In this paper we present lattice Boltzmann (LB) schemes for convection diffusion coupled to fluid flow on two-dimensional rectangular lattices. Via inverse Chapman-Enskog analysis of LB schemes including source terms, we show that for consistency with physics it is required that the moments of the equilibrium distributions equal those of the Maxwell-Boltzmann distribution. These constraints can...

Diffusion experiments, effective medium theory calculations and random walk simulations were carried out on hierarchical porous materials. The main throughput of the mesoscopic proposed here is tortuosity defined as ratio fluid mean square displacements calculated in absence presence medium. This a well-defined definition that has advantage to be comparable self-diffusion coefficients for bulk ...

In this paper, exact solutions of velocity and stresses are obtained for the magnetohydrodynamic (MHD) flow of a Maxwell fluid in a porous half space by the Laplace transform method. The flows are caused by the cosine and sine oscillations of a plate. The derived steady and transient solutions satisfy the involved differential equations and the given conditions. Graphs for steady-state and tran...

Some important fundamental aspects of fluid mechanics and rheology are discussed. First, we examine the basis for the continuum approximation of fluids, and the formulation of equations in the continuum description. Then, we look at stress-strain rate relationships for simple shear flows of both viscous and viscoelastic fluids. The extension of the description to complex flows, which involves t...

We study the diffusive expansion for solutions around Maxwellian equilibrium and in a periodic box to the Vlasov-Maxwell-Boltzmann system, the most fundamental model for an ensemble of charged particles. Such an expansion yields a set of dissipative new macroscopic PDE’s, the incompressible Vlasov-Navier-Stokes-Fourier system and its higher order corrections for describing a charged fluid, wher...

A lattice Boltzmann model for binary mixtures is formally derived from a two-fluid kinetic model for Maxwell molecules by discretizing the Boltzmann equation. In this model, collisions among the same and different species are treated separately, as non-linear BGK terms, enabling the independent management of the species viscosities and thermal conductivities from the binary diffusion coefficien...

We examine the problem of the construction of a first order symmetric hyperbolic evolution system for the Einstein-Maxwell-Euler system. Our analysis is based on a 1 + 3 tetrad formalism which makes use of the components of the Weyl tensor as one of the unknowns. In order to ensure the symmetric hyperbolicity of the evolution equations implied by the Bianchi identity, we introduce a tensor of r...

high weissenberg boundary layer flow of viscoelastic fluids on a stretching surface has been studied. the flow is considered to be steady and two dimensional. flows of viscoelastic liquids at high weissenberg number exhibit stress boundary layers near walls. these boundary layers are caused by the memory of the fluid. upon proper scaling and by means of an exact similarity transformation, the n...

Using the classical catenary as a motivating example, we use slender-body theory to derive a general theory for thin filaments of arbitrary rheology undergoing large combined stretching and bending, which correctly accounts for the nonlinear geometry of deformation and uses integrated state variables to properly represent the complete deformation state. We test the theory for soft catenaries ma...

The polarization magnetization effects associated with the dynamical reduction leading to the nonlinear gyrokinetic Vlasov–Maxwell equations are shown to introduce nonlinear finite-Larmor-radius FLR effects into a set of nonlinear reduced-fluid equations previously derived by the Lagrangian variational method A. J. Brizard, Phys. Plasmas 12, 092302 2005 . These intrinsically nonlinear FLR effec...