Abstract
A dynamic two-scale model is developed for describing the mechanical behavior of suspensions of permeable ellipsoidal particles. The particle dynamics in the proposed model is described in terms of particle positions as well as conformation tensors that capture their size, shape, and orientation. Using non-equilibrium thermodynamics, the macroscopic fluid-dynamics and the particle dynamics on the microstructural level are mutually coupled in a consistent manner. So doing, the link between the macroscopic behavior, e.g. stresses, and the dynamics of the microstructure, e.g. particle shape and size, is established. Finally, the model is cast into a form in which the shape tensor is split into its volumetric and isochoric shape contributions, making it possible to model particles with both shape-preserving size-changes (e.g. swellable particles) and volume-preserving shape-changes (e.g. incompressible yet deformable particles). The size-shape model distinguishes itself in unifying prior knowledge of purely-shape models with that of purely-size models by appropriate choices of the Helmholtz free energy and the generalized mobility.
Highlights
A wide variety of applications nowadays relies on materials where their overall properties can be tailored to meet specific requirements
This paper presents a dynamic two-scale model that describes the mechanics of suspensions of permeable ellipsoidal particles
Following the principles of non-equilibrium thermodynamics, the macroscopic fluid dynamics is consistently coupled with the particle dynamics
Summary
A wide variety of applications nowadays relies on materials where their overall properties can be tailored to meet specific requirements. The elasticity of the supporting network of the individual particle gives rise to its elastic behavior. The flow of the viscous suspending solvent through this elastic network, on the other hand, results in its viscoelastic behavior. The rich behavior of permeable-particle suspensions emerges from the fact that permeable particles can undergo size and shape changes in response to different stimuli. Permeable particles in a sufficiently-jammed state undergo rate-dependent volume changes as the viscous background solvent is expelled from the interior of the particle [6,7]. While elastic shape-changes can be accounted for through soft-interaction potentials [8,9,10], the effect of the viscous background solvent on both the shape and size dynamics requires accounting for the particle internal degrees of freedom explicitly
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