Kinetic Theory Microstructure Modeling in Concentrated Suspensions

Abstract

When suspensions involving rigid rods become too concentrated, standard dilute theories fail to describe their behavior. Rich microstructures involving complex clusters are observed, and no model allows describing its kinematics and rheological effects. In previous works the authors propose a first attempt to describe such clusters from a micromechanical model, but neither its validity nor the rheological effects were addressed. Later, authors applied this model for fitting the rheological measurements in concentrated suspensions of carbon nanotubes (CNTs) by assuming a rheo-thinning behavior at the constitutive law level. However, three major issues were never addressed until now: (i) the validation of the micromechanical model by direct numerical simulation; (ii) the establishment of a general enough multi-scale kinetic theory description, taking into account interaction, diffusion and elastic effects; and (iii) proposing a numerical technique able to solve the kinetic theory description. This paper focuses on these three major issues, proving the validity of the micromechanical model, establishing a multi-scale kinetic theory description and, then, solving it by using an advanced and efficient separated representation of the cluster distribution function. These three aspects, never until now addressed in the past, constitute the main originality and the major contribution of the present paper.

On the multiscale description of dilute suspensions of non-Brownian rigid clusters composed of rods

“…The predicted angular velocity was compared to the one obtained by existing models for cylindrical particles, where an excellent agreement was found for large and small cylinder aspect ratios (representing rods and disks respectively); small deviations were noticed when r % 1 that depend on the particular cluster configuration. Kinematics of rigid clusters with arbitrary shape were compared in the 2D case with direct numerical simulations in [1] and both predictions were in excellent agreement.…”

From dilute to entangled fibre suspensions involved in the flow of reinforced polymers: A unified framework

“…First, following the general framework proposed in our former works for addressing rods [3], aggregates [1,2], confinement [36,41] and non-Newtonian matrices [13], most of them collected in chapter 2 of [12], we proposed below a new extended model able to address the rod kinematics previously discussed. For that purpose, we consider the fibre consisting of two beads connected by a rigid connector (dumbbell model).…”

“…The size effect that appears as soon as the flow does not exhibit a uniform strain-rate along the rod length, was deeply discussed in [3], where moreover bending mechanics were activated by the richer kinematics. Entangled systems as the ones discussed in [32,33] exhibit aggregates whose kinematics was addressed in [1,2,15] and chapter 2 in [12].…”

Efficient Stabilization of Advection Terms Involved in Separated Representations of Boltzmann and Fokker-Planck Equations

“…Finally, PGD was implemented in [16] to solve the stochastic equation within the framework of Brownian Configuration Fields. Models involving suspensions and colloidal systems were considered in [1,22,27,28,41,43] and kinetic descriptions of microstructural mixing in [17,42]. The interested reader can consult [19] for an exhaustive overview of PGD applications in computational rheology and the more general reviews [18,20,21].…”

“…The domain Ω x is the circle of unit diameter centered at the origin of coordinates O=(0,0). The velocity domain is the square 1]. At the inflow boundary of Ω x ×Ω v the velocity distribution depicted in Fig.…”