Related papers: Micro-macro models for viscoelastic fluids: modell…
We propose a new material viscoelastic model and mathematical solution to simulate relaxation modulus and viscoelastic response. The model formula of relaxation modulus is extended from sigmoidal function considering nonlinear strain…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
This paper aims to provide an introduction to a basic form of the ${\bf Q}$-tensor approach to modelling liquid crystals, which has seen increased interest in recent years. The increase in interest in this type of modelling approach has…
This paper deals with the micro-macro derivation of virus models coupled with a reaction diffusion models that generates the dynamics in space of the virus particles. The first part of the presentation focuses, starting from [5, 6] on a…
In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…
This paper deals with the rigorous study of the diffusive stress relaxation in the multidimensional system arising in the mathematical modeling of viscoelastic materials. The control of an appropriate high order energy shall lead to the…
This work extends the classical dumbbell (two-bead) model of polymer chains to a more detailed multi-bead representation, where each polymer chain consists of $N$ beads connected by $N-1$ springs. We develop a thermodynamically consistent…
Many microorganisms swim in fluids with complex rheological properties. Although much is now understood about motion of these swimmers in Newtonian fluids, the understanding is still developing in non-Newtonian fluids --- this understanding…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
Microfluidics, the study of fluids in microscopic channels, has led to important advances in fields as diverse as microelectronics, biotechnology and chemistry. Microfluidic research is primarily based on the use of microfluidic chips,…
It is well-known that the architecture of macromolecules plays an important role in the hydrodynamics and viscosity of its semi-diluted solutions. However, the systematic study of the rheology of macromolecules with complex topology, such…
A non-hydrostatic depth-averaged model for dry granular flows is proposed, taking into account vertical acceleration. A variable friction coefficient based on the $\mu(I)$ rheology is considered. The model is obtained from an asymptotic…
We review the influence of micromechanical parameters on the macroscopic mechanical behaviour of granular materials, as numerically simulated in discrete element approaches, both in quasistatic conditions an din dense flow. We insist in…
Microfluidic devices are increasingly used in biological and chemical experiments due to their cost-effectiveness for rheological estimation in fluids. However, these devices often face challenges in terms of accuracy, size, and cost. This…
The equations governing the conditions of mechanical equilibrium in fluid membranes subject to bending are revisited thanks to the principle of virtual work. The note proposes systematic tools to obtain the shape equation and the line…
In this paper, thermodynamics of a moving medium is considered. Main goal of this paper is to describe thermodynamics state equations and equations of co-existence manifolds of media on two- and three-dimensional manifolds. To this end the…
The locomotion of microorganisms and spermatozoa in complex viscoelastic fluids is of critical importance in many biological processes such as fertilization, infection, and biofilm formation. Depending on their propulsion mechanisms,…
The goal of these lecture notes is to present in a unified way various models for the dynamics of aligning self-propelled rigid bodies at different scales and the links between them. The models and methods are inspired from [12,13], but, in…
We propose a new reduced model for gravity-driven free-surface flows of shallow elastic fluids. It is obtained by an asymptotic expansion of the upper-convected Maxwell model for elastic fluids. The viscosity is assumed small (of order…
Viscoelastic surface rheology plays an important role in multiphase systems. A typical example is the actin cortex which surrounds most animal cells. It shows elastic properties for short time scales and behaves viscous for longer time…