Related papers: On three-dimensional flows of pore pressure activa…
In this work, we investigate the asymmetric Bingham fluid equations. The asymmetric fluid of Bingham includes symmetric and antisymmetric stresses with such stresses appearing as an elastic response to the micro-rotational deformations of…
Long-time and large-data existence of weak solutions for initial- and boundary-value problems concerning three-dimensional flows of \emph{incompressible} fluids is nowadays available not only for Navier--Stokes fluids but also for various…
We investigate mathematical properties of the system of nonlinear partial differential equations that describe, under certain simplifying assumptions, evolutionary processes in water-saturated granular materials. The unconsolidated solid…
We analyze the Navier-Stokes equations for incompressible fluids with the {\lq\lq}viscous stress tensor{\rq\rq} $\mathbb{S}$ in a family which includes the Bingham model for viscoplastic fluids (more generally, the Herschel-Bulkley model).…
The flow of non-Newtonian fluids is ubiquitous in many applications in the geological and industrial context. We focus here on yield stress fluids (YSF), i.e. a material that requires minimal stress to flow. We study numerically the flow of…
We consider the system of partial differential equations governing two-dimensional flows of a robust class of viscoelastic rate-type fluids with stress diffusion, involving a general objective derivative. The studied system generalizes the…
We study the dynamics of compressible fluids in rotating heterogeneous porous media. The fluid flow is of {F}orchheimer-type and is subject to a mixed mass and volumetric flux boundary condition. The governing equations are reduced to a…
We inroduce a new model for Bingham fluids with a complicated dependence of the deformation velocity on the shear stress. Specific features of the flow rate for such fluid are studied. This model embraces many special and limiting cases,…
The flow of yield stress fluids in porous media presents interesting complexity due to the interplay between the non-linear rheology and the heterogeneity of the medium. A remarkable consequence is that the number of flow paths increases…
A comprehensive Darcy-type law for viscoplastic fluids is proposed. Different regimes of yield-stress fluid flow in porous media can be categorised based on the Bingham number (i.e. the ratio of the yield stress to the characteristic…
The purpose of this paper is to deal with the issue of well-posedness for a class of non-Newtonian fluid dynamics equations. These sets of equations are commonly used to describe various complex models that appear in nature, industry, and…
We derive an expression for the velocity profile of a pressure-driven yield-stress Bingham fluid flowing around a 2D concentric annulus. The formula requires the numerical solution of a nonlinear equation for the positions of the yield…
A new numerical scheme for solving incompressible Bingham flows with variable density, plastic viscosity and yield stress is proposed. The mathematical and computational difficulties due to the non-differentiable definition of the stress…
By using dimension reduction and homogenization techniques, we study the steady flow of an incompresible viscoplastic Bingham fluid in a thin porous medium. A main feature of our study is the dependence of the yield stress of the Bingham…
In this work we consider a poroelastic flexible material that may deform largely which is situated in an incompressible fluid driven by the Navier-Stokes equations in two or three space dimensions. By a variational approach we show…
In this paper, the existence of a weak solution for homogeneous incompressible Bingham fluid is investigated. The rheology of such a fluid is defined by a yield stress $\tau_y$ and a discontinuous stress-strain law. This non-Newtonian fluid…
In order to describe behavior of various liquid-like materials at high pressures, incompressible fluid models with pressure dependent viscosity seem to be a suitable choice. In the context of implicit constitutive relations involving the…
We consider the fluid mechanical problem of identifying the critical yield number $Y_c$ of a dense solid inclusion (particle) settling under gravity within a bounded domain of Bingham fluid, i.e. the critical ratio of yield stress to…
We investigate the flow of various non-Newtonian fluids through three-dimensional disordered porous media by direct numerical simulation of momentum transport and continuity equations. Remarkably, our results for power-law (PL) fluids…
We consider an incompressible Bingham flow in a thin domain with rough boundary, under the action of given external forces and with no-slip boundary condition on the whole boundary of the domain. In mathematical terms, this problem is…