Related papers: A passive Stokes flow rectifier for Newtonian flui…
Soft hydraulics, which addresses the interaction between an internal flow and a compliant conduit, is a central problem in microfluidics. We analyze Newtonian fluid flow in a rectangular duct with a soft top wall at steady state. The…
Swimming at low Reynolds number in Newtonian fluids is only possible through non-reciprocal body deformations due to the kinematic reversibility of the Stokes equations. We consider here a model swimmer consisting of two linked spheres,…
We investigate in this article the boundary layers appearing for a fluid under moderate rotation when the viscosity is small. The fluid is modeled by rotating type Stokes equations known also as the Barotropric mode equations in the…
Fluids with shear-rate-dependent viscosity form a special class of non-Newtonian fluids that play a crucial role in continuum dynamics. We consider a compressible barotropic flow of such fluids, governed by a generalized Navier-Stokes…
For the incompressible Navier--Stokes equation, the Reynolds number ($\mathrm{Re}$) is a dimensionless parameter quantifying the relative importance of inertial over viscous forces. In the low-$\mathrm{Re}$ regime ($\mathrm{Re} \ll 1$), the…
A simulation of the hydrodynamics on the two dimensional non-commutative space is performed, in which the space coordinates $(x, y)$ are non-commutative, satisfying the commutation relation $[x, y]=i \theta$. The Navier-Stokes equation has…
This paper seeks to carry out the rigorous homogenization of a particulate flow consisting of a non-dilute suspension of a viscous Newtonian fluid with magnetizable particles. The fluid is assumed to be described by the Stokes flow, while…
Motivated by recent advances in vesicle engineering, we consider theoretically the locomotion of shape-changing bilayer vesicles at low Reynolds number. By modulating their volume and membrane composition, the vesicles can be made to change…
We make a consistent derivation, from the governing equations, of the pressure transfer function in the small-amplitude Stokes wave regime and the hydrostatic approximation in the small-amplitude solitary water wave regime, in the presence…
It is a classical problem in fluid dynamics about the stability and instability of different hydrodynamic patterns in various physical settings, in particular in the high Reynolds number limit of laminar flow with boundary layer. However,…
In this study we revisit the problem of computing steady Navier-Stokes flows in two-dimensional unbounded domains. Precise quantitative characterization of such flows in the high-Reynolds number limit remains an open problem of theoretical…
This paper addresses a nonstationary flow of heat-conductive incompressible Newtonian fluid with temperature-dependent viscosity coupled with linear heat transfer with advection and a viscous heat source term, under Navier/Dirichlet…
This paper investigates the nonlinear dynamics of Newton's problem of minimal resistance in radial fields. We move beyond classical translational symmetry to analyze two non-equilibrium scenarios: a scale-invariant free expansion and an…
Exact solutions for laminar stratified flows of Newtonian/non-Newtonian shear-thinning fluids in horizontal and inclined channels are presented. An iterative algorithm is proposed to compute the laminar solution for the general case of a…
We consider the Stokes system in a thin porous medium $\Omega_\varepsilon$ of thickness $\varepsilon$ which is perforated by periodically distributed solid cylinders of size $\varepsilon$. On the boundary of the cylinders we prescribe…
We study the stationary Navier--Stokes equations in the region between two rotating concentric cylinders. We first prove that, under the small Reynolds number, if the fluid is axisymmetric and if its velocity is sufficiently small in the…
Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes…
Analytical expressions correlating the volumetric flow rate to the inlet and outlet pressures are derived for the time-independent flow of Newtonian fluids in cylindrically-shaped elastic tubes using a one-dimensional Navier-Stokes flow…
We solve the stationary Navier-Stokes equations for non-Newtonian incompressible fluids with shear dependent viscosty in domains with unbounded outlets, in the case of shear thickening viscosity, i.e. the viscosity is given by the shear…
The purpose of this paper is to derive rigorously the so called viscous shallow water equations given for instance page 958-959 in [A. Oron, S.H. Davis, S.G. Bankoff, Rev. Mod. Phys, 69 (1997), 931?980]. Such a system of equations is…