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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]