Partner: Antoine Sellier

École Polytechnique (FR)

Recent publications
1.Feuillebois F., Ekiel-Jeżewska M.L., Wajnryb E., Sellier A., Bławzdziewicz J., High-frequency effective viscosity of a dilute suspension of particles in Poiseuille flow between parallel walls, JOURNAL OF FLUID MECHANICS, ISSN: 0022-1120, DOI: 10.1017/jfm.2016.378, Vol.800, pp.111-139, 2016
Abstract:

It is shown that the formal expression for the effective viscosity of a dilute suspension of arbitrary-shaped particles in Poiseuille flow contains a novel quadrupole term, besides the expected stresslet. This term becomes important for a very confined geometry. For a high-frequency flow field (in the sense used in Feuillebois et al. (J. Fluid Mech., vol. 764, 2015, pp. 133–147), the suspension rheology is Newtonian at first order in volume fraction. The effective viscosity is calculated for suspensions of N-bead rods and of prolate spheroids with the same length, volume and aspect ratio (up to 6), entrained by the Poiseuille flow between two infinite parallel flat hard walls. The numerical computations, based on solving the Stokes equations, indicate that the quadrupole term gives a significant positive contribution to the intrinsic viscosity [μ] if the distance between the walls is less than ten times the particle width, or less. It is found that the intrinsic viscosity in bounded Poiseuille flow is generally smaller than the corresponding value in unbounded flow, except for extremely narrow gaps when it becomes larger because of lubrication effects. The intrinsic viscosity is at a minimum for a gap between walls of the order of 1.5–2 particle width. For spheroids, the intrinsic viscosity is generally smaller than for chains of beads with the same aspect ratio, but when normalized by its value in the bulk, the results are qualitatively the same. Therefore, a rigid chain of beads can serve as a simple model of an orthotropic particle with a more complicated shape. The important conclusion is that the intrinsic viscosity in shear flow is larger than in the Poiseuille flow between two walls, and the difference is significant even for relatively wide channels, e.g. three times wider than the particle length. For such confined geometries, the hydrodynamic interactions with the walls are significant and should be taken into account.

Keywords:

low-Reynolds-number flows

Affiliations:
Feuillebois F.-Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (FR)
Ekiel-Jeżewska M.L.-IPPT PAN
Wajnryb E.-IPPT PAN
Sellier A.-École Polytechnique (FR)
Bławzdziewicz J.-Texas Tech University (US)
2.Feuillebois F., Ekiel-Jeżewska M.L., Wajnryb E., Sellier A., Bławzdziewicz J., High-frequency viscosity of a dilute suspension of elongated particles in a linear shear flow between two walls, JOURNAL OF FLUID MECHANICS, ISSN: 0022-1120, DOI: 10.1017/jfm.2014.690, Vol.764, pp.133-147, 2015
Abstract:

A general expression for the effective viscosity of a dilute suspension of arbitrary-shaped particles in linear shear flow between two parallel walls is derived in terms of the induced stresslets on particles. This formula is applied to N-bead rods and to prolate spheroids with the same length, aspect ratio and volume. The effective viscosity of non-Brownian particles in a periodic shear flow is considered here. The oscillating frequency is high enough for the particle orientation and centre-of-mass distribution to be practically frozen, yet small enough for the flow to be quasi-steady. It is known that for spheres, the intrinsic viscosity [μ] increases monotonically when the distance H between the walls is decreased. The dependence is more complex for both types of elongated particles. Three regimes are theoretically predicted here: (i) a ‘weakly confined’ regime (for H>l, where l is the particle length), where [μ] is slightly larger for smaller H; (ii) a ‘semi-confined’ regime, when H becomes smaller than l, where [μ] rapidly decreases since the geometric constraints eliminate particle orientations corresponding to the largest stresslets; (iii) a ‘strongly confined’ regime when H becomes smaller than 2–3 particle widths d, where [μ] rapidly increases owing to the strong hydrodynamic coupling with the walls. In addition, for sufficiently slender particles (with aspect ratio larger than 5–6) there is a domain of narrow gaps for which the intrinsic viscosity is smaller than that in unbounded fluid.

Keywords:

complex fluids, low-Reynolds-number flows, suspensions

Affiliations:
Feuillebois F.-Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (FR)
Ekiel-Jeżewska M.L.-IPPT PAN
Wajnryb E.-IPPT PAN
Sellier A.-École Polytechnique (FR)
Bławzdziewicz J.-Texas Tech University (US)