Einstein viscosity with fluid elasticity

Abstract

We give the first correction to the suspension viscosity due to fluid elasticity for a dilute suspension of spheres in a viscoelastic medium. Our perturbation theory is valid to O(φWi 2 ) in the Weissenberg number Wi =γλ, whereγ is the typical magnitude of the suspension velocity gradient, and λ is the relaxation time of the viscoelastic fluid. For shear flow we find that the suspension shear-thickens due to elastic stretching in strain 'hot spots' near the particle, despite the fact that the stress inside the particles decreases relative to the Newtonian case. We thus argue that it is crucial to correctly model the extensional rheology of the suspending medium to predict the shear rheology of the suspension. For uniaxial extensional flow we correct existing results at O(φWi), and find dramatic strain-rate thickening at O(φWi 2 ). We validate our theory with fully resolved numerical simulations.arXiv:1705.06770v3 [physics.flu-dyn]

Force moments of an active particle in a complex fluid

“…which corresponds to recent results [14], except that here we used disturbance fields for the non-Newtonian flow to obviate the evaluation of surface integrals in the far-field. To recover the form given by Einarsson et al [14], we use far field asymptotic results from that work to obtain…”

“…Although less compact, this form allows one to differentiate between the non-Newtonian stress acting directly on the body from the effects of the modification of the flow due to the complex rheology [14,20].…”

“…To recover the form given by Einarsson et al [14], we use far field asymptotic results from that work to obtain…”

“…This approach was extended to find the motion of active particles in otherwise quiescent fluids [6,7] and background flows [8] and may also be used to describe the motion of multiple particles in complex fluids [9] (and Newtonian fluids [10]). Recently, the reciprocal theorem has also been used to find the first force moment on a passive sphere in a viscoelastic linear flow [11][12][13][14].…”

Jeffery orbits in shear-thinning fluids

“…As noted above, most prior studies have focused on Newtonian fluids, but for suspensions in non-Newtonian fluids the fundamental building blocks governing the rheology are still being developed. Non-Newtonian carrier fluids can produce qualitative changes in the rheological behaviour of suspensions in comparison with Newtonian fluids, as an example, recent studies have calculated modifications of the Einstein viscosity for dilute suspensions of spheres in weakly nonlinear viscoelastic fluids [33], and shear-thinning fluids [34].…”