相关论文: Derivation of Batchelor-Green formula for random s…
We provide a rigorous derivation of Einstein's formula for the effective viscosity of dilute suspensions of $n$ rigid balls, $n \gg 1$, set in a volume of size $1$. So far, most justifications were carried under a strong assumption on the…
We provide a mathematical analysis of the effective viscosity of suspensions of spherical particles in a Stokes flow, at low solid volume fraction $\phi$. Our objective is to go beyond the Einstein's approximation…
We prove a local variant of Einstein's formula for the effective viscosity of dilute suspensions, that is $\mu^\prime=\mu (1+\frac 5 2\phi+o(\phi))$, where $\phi$ is the volume fraction of the suspended particles. Up to now rigorous…
We propose an improved effective-medium theory to obtain the concentration dependence of the viscosity of particle suspensions at arbitrary volume fractions. Our methodology can be applied, in principle, to any particle shape as long as the…
This work is devoted to the definition and the analysis of the effective viscosity associated with a random suspension of small rigid particles in a steady Stokes fluid. While previous works on the topic have been conveniently assuming that…
Suspensions of self-propelled particles are studied in the framework of two-dimensional (2D) Stokesean hydrodynamics. A formula is obtained for the effective viscosity of such suspensions in the limit of small concentrations. This formula…
This paper is a follow-up of article [6], on the derivation of accurate effective models for viscous dilute suspensions. The goal is to identify an effective Stokes equation providing a $o(\lambda^2)$ approximation of the exact…
In his PhD thesis, Einstein derived an explicit first-order expansion for the effective viscosity of a Stokes fluid with a suspension of small rigid particles at low density. His formal derivation relied on two implicit assumptions: (i)…
We present a mathematical proof of Einstein's formula for the effective viscosity of a dilute suspension of rigid neutrally--buoyant spheres when the spheres are centered on the vertices of a cubic lattice. We keep the size of the container…
We propose a simple and general model accounting for the dependence of the viscosity of a hard sphere suspension at arbitrary volume fractions. The model constitutes a continuum-medium description based on a recursive-differential method…
In this letter, following an extensive experimental validation, we perform constant-volume shearing simulations of non-Brownian granular suspensions using the discrete element method coupled with the lattice Boltzmann method. We choose a…
We give the first correction to the suspension viscosity due to fluid elasticity for a dilute suspension of spheres in a viscoelastic medium. Our perturbation theory is valid to $O(\phi\mathrm{Wi}^2)$ in the Weissenberg number…
We report on calculations of the reduced sedimentation velocity $U/U_{0}$ in homogenous suspensions of strongly and weakly charged colloidal spheres as a function of particle volume fraction $\phi$. For dilute suspensions of strongly…
We compute the first order correction of the effective viscosity for a suspension containing solid particles with arbitrary shapes. We rewrite the computation as an homogenization problem for the Stokes equations in a perforated domain.…
Recent experiments report that slowly-sheared noncolloidal particle suspensions can exhibit unexpected rate($\omega$)-dependent complex viscosities in oscillatory shear, despite a constant relative viscosity in steady shear. Using a minimal…
We consider liquid suspensions with dispersed nanoparticles. Using two-points Pade approximants and combining results of both hydrodynamic and molecular dynamics methods, we obtain the effective viscosity for any diameters of nanoparticles
Simple expressions are given for the Newtonian viscosity $\eta_N(\phi)$ as well as the viscoelastic behavior of the viscosity $\eta(\phi,\omega)$ of neutral monodisperse hard sphere colloidal suspensions as a function of volume fraction…
Starting with an expression, due originally to Einstein, for the shear viscosity \textit{$\eta $}(\textit{$\delta \phi $}) of a liquid having a small fraction \textit{$\delta \phi $}by volume of solid particulate matter suspended in it at…
We present a two-dimensional (2D) mathematical model of a highly concentrated suspension or a thin film of the rigid inclusions in an incompressible Newtonian fluid. Our objectives are two-fold: (i) to obtain all singular terms in the…
From a reanalysis of the published literature, the low-shear viscosity of suspensions of hard spheres is shown to have a dynamic crossover in its concentration dependence, from a stretched exponential at lower concentrations to a power law…