front to be small. So it acts approximately as a no-slip wall. The mechanisms of the fluctuation decay are the convection of large-scale concentration disturbances and the sedimentation-front deformations.

Journal of Fluid Mechanics, 2001

The flow induced by a sphere which undergoes unsteady motion in a Newtonian fluid at small Reynol... more The flow induced by a sphere which undergoes unsteady motion in a Newtonian fluid at small Reynolds number is considered at distances large compared with sphere radius a. Previous solutions of the unsteady Oseen equations (Ockendon 1968; Lovalenti & Brady 1993b) for rectilinear motion are refined. Three-dimensional Fourier transforms of the disturbance field are integrated over Fourier space to derive new concise equations for the velocity field and history force in terms of single history integrals.Various slip-velocity profiles are classified by the ratio A of the particle relative displacement, z′p(t′) − z′p(τ′), to the diffusion length, l′D = 2[v(t′ − τ′)]1/2, where v is the kinematic viscosity of the fluid. Most previous studies are concerned with large-displacement motions for which the ratio is large in the long-time limit. It is shown using asymptotic calculations that the flow at any point at large distance z past a sphere for arbitrary large-displacement and non-reversing ...

Fluid Dynamics, Sep 2, 1989

Sedimentation and Sediment Transport, 2003

Coherent structures in the turbulent boundary layer were investigated under different stability c... more Coherent structures in the turbulent boundary layer were investigated under different stability conditions. Qualitative analyses of the flow field, spatial correlation coefficient field and pre-multiplied wind velocity spectrum showed that the dominant turbulent eddy structure changed from small-scale motions to large-and very-large-scale motions and then to thermal plumes as the stability changed from strong stable to neutral and then to strong unstable. A quantitative analysis of the size characteristics of the three-dimensional turbulent eddy structure based on the spatial correlation coefficient field showed that under near-neutral stability, the streamwise, wall-normal and spanwise extents remained constant at approximately 0.3δ, 0.1δ and 0.2δ (δ, boundary layer height), respectively, while for other conditions, the extent in each direction varied in a log-linear manner with stability; only the spanwise extent under stable conditions was also independent of stability. The peak wavenumber of the pre-multiplied wind velocity spectrum moves towards small values from stable conditions to neutral condition and then to unstable conditions; thus, for the wind velocity spectrum, another form is needed that takes account the effects of the stability condition.

High Performance Computing in Science and Engineering ‘14, 2014

Compared to macroscopic systems, fluids on the micro-and nanoscales have a larger surface-to-volu... more Compared to macroscopic systems, fluids on the micro-and nanoscales have a larger surface-to-volume ratio, thus the boundary condition becomes crucial in determining the fluid properties. No-slip boundary condition has been applied successfully to wide ranges of macroscopic phenomena, but its validity in microscopic scale is questionable. A more realistic description is that the flow exhibits slippage at the surface, which can be characterized by a Navier slip length. We present a tunable-slip method by implementing Navier boundary condition in particle-based computer simulations (Dissipative Particle Dynamics as an example). To demonstrate the validity and versatility of our method, we have investigated two model systems: (i) the flow past a patterned surface with alternating no-slip/partialslip stripes and (ii) the diffusion of a spherical colloidal particle.

Physical Review E, 2015

Aligned superhydrophobic surfaces with the same texture orientation reduce drag in the channel an... more Aligned superhydrophobic surfaces with the same texture orientation reduce drag in the channel and generate secondary flows transverse to the direction of the applied pressure gradient. Here we show that a transverse shear can be easily generated by using superhydrophobic channels with misaligned textured surfaces. We propose a general theoretical approach to quantify this transverse flow by introducing the concept of an effective shear tensor. To illustrate its use, we present approximate theoretical solutions and Dissipative Particle Dynamics simulations for striped superhydrophobic channels. Our results demonstrate that the transverse shear leads to complex flow patterns, which provide a new mechanism of a passive vertical mixing at the scale of a texture period. Depending on the value of Reynolds number two different scenarios occur. At relatively low Reynolds number the flow represents a transverse shear superimposed with two co-rotating vortices. For larger Reynolds number these vortices become isolated, by suppressing fluid transport in the transverse direction.

The linear stability of incompressible boundary-layer flow of dusty gas is considered. Eigenvalue... more The linear stability of incompressible boundary-layer flow of dusty gas is considered. Eigenvalue problem for modified Orr-Sommerfeld equation is solved numerically using two approaches: a) directly by orthonormalization method, and b) by perturbation method. Particles most effectively suppress the instability waves when the relaxation length of their velocity is near to the wavelength of Tollmien-Schlicting (TS) wave. In this case 4% of mass particle content may reduce the growth more than one third. There is a region in the stable part of the flow where one more discrete mode of TS wave is added and the region where the eigenvalue problem has no solution.

On the basis of the quantitative physical model of gas-assisted laser cutting of thick metal in a... more On the basis of the quantitative physical model of gas-assisted laser cutting of thick metal in air or oxygen the maximum cutting velocity and thickness are calculated. The effect of beam shape on cutting efficiency is considered. The theoretical results are in qualitative agreement with the experimental data at the carbon-dioxide-laser of 7...15 kW. It is shown that the cutting velocity can be increased substantially by means of beam shape and gas jet optimization.

ABSTRACT In a shear flow, a small sphere may experience a lift force due to fluid inertia. Most p... more ABSTRACT In a shear flow, a small sphere may experience a lift force due to fluid inertia. Most previous workers assumed that the particle was stationary so that they could treat the fluid motion as steady. In spite of this, the results of previous analyses have generally been applied to problems in which particles move in an unsteady fashion. This paper presents the results of singular perturbation calculations of the lift on a sphere in a linear shear flow. The velocity of the sphere oscillates sinusoidally in time. Although the problem is idealized, the results provide some physical understanding of the effects of unsteadiness and the frequency regime in which one may assume quasisteady conditions.

Non-Brownian particles migrate randomly across the streamlines of a carrier flow in sheared suspe... more Non-Brownian particles migrate randomly across the streamlines of a carrier flow in sheared suspensions at small Reynolds numbers. A random motion is very similar to that in turbulent flows but result not from a flow instability but from the hydrodynamic interactions of particles. It is characterized by the coefficient of particle self-diffusion Ds. Several mechanisms of diffusivity in dilute suspensions based on the interactions of two isolated particles were considered [1],[2]. The model of interactions of rough spheres [1] gives correct linear dependence of Ds on particle volume fraction o. However, the experimental value of the diffusivity [3] is an order of magnitude greater than the theoretical predictions. Another mechanism of the diffusivity was proposed [2] for a wall-bounded shear flow. Two particles do not pass each other in such a configuration but exchange their positions in the normal direction. Swapping trajectories result in a particle cross-stream migration.

Within the framework of the model of two interpenetrating continua, a horizontal laminar dilute-s... more Within the framework of the model of two interpenetrating continua, a horizontal laminar dilute-suspension flow in a vertical Hele-Shaw cell is investigated. Using the method of matched asymptotic expansions, an asymptotic model of the transverse migration of sedimenting particles is constructed. The particle migration in the horizontal section of the cell is caused by an inertial lateral force induced by the particle sedimentation and the shear flow of the carrier phase. A characteristic longitudinal length scale is determined, on which the particles migrate across the slot through a distance of the order of the slot half-width. The evolution of the particle number concentration and velocity fields along the channel is studied using the full Lagrangian method. Depending on the particle inertia parameter, different particle migration regimes (with and without crossing of the channel central plane by the particles) are detected. A critical value of the particle inertia parameter corresponding to the change in migration regime is found analytically. The possibility of intersection of the particle trajectories and the formation of singularities in the particle number concentration is demonstrated.

ABSTRACT Particle migration in a horizontal flow of dilute suspension through a vertical slot wit... more ABSTRACT Particle migration in a horizontal flow of dilute suspension through a vertical slot with porous walls is studied using the two-continua approach. The lateral migration is induced by two opposite effects: an inertial lift force due to particle settling and directed toward the slot centre-line, and a drag due to leak-off entraining particles toward the walls. An expression for the inertial lift on a settling particle in a horizontal channel flow found recently is generalized to the case of a low leak-off velocity. The evolution of an initial uniform particle concentration profile is studied within the full Lagrangian approach. Four migration regimes are found differing by the direction of particle migration and numbers of equilibrium positions. Conditions of the regime change and a critical value of dimensionless leak-off velocity for particle deposition on the walls are obtained analytically. Suspension flows with zones where the particle concentration is zero or increases infinitely, are studied numerically.

Soft Matter, 2013

Superhydrophobic one-dimensional surfaces reduce drag and generate transverse hydrodynamic phenom... more Superhydrophobic one-dimensional surfaces reduce drag and generate transverse hydrodynamic phenomena by combining hydrophobicity and roughness to trap gas bubbles in microscopic textures. Recent works in this area have focused on specific cases of superhydrophobic stripes. Here we provide some theoretical results to guide the optimization of the forward flow and transverse hydrodynamic phenomena in a parallel-plate channel with a superhydrophobic trapezoidal texture, varying on scales larger than the channel thickness. The permeability of such a thin channel is shown to be equivalent to that of a striped one with greater average slip. The maximization of a transverse flow normally requires largest possible slip at the gas areas, similarly to a striped channel. However, in case of trapezoidal textures with a very small fraction of the solid phase this maximum occurs at a finite slip at the gas areas. Exact numerical calculations show that our analysis, based on a lubrication theory, can also be applied for a larger gap. However, in this case it overestimates a permeability of the channel, and underestimates an anisotropy of the flow. Our results provide a framework for the rational design of superhydrophobic surfaces for microfluidic applications.

Physics of Fluids, 2002

The lateral migration of a small spherical particle translating within a vertical channel flow wi... more The lateral migration of a small spherical particle translating within a vertical channel flow with large channel Reynolds numbers Rc is investigated. The weak-shear case is studied when the ratio of the slip velocity to maximum velocity of the channel flow, Vs, is finite, while two other dimensionless groups, particle Reynolds number Rs and Rc−1, are asymptotically small. The disturbance flow at large distances from the sphere is governed by Oseen-like equations. The ratio of Oseen length to channel width is &egr;=ls/l=(Rc|Vs|)−1≪1, i.e., the Oseen region is only a small part of the channel while the major portion of the disturbance flow is inviscid. A solution of the governing equations is constructed in terms of two-dimensional Fourier transform of the disturbance field in a plane parallel to the channel walls. The ordinary differential equation for Fourier transform of lateral velocity Γz(k,z) is solved using the method of matched asymptotic expansions based on &egr;. Several domains in (k,z) space are distinguished that correspond to different regions in physical space: Oseen region, inviscid region, viscous wake, boundary, and critical layers. For the weak-shear case the dominant contribution to the lift gives not velocity disturbances within the Oseen region but the large-scale inviscid disturbances. For such disturbances both effects due to an inviscid interaction with the walls and the curvature of the undisturbed velocity profile should be taken into account. The particle equilibrium positions at the distances from the wall of the order of the channel width arise for both negative and positive slip velocities.

Physics of Fluids, 2008

The inertial migration of particles in a dilute suspension flow through the entry region of a pla... more The inertial migration of particles in a dilute suspension flow through the entry region of a plane channel ͑or a circular pipe͒ is considered. Within the two-fluid approach, an asymptotic one-way coupling model of the dilute suspension flow in the entry region of a channel is constructed. The carrier phase is a viscous incompressible Newtonian fluid, and the dispersed phase consists of identical noncolloidal rigid spheres. In the interphase momentum exchange, we take into account the drag force, the virtual mass force, the Archimedes force, and the inertial lift force with a correction factor due to the wall effect and an arbitrary particle slip velocity. The channel Reynolds number is high and the particle-to-fluid density ratio is of order unity or significantly larger unity. The solution is constructed using the matched asymptotic expansion method. The problem of finding the far-downstream cross-channel profile of particle number concentration is reduced to solving the equations of the two-phase boundary layer developing on the channel walls. The full Lagrangian approach is used to study the evolution of the cross-flow particle concentration profile. The inertial migration results in particle accumulation on two symmetric planes ͑an annulus͒ distanced from the walls, with a nonuniform concentration profile between the planes ͑inside the annulus͒ and particle-free layers near the walls. When the particle-to-fluid density ratio is of order unity, an additional local maximum of the particle concentration on inner planes ͑an inner annulus͒ is revealed. The inclusion of the corrected lift force makes it possible to resolve the nonintegrable singularity in the concentration profile on the wall, which persisted in all previously published solutions for the dilute suspension flow in a boundary layer. The numerical results are compared to the tubular pinch effect observed in experiments, and a qualitative analogy is found.

Physics of Fluids, 2009

The inertial lift force exerted on a small rigid sphere settling due to gravity in a horizontal c... more The inertial lift force exerted on a small rigid sphere settling due to gravity in a horizontal channel flow between vertical walls is investigated. The method of matched asymptotic expansions is used to obtain solutions for the disturbance flow on the length scales of the particle radius and the channel width ͑inner and outer regions, respectively͒. The channel Reynolds number is finite, while the particle Reynolds numbers that are based on the slip velocity and the mean shear rate are small. The inner flow is described by the linear Stokes equations. The outer problem is governed by the linear Oseen-like equations with the particle effect approximated by a point force. The outer equations are solved numerically using the two-dimensional Fourier transform of the disturbance velocity field. The lift coefficient is evaluated as a function of governing dimensionless parameters: the particle coordinate across the channel, the channel Reynolds number, and the slip parameter. The particle always migrates away from the walls, with an equilibrium position being on the channel centerline. Close to the walls, the lift coefficient is the same regardless of the slip velocity and the channel Reynolds number. At large channel Reynolds numbers, a local maximum of the migration velocity forms near the channel centerline due to a combined effect of the slip, the linear shear, and the curvature of the undisturbed velocity profile. The results obtained are extended to the case when the drag on a particle has components both parallel and perpendicular to the undisturbed flow. One of primary applications of the results is modeling of the cross-flow migration of settling particles during particle transport in a hydraulic fracture.

Physical Review E, 2008

Random migrations of non-Brownian neutrally buoyant particles in the flow of a dilute suspension ... more Random migrations of non-Brownian neutrally buoyant particles in the flow of a dilute suspension in a periodic Couette cell is simulated on the basis of a dipole model. A diffusivity is due to far-field collective hydrodynamic interactions. Large-scale fluctuations of particle concentration induce fluid velocity disturbances with a length scale comparable to the cell size. The calculated self-diffusivity coefficient is linear in particle volume content and agrees well with the experimental data.

Physical Review E, 2011

We analyze theoretically a high-speed drainage of liquid films squeezed between a hydrophilic sph... more We analyze theoretically a high-speed drainage of liquid films squeezed between a hydrophilic sphere and a textured super-hydrophobic plane, that contains trapped gas bubbles. A superhydrophobic wall is characterized by parameters L (texture characteristic length), b1 and b2 (local slip lengths at solid and gas areas), and φ1 and φ2 (fractions of solid and gas areas). Hydrodynamic properties of the plane are fully expressed in terms of the effective slip-length tensor with eigenvalues that depend on texture parameters and H (local separation). The effect of effective slip is predicted to decrease the force as compared with expected for two hydrophilic surfaces and described by the Taylor equation. The presence of additional length scales, L, b1 and b2, implies that a film drainage can be much richer than in case of a sphere moving towards a hydrophilic plane. For a large (compared to L) gap the reduction of the force is small, and for all textures the force is similar to expected when a sphere is moving towards a smooth hydrophilic plane that is shifted down from the super-hydrophobic wall. The value of this shift is equal to the average of the eigenvalues of the slip-length tensor. By analyzing striped super-hydrophobic surfaces, we then compute the correction to the Taylor equation for an arbitrary gap. We show that at thinner gap the force reduction becomes more pronounced, and that it depends strongly on the fraction of the gas area and local slip lengths. For small separations we derive an exact equation, which relates a correction for effective slip to texture parameters. Our analysis provides a framework for interpreting recent force measurements in the presence of super-hydrophobic surface.

Physical Review E, 2013

Understanding the influence of topographic heterogeneities on liquid flows has become an importan... more Understanding the influence of topographic heterogeneities on liquid flows has become an important issue with the development of microfluidic systems, and more generally for the manipulation of liquids at the small scale. Most studies of the boundary flow past such surfaces have concerned poorly wetting liquids for which the topography acts to generate superhydrophobic slip. Here we focus on topographically patterned but chemically homogeneous surfaces, and measure a drag force on a sphere approaching a plane decorated with lyophilic microscopic grooves. A significant decrease in the force compared with predicted even for a superhydrophobic surface is observed. To quantify the force we use the effective no-slip boundary condition, which is applied at the imaginary smooth homogeneous isotropic surface located at an intermediate position between top and bottom of grooves. We relate its location to a surface topology by a simple, but accurate analytical formula. Since groves represent the most anisotropic surface, our conclusions are valid for any texture, and suggest rules for the rational design of topographically patterned surfaces to generate desired drag.

Physical Review E, 2013

Anisotropic super-hydrophobic surfaces have the potential to greatly reduce drag and enhance mixi... more Anisotropic super-hydrophobic surfaces have the potential to greatly reduce drag and enhance mixing phenomena in microfluidic devices. Recent work has focused mostly on cases of superhydrophobic stripes. Here, we analyze a relevant situation of cosine variation of the local slip length. We derive approximate formulae for maximal (longitudinal) and minimal (transverse) directional effective slip lengths that are in good agreement with the exact numerical solution and lattice-Bolzmann simulations for any surface slip fraction. The cosine texture can provide a very large effective (forward) slip, but it was found to be less efficient in generating a transverse flow as compared to super-hydrophobic stripes.

Physical Review E, 2007

The evolution of large-scale fluctuations in a monodisperse dilute suspension sedimenting in a wa... more The evolution of large-scale fluctuations in a monodisperse dilute suspension sedimenting in a wall-bounded container is considered on the basis of a continuum model. The case when the velocity fluctuations are comparable with the Stokes settling velocity is studied. Small deformations of the sedimentation front is replaced by a flat interface with a surface force distribution. The front holds position ensuring the vertical fluid velocity across the front to be small. So it acts approximately as a no-slip wall. The mechanisms of the fluctuation decay are the convection of large-scale concentration disturbances and the sedimentation-front deformations.