相关论文: Macroscopic limit of a one-dimensional model for a…
We study mathematically a system of partial differential equations arising in the modelling of an aging fluid, a particular class of non Newtonian fluids. We prove well-posedness of the equations in appropriate functional spaces and…
In a previous work [math.AP/0305408] three of us have studied a nonlinear parabolic equation arising in the mesoscopic modelling of concentrated suspensions of particles that are subjected to a given time-dependent shear rate. In the…
Based on a mesoscopic theory we investigate the non-equilibrium dynamics of a sheared nematic liquid, with the control parameter being the shear stress $\sigma_{\mathrm{xy}}$ (rather than the usual shear rate, $\dot\gamma$). To this end we…
Various experiments evidence spatial heterogeneities in sheared yield stress fluids. To account for heterogeneities in the velocity gradient direction, we use a simple model corresponding to a non-monotonous local constitutive curve and…
The ubiquitous appearance of regions of localized deformation (shear bands) in different kinds of disordered materials under shear is studied in the context of a mesoscopic model of plasticity. The model may or may not include relaxational…
In this paper we study the convergence of a power-law model for dilatant compressible fluids to a class of models exhibiting a maximum admissible shear rate, called thick compressible fluids. These kinds of problems were studied previously…
We develop an elasto-plastic description for the transient dynamics prior to steady flow of athermally yielding materials. Our mean-field model not only reproduces the experimentally observed non-linear time dependence of the shear-rate…
Yield stress fluids display complex dynamics, in particular when driven into the transient regime between the solid and the flowing state. Inspired by creep experiments on dense amorphous materials, we implement mesocale elasto-plastic…
This paper is concerned with an initial and boundary value problem of the one-dimensional planar MHD equations for viscous, heat-conducting, compressible, ideal polytropic fluids with constant transport coefficients and large data. The…
This paper is concerned with an initial and boundary value problem of the one-dimensional planar MHD equations for viscous, heat-conducting, compressible, ideal polytropic fluids with constant transport coefficients and large data. The…
We consider the system of equations describing the flow of incompressible fluids in bounded domain. In the considered setting, the Cauchy stress tensor is a monotone mapping and has asymptotically $(s-1)$-growth with the parameter $s$…
Dense mixture of granules and liquid often shows a sever shear thickening and is called a dilatant fluid. We construct a fluid dynamics model for the dilatant fluid by introducing a phenomenological state variable for a local state of…
A theory for the non-local shear stress correlations in supercooled liquids is derived from first principles. It captures the crossover from viscous to elastic dynamics at an idealized liquid to glass transition and explains the emergence…
We investigate the anisotropic evolution of spacetime driven by perfect fluid with off-diagonal shear-viscosity components. We consider the simplest form of the equation of state for fluid, for which the pressure and the shear stress are…
We construct a mean-field elastoplastic description of the dynamics of amorphous solids under arbitrary time-dependent perturbations, building on the work of Lin and Wyart [Phys. Rev. X 6, 011005 (2016)] for steady shear. Local stresses are…
We consider Kasner space-time describing anisotropic three dimensional expansion of the fluid and obtain the dissipative evolution equations for shear stress tensor and energy density from kinetic theory. For this, we use the iterative…
A microfluidic approach to probing the first normal stress difference from single-point pressure measurements in transient shear flows is presented. Using an original experimental design, we examine the near-zero-mean pulsatile flow of…
A three-dimensional, steady, laminar shear-layer flow spatially developing under a boundary-layer approximation with mixing, chemical reaction, and imposed normal strain is analyzed. The imposed strain creates a counterflow that stretches…
Recent flow cessation experiments on soft materials have shown a counter-intuitive non-monotonic relaxation of the shear stress: following the switch-off of a steady imposed shear flow, the stress initially decays before later increasing…
We establish the long-time existence of large-data weak solutions to a system of nonlinear partial differential equations. The system of interest governs the motion of non-Newtonian fluids described by a simplified viscoelastic rate-type…