Suspension flow modeling for general geometries

Deterministic solution of the kinetic theory model of colloidal suspensions of structureless particles

“…The pair correlation function is highly influenced by the flow kinematics, i.e., influenced by both the type and the strength of the flow. Thus, we allow the suspensions to be spatially inhomogeneous in the sense that the pair correlation function g is a function of R and also of x, but we assume that the density n p of the suspended spheres remains a constant independent of both x and the time t. It is well-known (see, e.g., Morris (2009) andMiller et al (2009)) that in flows with varying shear rate, the spheres migrate and thus n p becomes a function of both x and t. It is therefore necessary to adopt n p (x, t) as an additional state variable joining the velocity v(x, t) and the pair correlation function g(x, R, t). We intend to discuss rigid sphere suspensions in such extended setting in a future paper.…”

The suspension balance model revisited

“…Despite the aforementioned flaws, many studies [19][20][21]24 have used the suspension balance model with success to capture the observed features of particle migration in many simple flows. This suggests that the phenomenological form of ⌺ h͑p͒ assumed in these studies may be qualitatively similar to that of the particle phase stress.…”

“…However, the normal stress differences of the particle phase are not the same as that of the suspension. The numerous studies [19][20][21][22][23][24][25][26][27] that have used and extended the SBM have retained the error of equating ͗ h ͘ p with ⌺ h͑p͒ . The outline of this paper is as follows.…”

A new rate-independent tensorial model for suspensions of noncolloidal rigid particles in Newtonian fluids

“…Although the precise mechanisms remain to be elucidated, it is generally interpreted as resulting from chaotic dynamics induced by the nonlinearity of the multi-body hydrodynamic interactions [12], and/or from even weak perturbations of the hydrodynamic interactions by non-hydrodynamic near-contact forces [13,14]. Note that the asymmetric microstructure, and the associated normal stresses, are also at the origin of the cross-stream particle migration process observed in these suspensions when the shear rate is heterogeneous [15,16].…”

“…However, as a counterpart for its simplicity, this model is devoid of any time or strain scale, and therefore unable to account for transients observed during shear reversal experiments. In addition, earlier versions were not invariant by changes of reference frame, although an ad hoc frame-invariant extension has been proposed [16]. In the second group of models, particle stress is made explicitly dependent on the microstructure through the consideration of a local conformation tensor that is inspired from the orientation distribution tensor defined for dilute fiber suspensions (see e.g.…”