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The flow of air inside a vertical slender long duct with a temperature difference between the horizontal walls characterized by the Rayleigh number R a and a pressure gradient in the horizontal direction characterized by the Reynolds number R e is studied using the lattice Boltzmann method. In this case, the longitudinal rolls found in ducts with a width larger than the height cannot develop and the flow remains quasi-two-dimensional. Therefore, a two-dimensional approach is used, considering periodic boundary conditions on the vertical walls. For R a c < R a ≤ 2. 0 × 1 0 5 with R a c the critical Rayleigh number for thermal convection, there are two transitions at R e 0 (R a) and R e C P (R a) , R e 0 < R e C P . The first transition at R e 0 has a sharp decrease in the average Nusselt number and for 0 < R e < R e 0 the temperature difference between the horizontal walls is more important than the pressure gradient. The second transition at R e C P marks the appearance of a conductive Poiseuille flow with no thermal convection. For 1. 0 × 1 0 5 ¡ R a there is a third transition at R e M , R e 0 < R e M < R e C P . For R a < 1. 0 × 1 0 5 and R e 0 < R e < R e C P , and for 1. 0 × 1 0 5 < R a and R e M < R e < R e C P , the pressure gradient dominates over the pressure gradient. Both the temperature difference and the pressure gradient are important for 1. 0 × 1 0 5 < R a and R e 0 < R e < R e M with an appreciable decrease of the average Nusselt number at R e 0 and R e M . [ABSTRACT FROM AUTHOR]

The fully developed, steady, incompressible, laminar flow in a channel delimited by rough and/or permeable walls is considered. The influence of the micro-structured bounding surfaces on the channel flow behavior is mimicked by imposing high-order effective boundary conditions which stem from homogenization theory and do not contain empirical parameters. A closed-form solution of the Navier–Stokes equations is found for the flow in the channel, with conditions at each virtual boundary linking the slip velocities to shear stress and streamwise pressure gradient. The boundary condition for the longitudinal velocity coincides with a little-noticed extension of the so-called Beavers-Joseph condition, first derived by Saffman (1971); it applies to both permeable and rough surfaces, including the case of separated flow (Couette-Poiseuille motion with adverse pressure gradient). The analytical solution obtained for the velocity distribution in the channel is validated against full feature-resolving simulations of the flow for either highly ordered or random textures, highlighting the accuracy and the applicability range of the model. The Stokes-based model used to identify slip and interface permeability coefficients in the effective boundary conditions is found to be reliable and accurate up to ϵ R e τ ≈ 10 , with ϵ ratio of microscopic to macroscopic length scales and R e τ the shear-velocity Reynolds number. Above this threshold, the coefficients must account for advective effects: a new upscaling procedure, based on an Oseen's approximation , is thus proposed and validated, extending considerably beyond the Stokes regime. • Laminar Poiseuille and Couette-Poiseuille flows in channels with non-smooth boundaries are studied. • Effective boundary conditions, based on homogenization theory, mimic flow interaction with textured walls. • Analytical solutions for channel flows are derived and extensively validated. • A new approach is proposed where macroscopic coefficients are advection-sensitive. • Improved model is highly accurate, beyond the Stokes regime. [ABSTRACT FROM AUTHOR]

We consider the micro- and the macro-scale to investigate the motion of single grains in a dilute suspension under shear flow and Poiseuille flow to analyze effects like shear-wall migration and rolling of grains as observed in physical experiments. To be able to simulate the behavior of fresh concrete or mud flow, as realistically as possible, we are taking into account a non-Newtonian Bingham–Papanastasiou rheology for the carrier fluid. Due to a surface coupled approach, Smoothed Particle Hydrodynamics (SPH) gives the opportunity to consider both, the motion of a solid particle, by tracking its center of mass and also surface points, and the interaction and influence on the near field of the velocity field in the fluid phase. We show an independence of the motion of solid grains from the surrounding carrier fluid. While the macroscopic flow reaches a stationary flow field quite fast, the motion of the solid grains still oscillates between parts of the fluid that flow with different velocities and does not show a stable steady state. Providing a comparison between the motion in a Newtonian and a non-Newtonian fluid, we point out the differences and thus the importance of the choice of the material model for the carrier fluid in numerical simulations. • SPH simulations of suspensions with Newtonian or non-Newtonian carrier fluid. • Detailed analysis of the motion of solid grains in a suspension on different scales. • Focus on the analysis of the near velocity field at the surface of solid grains. [Display omitted] [ABSTRACT FROM AUTHOR]

Analytical solutions are derived for the cessation of annular Poiseuille and Couette flows of a Newtonian fluid in the presence of dynamic wall slip. We employ linear dynamic slip law involving a slip relaxation parameter, which results in the appearance of the eigenvalue parameters in the boundary conditions and thus leads to distinct Sturm–Liouville problems that differ from their static slip counterparts. The proper orthogonality condition is derived and closed-form analytical solutions are obtained for both flows of interest. Representative results are then presented and discussed. In agreement with previous reports for other flows with dynamic wall slip, the present solutions show that wall slip slows down flow dynamics and this effect becomes more pronounced as the slip-relaxation parameter is increased. • Analytical solutions of Newtonian annular flows with dynamic wall slip are derived. • The proper Sturm-Liouville problems are considered. • The cessation of annular Poiseuille and annular Couette flows is investigated. • Wall slip and the slip relaxation parameter are shown to damp flow dynamics. [ABSTRACT FROM AUTHOR]

For a horizontal channel flow of a weakly viscoelastic liquid that follows the constitutive model of Walters' liquid B ′ ′ , a linear stability analysis is performed when the channel walls are slippery. In this case, the viscoelastic channel flow is driven by the streamwise pressure gradient. We explore the primary instability for a symmetric slip flow with the same slip length of the channel walls, an asymmetric slip flow with different slip lengths of the channel walls, and an analogy to the Poiseuille–Couette flow of a viscoelastic liquid with a slip effect on the lower wall but no slip effect on the upper wall. We observe that the viscoelastic parameter shows a destabilizing impact, but the slip length shows a stabilizing impact on the most unstable shear mode in all three flow configurations. Moreover, the Poiseuille and Poiseuille–Couette flows for the viscoelastic liquid are linearly more unstable to infinitesimal disturbances than those of the Newtonian liquid. As a result, wall velocity needs to be higher than in the Newtonian liquid to stabilize the viscoelastic Poiseuille–Couette flow. Using the asymptotic analysis, we have determined the critical value of the slip length, or equivalently, the critical value of the lower wall velocity, above which the asymmetric slip flow and the Poiseuille–Couette flow of the viscoelastic liquid are permanently stable to infinitesimal disturbances. [Display omitted] • Viscoelastic parameter shows a destabilizing influence on shear mode instability. • Slip length shows a stabilizing influence on shear mode instability. • Viscoelastic asymmetric slip flow is more unstable than viscoelastic Poiseuille–Couette flow. • Viscoelastic asymmetric slip flow is linearly stable if slip length exceeds critical value. • Viscoelastic Poiseuille–Couette flow is linearly stable if wall velocity exceeds critical value. • Critical value of slip length for Walters' liquid B ′ ′ is larger than that of Newtonian liquid. • If slip effect is included on upper wall, transition from laminar to turbulence becomes slower. [ABSTRACT FROM AUTHOR]

The lattice Boltzmann (LB) method has been extensively applied to the simulation of various fluid flows. Nonetheless, the standard LB model in rectangular coordinates faces some challenges when attempts are made to use it to simulate single-phase liquid flows involving super-hydrophobic cylindrical surfaces with a large slip length. Therefore, in this paper, boundary conditions for an axisymmetric LB model are proposed for the simulation of liquid slip at both convex and concave cylindrical surfaces. Based on the Navier slip boundary conditions, an equilibrium–nonequilibrium boundary scheme is developed to obtain the liquid slip in the azimuthal direction, with a combined bounce-back and specular-reflection boundary condition being developed to obtain the liquid slip in the axial direction. These boundary schemes are verified by simulating several established cases, namely, cylindrical Couette flow, harmonic oscillatory cylindrical Couette flow, Hagen–Poiseuille flow, and annular Poiseuille flow. The results are in excellent agreement with analytical results. Furthermore, some more complex flows involving super-hydrophobic cylindrical surfaces, such as stepwise oscillatory cylindrical Couette flow, are also simulated and studied using the proposed LB model. The axisymmetric LB model presented here overcomes the inability of standard LB models to accurately and efficiently simulate single-phase liquid flows involving super-hydrophobic cylindrical surfaces with a large slip length. • Slip boundary scheme of axisymmetric LB model is proposed for cylindrical surfaces. • Liquid slip in both the azimuthal and axial directions can be well captured. • The LB model is applied to fluid flows with super-hydrophobic cylindrical surfaces. • Numerical tests validate the reliability and generality of the proposed scheme. [ABSTRACT FROM AUTHOR]

We will study the nonlinear stability of plane Couette and Poiseuille flows with the Lyapunov second method by using the classical L 2 -energy. We will prove that the streamwise perturbations are L 2 -energy stable for any Reynolds number. This contradicts the results of Joseph (1966), Joseph and Carmi (1969) and Busse (1972), and allows us to prove, with a conjecture, that the critical nonlinear Reynolds numbers are obtained along two-dimensional perturbations, the spanwise perturbations, as Orr (1907) had supposed. This conclusion combined with some recent results by Falsaperla et al. (2019) on the stability with respect to tilted rolls, provides a possible solution to the "mismatch" between the critical values of linear stability, nonlinear monotonic energy stability and the experiments. [ABSTRACT FROM AUTHOR]

We comment on the series solutions presented in the paper "Newtonian Poiseuille flow in ducts of annular-sector cross-sections with Navier slip" for the no-slip case. [ABSTRACT FROM AUTHOR]

Lattice Boltzmann (LB) method, which is a mesoscopic numerical method, has been considered as a powerful tool to study microscale gas and liquid flows. Boundary slip phenomenon, which is a significant feature of both microscale gas and liquid flows, has been extensively studied by the LB method in the past decade. However, most of the previous works have focused on the microchannel flows and studies on the microtube flows are very rare. In this paper, we investigate the widely used slip boundary conditions, i.e., combined bounce-back and specular-reflection (BS) scheme, combined Maxwell-diffusion and specular-reflection (MS) scheme, and combined Maxwell-diffusion and bounce-back (MB) scheme, for the axisymmetric LB model with multi-relaxation-time (MRT) in detail. In order to realize the Navier slip boundary condition for liquid flows, we put forward to a reasonable strategy for determining the combination coefficients and the relaxation time. The proposed boundary schemes are validated by some numerical tests including the Hagen–Poiseuille flow, axisymmetric Womersley flow, Poiseuille flow in a circular annulus, and Womersley flow in a circular annulus. Numerical results are consistent with the analytical solutions, which demonstrate that the proposed boundary schemes are suitable for microscale liquid flows in microtube. • Axisymmetric MRT LB model with slip boundary conditions for liquid flow is proposed. • BS, MS, and MB schemes are essentially equivalent for liquid flow in microtube. • Combination coefficients and relaxation time τ q are dependent on the slip length. • Numerical tests validate the reliability and generality of the proposed schemes. [ABSTRACT FROM AUTHOR]

We study the linear stability of the Poiseuille flow of a viscoelastic upper convected Maxwell fluid in which the rheological parameters depend on the concentration of particles suspended in the fluid (dense suspension with negligible diffusion). After determining the basic flow and basic concentration profile we consider a temporal three dimensional perturbation in the form of a stream-wise and span-wise wave. We derive the linearized perturbed equation and prove the validity of Squire's theorem, extending the result of Tlapa and Bernstein (1970) in which the theorem was proved for constant rheological parameters. We discuss the relation between the Weissenberg and the Reynolds numbers. We finally study the 2D eigenvalue problem for the case of constant coefficients and for non-constant coefficients with low Weissenberg number. We solve the problem numerically by means of a spectral collocation method and we plot the marginal stability curves discussing how stability depends on the fluid rheology. • We study linear stability of a viscoelastic suspension. • Rheology depends on particles concentration. • We prove Squire's theorem • We solve the generalized Orr–Sommerfeld equation. • We plot the marginal stability curves. [ABSTRACT FROM AUTHOR]

With increasing application of technologies related to electric field being used to enhance heat transfer, it is important to understand better the effects of electric field and lateral advection on the thermal field. In this work, we present a detailed study of the linear dynamics of the flows subjected to simultaneously a thermal field and an electric field (which we call electro–thermo–hydrodynamic flow, ETHD) with a pressure-driven cross-flow from the perspective of modal and non-modal linear stability analyses. The flow takes place in a planar layer of a dielectric fluid heated from below and is subjected to unipolar space-charge-limited injection from above. The effects of various parameters are studied and energy analyses are performed to gain more physical insights into these effects. Our results of the linear modal stability analysis indicate that at a small Reynolds number (R e , quantifying inertia to viscosity), the critical Rayleigh number (R a , measuring the strength of thermal gradient) increases monotonically with increasing R e when the Coulomb force is weak, while the trend becomes non-monotonic in a stronger electric field. The critical electric Rayleigh number (T , quantifying the strength of electric field) first decreases and then increases with increasing R e. Besides, the linear system becomes more stable with increasing Prandtl number (P r , a ratio of kinematic viscosity to thermal diffusivity) and mobility ratio (M , a ratio of hydrodynamic mobility to ion mobility) at the R e investigated. In the non-modal results, we demonstrate that the large- R e scaling law holds in the ETHD–Poiseuille flow when the flow is inertia-dominant. The results at large R e indicate that at sufficiently large P r , R a exerts a negligible influence on the transient growth. Furthermore, an input–output analysis is adopted to demonstrate that electric field perturbations can boost the transient growth of total perturbation energy compared to the case without the electric field. This result may be helpful for subsequent investigations of heat transfer enhancement using an electric field. • A detailed modal and non-modal stability analysis of the ETHD flow with a cross-flow. • Effects of various flow parameters on the linearised ETHD flow are investigated. • Input-output analyses show that electric field can boost transient energy growth. • Energy analyses are performed to gain more physical insights into the results. [ABSTRACT FROM AUTHOR]

We investigate the axisymmetric slow viscous liquid flow around a spherical bubble located on the axis of a long circular tube analytically based on the Stokes approximation. The bubble translates along the axis of the tube with a constant velocity within Hagen–Poiseuille flow flowing far from the bubble. The translating velocity of the bubble and mean velocity of the Hagen–Poiseuille flow are given arbitrarily. To analyze Stokes equation, we use the method of complex eigenfunction expansions and the method of least squared error. As results, the streamline patterns and the pressure contour lines in the flow field are drawn for some radii of the bubble. The drag exerted on the bubble and the pressure change induced by the bubble are determined according to the radius of the bubble. For a small bubble radius in the tube, we compared results with previous asymptotic results. The drift velocity of the bubble due to the Hagen–Poiseuille flow in the circular tube is calculated according to the bubble radius. We show that extra pressure drop due to the drift bubble in the Hagen–Poiseuille flow becomes positive or negative depending on the radius of the bubble. When the bubble moves along a circular tube in the absence of the Hagen–Poiseuille flow, a series of viscous toroidal eddies appears in the anterior and posterior directions of the bubble. Moreover, we discuss the pressure and normal stress distributions on the bubble surface, which depend on the radius of the bubble. [ABSTRACT FROM AUTHOR]

We study a generalization of the Pokrovski–Vinogradov model for flows of solutions and melts of an incompressible viscoelastic polymeric medium to nonisothermal flows in an infinite plane channel under the influence of magnetic field. For the linearized problem (when the basic solution is an analogue of the classical Poiseuille flow for a viscous fluid described by the Navier–Stokes equations) we find a formal asymptotic representation for the eigenvalues under the growth of their modulus. We obtain a necessary condition for the asymptotic stability of the Poiseuille-type shear flow. For analysis we use new result, that generalizes Birkhoff theorem on the case, when the coefficient matrix of the eigenvalue itself has zero with multiplicity greater than one as an eigenvalue. We also get the necessary condition for Lyapunov stability of the shear Poiseuille-type flow as a result of acquired representation. [ABSTRACT FROM AUTHOR]

The nonlinear dynamics of two immiscible superposed viscous fluid layers in a channel is examined using asymptotic modelling and direct numerical simulations (DNS). The flow is driven by an imposed axial pressure gradient. Working on the assumption that one of the layers is thin, a weakly-nonlinear evolution equation for the interfacial shape is derived that couples the dynamics in the two layers via a nonlocal integral term whose kernel is determined by solving the linearised Navier–Stokes equations in the thicker fluid. The model equation incorporates salient physical effects including inertia, gravity, and surface tension, and allows for comparison with DNS at finite Reynolds numbers. Direct comparison of travelling-wave solutions obtained from the model equation and from DNS show good agreement for both stably and unstably stratified flows. Both the model and the DNS indicate regions in parameter space where unimodal, bimodal and trimodal waves co-exist. Nevertheless, the asymptotic model cannot capture the dynamics for a sufficiently strong unstable density stratification when interfacial break-up and eventual dripping occurs. In this case, complicated interfacial dynamics arise from the dominance of the gravitational force over the shear force due to the underlying flow, and this is investigated in detail using DNS. [ABSTRACT FROM AUTHOR]

The computation of the mass flow rate in the Poiseuille and thermal creep flows and of the pressure difference in the thermomolecular pressure difference (TPD) flow through long capillaries is well-known and available in the literature. Here, the uncertainty in the solution due to induced uncertainties in the input data, namely, the capillary radius and length, the pressure and/or temperature imposed at the capillary ends and the accommodation coefficient of the Maxwell diffuse-specular boundary conditions, is investigated. The uncertainty analysis is performed by the Monte Carlo Method. Conducting the required number of trials the distribution function of the output quantity and its associated uncertainty are obtained. In most cases, the uncertainty in the input quantity driving the flow has the largest effect on the output uncertainties. This is always true in the TPD flow and for small pressure and temperature differences in the Poiseuille and thermal creep flows respectively. In the case of large driving thermodynamic forces, in the latter two flows, the radius becomes the most important source of uncertainty. The accommodation coefficient uncertainty is always the less important one. Documenting the expected effect of the uncertainty in each input parameter is certainly beneficial in computational as well as experimental work. [ABSTRACT FROM AUTHOR]

In this paper, numerical study of emulsion of drops in a channel under uniform electric field is investigated. The electric field is created by imposing an electric potential difference across the channel walls. The leaky dielectric model developed by Taylor is used to compute the electric force. The electric conductivity ratio σ r = σ i σ o and electric permittivity ratio ε r = ε i ε o are used to study oblate and prolate drops The interaction of drop-to-wall and drop-to-drop are investigated by changing the dimensionless numbers. Oblate drops and prolate drops with σ r < ε r , are always attracted to the walls, but prolate drops with σ r > ε r , are attracted by or repelled from the walls depending on the initial distance and electric properties. Drop-to-drop interaction depends on the initial configuration of drops. Drop pairs that are placed at an angle relative to the direction of the electric field, are always attracted towards each other. If they have an initial separation distance in the direction of the electric field, they are attracted to the walls or towards each other depending on their separation distance. Prolate drops with σ r > ε r , obtain a different configuration in their final state. They may stick together or have a small separation distance, depending on their electric properties. Increasing the electric capillary number, changes the vertical and horizontal separation distance of drop pairs at steady state configuration. It also decreases the time required to reach steady state configuration. The behavior of emulsion of drops is studied by considering oblate drops, prolate drops with σ r < ε r and prolate drops with σ r > ε r . All drops form fiber chains in the direction of the electric field that will break in stronger Poiseuille flow. Oblate drops either settle on the walls or migrate to the channel center line, but prolate drops form chains of fibers that sometimes extend between the walls. Presence of drops will change the well-known parabolic velocity profile especially for prolate drops that are suspended in the channel. The channel flow rate is also studied for different emulsion of drops and electric field. At a constant electric field and pressure gradient, the channel flow rate for oblate emulsion is higher than prolate ones. As the electric field strength increases, the channel flow rate will also increase for oblate emulsions. • Interaction of two oblate and prolate drops is studied. • Interaction of oblate and prolate drop with the channel wall is studied. • Emulsion of oblate drops is studied in three dimensions. • Emulsion of prolate drops is studied in three dimensions. [ABSTRACT FROM AUTHOR]

We investigate the axisymmetric slow viscous flow around a sphere located on the axis of a long circular cylinder analytically based on the Stokes approximation. The sphere translates along the centerline of the cylinder with a constant velocity within Hagen–Poiseuille flow flowing far from the sphere. The translating velocity of the sphere and mean velocity of the Hagen–Poiseuille flow are arbitrary constant. To analyze Stokes equation, we use the method of complex eigenfunction expansions and the method of least squared error. As results, the streamline patterns and the pressure contour lines in the flow field are drawn for some radii of the sphere. The drag exerted on the sphere and the pressure change by the sphere are determined as the radius of the sphere. For a small sphere radius and for a sphere fitted closely in the cylinder, we compared results with previous asymptotic results and lubrication theory results, respectively. The velocity of the drifting sphere by the Hagen–Poiseuille flow in the circular cylinder is determined as the sphere radius. The pressure change induced by the drifting sphere in the Hagen–Poiseuille flow is also obtained. When the sphere translates along the plugged circular cylinder, a series of viscous toroidal eddies appears each side of the cylinder expectably. Moreover, we discussed the pressure and shear stress on the sphere surface and showed some critical range of these stresses. [ABSTRACT FROM AUTHOR]

Abstract A pseudo-potential based single component multiphase Lattice Boltzmann flow solver was developed. Peng–Robinson equation of state was coupled with Exact Difference Method to incorporate interaction forces. This solver was developed for a D2Q9 lattice structure. The solver was thoroughly validated against several canonical problems like estimation of coexistence curve, surface tension estimation from Laplace Law and growth of a cavitating bubble in quiescent flow. The solver was found to be numerically stable for density ratios up to 103. The solver was then used to simulate bubble dynamics for cavitating flows in different flow configurations. Fluid flow characteristics of a single cavitating bubble for Poiseuille flow with stationary and non-stationary walls at Reynolds number of 1 and 10 were investigated. Temporal evolution of the bubble when it is placed along the channel centreline and at an offset is presented here. [ABSTRACT FROM AUTHOR]

Abstract This paper is on the propagation of disturbances causing transition in a fully developed spiral annular flow. The problem is approached through reformulation of the linearised equations of motion in an alternative parameter space comprising a suitably defined Reynolds number, a swirl parameter and the ratio of the annular gap to the mean diameter of the cylinders. In the limits of the swirl parameter assuming values close to 0 or ∞ , the newly derived generalised Orr–Sommerfeld and Squire equations for disturbance propagation in the revised parameter space reduce to the corresponding equations for the limiting cases of disturbance propagation as the swirl parameter goes to 0 or ∞ respectively, known from literature. The equations lead to the analytical expression for the location of the critical layer in spiral annular flow and to the equation governing the flow dynamics in the critical layer , thus revealing the effect of swirl on the critical layer. [ABSTRACT FROM AUTHOR]

Abstract We consider the Newtonian Poiseuille flow in a duct the cross section of which is either a circular or an annular sector assuming that Navier slip occurs either along both the cylindrical walls or only along the outer cylindrical wall. A general analytical solution is derived and the results for the latter case are discussed and the effects of the angle of the sector, the radii ratio and the slip number are analysed. Highlights • The Newtonian Poiseuille flow in ducts of annular-sector or circular-sector cross-sections is considered. • Navier slip is assumed to occur along the circular walls. • A general analytical solution is derived for the above flow. • The effects of the sector angle, the radii ratio and the slip number are analysed. [ABSTRACT FROM AUTHOR]

The axisymmetric Stokes flow around a disk in a circular tube is investigated based on a Stokes approximation, where the radius of the disk, located coaxially with the circular tube, is arbitrary. The disk translates perpendicularly to its own plane along the centerline of the tube, and a Hagen–Poiseuille flow exists far upstream and downstream from the disk. The velocities of the translating disk and the Hagen–Poiseuille flow are given arbitrarily. The problem is investigated through an analysis of the Stokes equation using a complex eigenfunction expansion and the least squares method. The streamline patterns from the stream function, and the pressure distributions of the flow fields, are shown for some typical radii of the disk. The force exerted on the disk, and the pressure drop created by the disk itself, are both calculated as functions of the disk radius. For a small disk radius, the results of the force are coincident with previous asymptotic expressions. For a given velocity of the Hagen–Poiseuille flow in the tube, the translational drift velocity of the disk is determined as a function of the disk radius. The results show that this drift velocity is slightly lower than the mean velocity of the Hagen–Poiseuille flow component projected by the disk. The induced pressure drop from the disk drifting in the Hagen–Poiseuille flow is quite small. When the disk translates in a stagnant circular tube, a series of viscous toroidal eddies appears in the tube apart from the disk, as expected. [ABSTRACT FROM AUTHOR]

A perturbation solution is derived for weakly compressible force-driven flow through a cylinder of fixed cross-section, with pressure-dependent viscosity and Navier-slip at the wall. The compressibility number is used as the perturbation parameter and a solution is derived up to second order. The perturbation solution is used to assess changes in flow for different Reynolds numbers, Froude numbers, aspect ratios, compressibilities, pressure-dependent viscosities and slip values. The viscosity–pressure dependence is controlled by compressibility and by a viscosity–density parameter. The following results are found: the viscosity–density parameter appears only at second-order for axial velocity, density and average volumetric flow rate, while at first order for pressure, average pressure drop and average Darcy friction factor; the volumetric flow rate decreases with increasing compressibility if forcing is small enough, increases with slip, and decreases with viscosity–density parameter; the average Darcy friction factor and average pressure drop can increase with increasing compressibility if the viscosity–density parameter is large enough. Although these results are as expected, the key contribution of this paper is the derivation of analytical expressions for the flow that incorporate the pressure dependence effects. [ABSTRACT FROM AUTHOR]

The performance of standard Lattice Boltzmann, LB, is confined to the micro scale flows with a Knudsen number, Kn , less than 0.1. In the previous works we proposed a modified LB which is able to extend the ability of LBM to simulate wide range of Knudsen flow regimes. To study the ability of this model for porous media, in the present work we investigate nanoscale gaseous flows through porous media confined between parallel plates by means of LB, and molecular dynamics, MD, simulations. The comparison between modified LB and MD shows a very good agreement at sufficiently low solid fractions. In addition, flow characteristics through various porous structures are studied via the MD simulation and the effect of various parameters such as driving force, porosity and Knudsen number on the velocity and temperature distributions is investigated. Our results demonstrate the good ability of MDS for investigating different flow phenomena such as permittivity and Darcian flow in porous media. [ABSTRACT FROM AUTHOR]

In this paper, we postulate a generalized bounce-back formulation, which can be simplified to the classic bounce-back method, the Ladd method (Ladd, 1994), and the midpoint method (Yin and Zhang, 2012) in the lattice Boltzmann method (LBM). The postulation process explicitly highlights the assumptions and constraints associated with these widely used boundary methods. Our demonstration simulations numerically confirm our analysis, and they also show that some artificial phenomena observed in previous studies, such as the boundary slip in Poiseuille flows and the mass leakage and apparent velocity in a hydrostatic system, are actually due to the violation of assumptions behind the formulations of these bounce-back methods. With proper modifications of these methods, these unphysical observations can be completely removed and the LBM solutions can match theoretical predictions up to the computer round-off resolution. Although the generalized bounce-back relation lacks practical usefulness, the analysis, simulations, and discussions in this work could be valuable for boundary method analysis, modification, development, and selection in LBM simulations of fluid flows and other processes. [ABSTRACT FROM AUTHOR]

A non-modal stability analysis is presented for annular Poiseuille–Couette flow (APCF) which serves to complement existing linear and nonlinear stability studies. Modal linear stability analyses indicate a stabilizing trend for increasing inner cylinder velocity V , though this is at odds with experimental studies of transition such as Shands et al. (1980) who find that increasing V is destabilizing. Using the maximum achievable energy growth available at a given parameter regime as a measure of the non-modal stability of the flow, we also find that APCF is destabilized with increasing inner cylinder velocity V . Thus we conjecture that the transition mechanism in APCF is akin to that of the canonical subcritical shear flows, where linear instability of the base flow is not relevant. [ABSTRACT FROM AUTHOR]

In this paper, we address a new wall slip formulation based on a series expansion of both differential and exponential forms of wall shear stress. As this is initially considered as an infinite series, we use a truncated version of it to get a slip law having three slip coefficients, where we have considered the exponential form only. We use our new truncated triple-slip-coefficients wall slip law to analyze a particular class of viscoelastic non-Newtonian fluid. This special case follows the Phan–Thien–Tanner fluid model. Moreover, for this fluid, we identify Weissenberg number as one salient parameter affecting slip. In particular, our new model is tested on a familiar planar Couette and planar Poiseuille flow problem, where two parallel and infinitely long plates have been used. Furthermore, slip-dependent analytical expressions for field quantities such as velocity and shear stress at the walls and beyond, are derived and numerically analyzed for both problems. In addition, the pressure and flow-rate are derived for various slip coefficients for Poiseuille flow case. Our results obtained prove reasonable as represented by physically realistic plots herein. This feasibility is especially dictated by the velocity profile across channel width for both application problems. Thus, we can infer from all these, that this new model has the potential of providing results which can match experimental data, that is, if the three slip-coefficients are properly chosen. [ABSTRACT FROM AUTHOR]

Flow through a twisted tube with square cross-section and helical corrugations of arbitrary pitch is computed under conditions of Stokes flow. The governing equations are formulated in non-orthogonal helical coordinates in terms of a coupled system of linear differential equations describing the longitudinal and transverse flow over the tube cross-section. Numerical solutions are computed by a finite-difference method on a staggered grid incorporating pressure nodes and three sets of velocity nodes. The results illustrate the structure of the secondary flow developing over the tube cross-section and document the effect of the helical corrugations on the axial flow rate. [ABSTRACT FROM AUTHOR]

We consider both the axisymmetric and planar steady-state Poiseuille flows of weakly compressible Newtonian fluids, under the assumption that both the density and the shear viscosity vary linearly with pressure. The primary flow variables, i.e. the two non-zero velocity components and the pressure, as well as the mass density and viscosity of the fluid are represented as double asymptotic expansions in which the isothermal compressibility and the viscosity–pressure-dependence coefficient are taken as small parameters. A standard perturbation analysis is performed and asymptotic, analytical solutions for all the variables are obtained up to second order. These results extend the solutions of the weakly compressible flow with constant viscosity and those of the incompressible flow with pressure-dependent viscosity. The combined effects of compressibility and the pressure dependence of the viscosity are analyzed and discussed. [ABSTRACT FROM AUTHOR]

Abstract: The hydrodynamic behavior of magnetic nanoparticles in a Poiseuille flow through the design of a High-Gradient Magnetic-Separator (HGMS) is studied. Using numerical solutions of the Langevin equations, to simulate the motion of colloidal suspensions in a continuous flow, at low Reynolds numbers, it is shown that the separation time is not affected by the flow velocity if single particles are considered. However, if hydrodynamic and dipole–dipole interactions are included, the separation time depends on flow properties. Then, the influence of flow velocity on the kinetics of aggregation is studied. It is shown that, in the irreversible aggregation regime, linear chains of particles are formed and steadily grow and their average size, , increases with time as a power law. The exponent, , of the mean chain-size growth, , is practically not affected by the flow velocity. The chain-size ( ) distribution function ( ) approaches (for long times) the following scaling form . [Copyright &y& Elsevier]

Abstract: Two-dimensional Stokes flow through a microchannel obstructed by a vertical plate is investigated on the basis of Stokes approximation. The plate translates along the center-line of the channel and plane Poiseuille flow exists upstream and downstream from the plate. The Stokes flow is analyzed analytically using the eigenfunction expansion and the point collocation method. The stream function and the pressure distribution of the flow field are obtained for an arbitrary translating velocity of the plate and arbitrary magnitude of the Poiseuille flow. The force exerted on the plate and the pressure drop induced by the plate are calculated as functions of blockage factor. From the results, the drift velocity of the plate, for which the force exerted on the plate vanishes and the plate translates freely in the Poiseuille flow, is determined. The drift velocity is slightly lower than the mean velocity of the Poiseuille flow component projected by the plate, and induced pressure drop due to the drifting plate in the Poiseuille flow is quite small. [Copyright &y& Elsevier]

Abstract: A polynomial expansion procedure and the ADO (analytical discrete-ordinates) method are used to solve a collection of basic flow problems based on the linearized Boltzmann equation for rigid-sphere interactions and the Cercignani–Lampis boundary conditions with a free choice of the accommodation coefficients at each boundary. In particular, three classical problems defined by flow in a plane-parallel channel (Poiseuille, thermal-creep, and Couette flow) are solved (essentially) analytically and evaluated to a very high numerical standard. Some comparisons with known kinetic models are also reported. [Copyright &y& Elsevier]

Abstract: A binary mixture of rarefied gases between two parallel plates is considered. The Poiseuille flow, thermal transpiration (flow caused by a temperature gradient of the plates) and concentration-driven flow (flow caused by a gradient of concentration of the component species) are analyzed on the basis of the linearized model Boltzmann equation with the diffuse reflection boundary condition. The analyses are first performed for mixtures of virtual gases composed of the hard-sphere or Maxwell molecules and the results are compared with those of the original Boltzmann equation. Then, the analyses for noble gases (He–Ne, He–Ar and Ne–Ar) are performed assuming more realistic molecular models (the inverse power-law potential and Lennard-Jones 12,6 models). By use of the results, flux databases covering the entire ranges of the Knudsen number and of the concentration and a wide range of the temperature are constructed. The databases are prepared for the use in the fluid-dynamic model for mixtures in a stationary nonisothermal microchannel derived in [S. Takata, H. Sugimoto, S. Kosuge, Eur. J. Mech. B/Fluids 26 (2007) 155], but can also be incorporated in the generalized Reynolds equation [S. Fukui, R. Kaneko, J. Tribol. 110 (1988) 253] in the gas film lubrication theory. The databases constructed can be downloaded freely from Electronic Annex 2 in the online version of this article. [Copyright &y& Elsevier]

Abstract: A possibility of making use of the Knudsen compressor as a gas separator is investigated. Starting from the description at the microscopic level on the basis of the kinetic theory of gases, a fluid-dynamic model describing the behaviour of the mixture in the Knudsen compressor is derived. Then, by the use of this model, it is numerically demonstrated that the Knudsen compressor works certainly as a gas separator. The separation performance is shown to reach a practical level by increasing the number of elemental units in the device. The numerical simulation is carried out for various molecular models, not only for fundamental models, the hard-sphere and Maxwell molecules, but also for more realistic models such as the inverse power-law potential and Lennard-Jones models, assuming the McCormack model equation at the microscopic level. The results show that the modelling by the celebrated Maxwell molecule (or the BGK-type model equation) fails to capture the phenomenon of the gas separation in the device. This presents a remarkable contrast to the capability of the other fundamental model, the hard-sphere molecule, even though this model exaggerates the phenomenon to some extent. [Copyright &y& Elsevier]

The Cercignani–Lampis scattering kernel of the gas–surface interaction is applied to numerical calculations of the Poiseuille flow and thermal creep through a long tube. The S model of the Boltzmann equation was numerically solved by the discrete velocity method. The calculations have been carried out in the wide ranges of the rarefaction parameter and of the accommodation coefficients. Comparing the present results with experimental data the values of the accommodation coefficients have been calculated. [Copyright &y& Elsevier]

A synthetic-kernel model (CES model) of the linearized Boltzmann equation is used along with an analytical discrete-ordinates method (ADO) to solve three fundamental problems concerning flow of a rarefied gas in a plane channel. More specifically, the problems of Couette flow, Poiseuille flow and thermal-creep flow are solved in terms of the CES model equation for an arbitrary mixture of specular and diffuse reflection at the walls confining the flow, and numerical results for the basic quantities of interest are reported. The comparisons made with results derived from solutions based on computationally intensive methods applied to the linearized Boltzmann equation are used to conclude that the CES model can be employed with confidence to improve the accuracy of results available from simpler approximations such as the BGK model or the S model. [Copyright &y& Elsevier]