Related papers: Scott-Blair models with time-varying viscosity
The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the…
We present a new rheological model depending on a real parameter $\nu \in [0,1]$ that reduces to the Maxwell body for $\nu=0$ and to the Becker body for $\nu=1$. The corresponding creep law is expressed in an integral form in which the…
Glassy solids may undergo a fluidization (yielding) transition upon deformation whereby the material starts to flow plastically. It has been a matter of debate whether this process is controlled by a specific time scale, from among…
We use experiments and theory to elucidate the size effect in capillary breakup rheometry, where pre-stretching in the visco-capillary stage causes the apparent relaxation time to be consistently smaller than the actual value. We propose a…
Soft materials often exhibit a distinctive power-law viscoelastic response arising from broad distribution of time-scales present in their complex internal structure. A promising tool to accurately describe the rheological behaviour of soft…
Recent experiments performed on a variety of soft glassy materials have demonstrated that any imposed shear flow serves to simultaneously fluidize these systems in all spatial directions [Ovarlez \textit{et al.} (2010)]. When probed with a…
Based on numerical simulations of a lattice kinetic model for soft-glassy materials, we characterize the global rheology of a dense emulsion-like system, under three representative load conditions: Couette flow, time-oscillating Strain and…
We present a modification of a recently developed volume of fluid method for multiphase problems, so that it can be used in conjunction with a fractional step-method and fast Poisson solver, and validate it with standard benchmark problems.…
We report numerical simulations of strongly vibrated granular materials designed to mimic recent experiments performed both in presence or absence of gravity. The coefficient of restitution used here depends on the impact velocity by taking…
Understanding a material's dissipative response is important for their use in many applications, such as adhesion or fracture resistance. In dispersions, the interplay between matrix and inclusions complicates any description. Fractional…
The time-dependent Bragg diffraction by multilayer gratings working by reflection or by transmission is investigated. The study is performed by generalizing the time-dependent coupled-wave theory previously developed for one-dimensional…
In this work, we study ageing behavior of aqueous laponite suspension, a model soft glassy material, in creep. We observe that viscoelastic behavior is time dependent and is strongly influenced by the deformation field; the effect is known…
The surface of a thin liquid film with nonconstant curvature is unstable, as the Laplace pressure drives a flow mediated by viscosity. We present the results of experiments on one of the simplest variable curvature surfaces: a stepped…
Motivated from the need to convert time-dependent rheometry data into complex frequency response functions, this paper studies the frequency response function of the creep compliance that is coined the complex creep function. While for any…
The rheological behaviour of a polymer was investigated by performing numerical simulations in complex flow and comparing them to experiments. For our simulations, we employed a Smoothed Particle Hydrodynamics scheme, utilizing an integral…
We investigate the well-posedness of a coupled Navier-Stokes-Fokker-Planck system with a time-fractional derivative. Such systems arise in the kinetic theory of dilute solutions of polymeric liquids, where the motion of noninteracting…
Granular materials are ubiquitous in nature and are used extensively in daily life and in industry. The modeling of these materials remains challenging; therefore, finding models with acceptable predictive accuracy that at the same time…
We study self-diffusion within a simple hopping model for glassy materials. (The model is Bouchaud's model of glasses [J.-P. Bouchaud, J. Physique I 2, 1705 (1992)], as extended to describe rheological properties [P. Sollich, F. Lequeux, P.…
We formulate a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite-strain setting in the Kelvin's-Voigt's rheology where the viscosity stress tensor complies with the principle of time-continuous frame-indifference.…
In this work, we introduce a time memory formalism in poroelasticity model that couples the pressure and displacement. We assume this multiphysics process occurs in multicontinuum media. The mathematical model contains a coupled system of…