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In this paper we consider a system of $N$ particles on the real line evolving according to Newton's law, interacting through a singular (repulsive) force deriving from the potential $\frac{|x|^{1-\alpha}}{1-\alpha}$ with $\alpha \in…
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…
Discrete simulation methods are efficient tools to investigate the complex behaviors of complex fluids made of either dry granular materials or dilute suspensions. By contrast, materials made of soft and/or concentrated units (emulsions,…
In this study, we investigate the dynamics of particles overcoming the hydrodynamic barrier posed by a thin fluid film to achieve contact in finite time, a phenomenon critical in various natural and engineered processes such as enzyme…
Motivated by experiments on cell segregation, we present a two-species model of interacting particles, aiming at a quantitative description of this phenomenon. Under precise scaling hypothesis, we derive from the microscopic model a…
We derive a mesoscopic modeling and simulation technique that is very close to the technique known as dissipative particle dynamics. The model is derived from molecular dynamics by means of a systematic coarse-graining procedure. Thus the…
This paper considers a family of non-diffusive active scalar equations where a viscosity type parameter enters the equations via the constitutive law that relates the drift velocity with the scalar field. The resulting operator is smooth…
We prove the existence of weak solutions of a class of multi-species cross-diffusion systems as well as the propagation of chaos result by means of nonlocal approximation of the nonlinear diffusion terms, coupling methods and compactness…
We derive a self-consistent hydrodynamic theory of coupled binary-fluid-surfactant systems from the underlying microscopic physics using Rayleigh's variational principle. At the microscopic level, surfactant molecules are modelled as…
The fluid-mechanics community is currently divided in assessing the boundaries of applicability of the macroscopic approach to fluid mechanical problems. Can the dynamics of nano-droplets be described by the same macroscopic equations as…
We propose a simple model, supported by contact-dynamics simulations as well as rheology and friction measurements, that links the transition from continuous to discontinuous shear-thickening in dense granular pastes to distinct lubrication…
Explicit analytical expressions for the drag and diffusion coefficients of a spherical particle attached to the interface between two immiscible fluids are constructed for the case of a small viscosity ratio between the fluid phases. The…
As a complementary tool to laboratory experiments, discrete numerical simulation, applied to granular materials, provides valuable information on the grain and contact scale microstructure, thereby enabling one to better understand the…
We consider a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. In a previous paper we have found mass-preserving, nonnegative weak solutions of the equation satisfying energy…
We show that a general density functional approach for calculating the force between two big particles immersed in a solvent of smaller ones can describe systems that exhibit fluid-fluid phase separation: the theory captures effects of…
We consider compressible pressureless fluid flows in Lagrangian coordinates in one space dimension. We assume that the fluid self-interacts through a force field generated by the fluid itself. We explain how this flow can be described by a…
We study the flow close to an advancing contact line in the limit of small capillary number. To take into account wetting effects, both long and short-ranged contributions to the disjoining pressure are taken into account. In front of the…
We describe, at the microscopic level, the dynamics of N interacting components where the probability is very small when N is large that a given component interact more than once, directly or indirectly, up to time t, with any other…
In order to reveal the coupling effect among the chemical activity and the hydraulic seepage as well as the mechanical properties, a constitutive theoretical framework considering the chemical activity for saturated porous media is derived…
We consider a system of nonlinear partial differential equations modelling the steady motion of an incompressible non-Newtonian fluid, which is chemically reacting. The governing system consists of a steady convection-diffusion equation for…