Micro-geometry effects on the nonlinear effective yield strength response of magnetorheological fluids

We use the novel constitutive model in [15], derived using the homogenization method, to investigate the effect particle chain microstructures have on the properties of the magnetorheological fluid. The model allows to compute the constitutive coefficients for different geometries. Different geometrical realizations of chains can significantly change the magnetorheological effect of the suspension. Numerical simulations suggest that particle size is also important as the increase of the overall particle surface area can lead to a decrease of the overall magnetorheological effect while keeping the volume fraction constant

Micro-geometry effects on the nonlinear effective yield strength response of magnetorheological fluids

We use the novel constitutive model in [15], derived using the homogenization method, to investigate the effect particle chain microstructures have on the properties of the magnetorheological fluid. The model allows to compute the constitutive coefficients for different geometries. Different geometrical realizations of chains can significantly change the magnetorheological effect of the suspension. Numerical simulations suggest that particle size is also important as the increase of the overall particle surface area can lead to a decrease of the overall magnetorheological effect while keeping the volume fraction constant

Steady state non-Newtonian flow with strain rate dependent viscosity in domains with cylindrical outlets to infinity

The paper deals with a stationary non-Newtonian flow of a viscous fluid in unbounded domains with cylindrical outlets to infinity. The viscosity is assumed to be smoothly dependent on the gradient of the velocity. Applying the generalized Banach fixed point theorem, we prove the existence, uniqueness and high order regularity of solutions stabilizing in the outlets to the prescribed quasi-Poiseuille flows. Varying the limit quasi-Poiseuille flows, we prove the stability of the solution

Asymptotic analysis of singular problems in perforated cylinders.

In this paper, we deal with elliptic problems having terms singular in the variable uu which represents the solution. The problems are posed in cylinders Ωnε of height 2n and perforated according to a parameter ε. We study existence, uniqueness and asymptotic behavior of the solutions uεn as the cylinders become infinite (n→+∞) and the size of the holes decreases while the number of the holes increases (ε→0)

Homogenisation of Two-Phase Emulsions

We consider an emulsion of two Stokes fluids, one of which is periodically distributed in the form of small spherical bubbles. The effects of surface tension on the bubble boundaries are modelled mathematically, as in the work of G. I. Taylor, by a jump only in the normal component of the traction. For a given volume fraction of bubbles, we consider the two-scale convergence, and in the fine phase limit we find that the bulk flow is described by an anisotropic Stokes fluid. The effective viscosity tensor is consistent with the bulk stress formula obtained by Batchelor [2]. © 1994, Royal Society of Edinburgh. All rights reserved

HOMOGENIZATION FOR A MULTI-SCALE MODEL OF MAGNETORHEOLOGICAL SUSPENSION

Using the homogenization method we obtain a model describing the behavior of the suspension of solid magnetizable particles in a viscous non-conducting fluid in the presence of an externally applied magnetic field. We use the quasi-static Maxwell equations coupled with the Stokes equations to capture the magnetorheological (MR) effect. The model generalizes the one introduced by Neuringer and Rosensweig [14], for quasistatic phenomena. The macroscopic constitutive properties are given explicitly in terms of the solutions of the local problems. We determine the homogenized constitutive parameters for an aqueous MR fluid with magnetite particles using the finite element method. The Poiseuille flow, for the solution of our homogenized coupled system, approaches the Bingham flow profile for large values of the magnetic field. The stress–strain curves obtained for the Couette flow exhibit a yield stress close to the one determined experimentally

Critical radius, size effects and inverse problems for composites with imperfect interface

We provide new bounds on the interfacial barrier conductivity for isotropic particulate composites based on measured values of effective properties, known values of component volume fractions, and the formation factor for the matrix phase. These bounds are found to be sharp. Our tool is a new set of variational principles and bounds on the effective properties of composites with imperfect interface obtained by us [see R. Lipton and B. Vernescu, Proc. R. Soc. London Ser. A 452, 329 (1996)]. We apply the bounds to solve inverse problems. For isotropic polydisperse suspensions of spheres we are able to characterize the size distribution of the spherical inclusions based on measured values of the effective conductivity. © 1996 American Institute of Physics

Micro-geometry Effects on the Nonlinear Effective Yield Strength Response of Magnetorheological Fluids

We use the novel constitutive model in Nika and Vernescu (Z Angew Math Phys 71:1–19, 2020), derived using the homogenization method, to investigate the effect particle chain microstructures have on the properties of the magnetorheological fluid. The model allows to compute the constitutive coefficients for different geometries. Different geometrical realizations of chains can significantly alter the magnetorheological effect of the suspension. Numerical simulations suggest that particle size is also important as the increase in the overall particle surface area can lead to a decrease in the overall magnetorheological effect while keeping the volume fraction constant