https://doi.org/10.1140/epje/s10189-025-00479-2
Regular Article - Flowing Matter
Effective viscosity of a two-dimensional passive suspension in a liquid crystal solvent
1
Department of Mathematics, The Pennsylvania State University, University Park, USA
2
Institut Curie, Université PSL, Sorbonne Université, CNRS UMR168, Physique of Cells and Cancer, 75005, Paris, France
3
Department of Mathematics and Huck Institute for Life Sciences, The Pennsylvania State University, University Park, USA
Received:
21
October
2024
Accepted:
23
February
2025
Published online:
8
May
2025
Suspension of particles in a fluid solvent are ubiquitous in nature, for example water mixed with sugar or bacteria self-propelling through mucus. Particles create local flow perturbations that can modify drastically the effective (homogenized) bulk properties of the fluid. Understanding the link between the properties of particles and the fluid solvent, and the effective properties of the medium is a classical problem in fluid mechanics. Here we study a special case of a two-dimensional model of a suspension of undeformable particles in a liquid crystal solvent. In the dilute regime, we calculate asymptotic solutions of the perturbations of the velocity and director fields and derive an explicit formula for an effective shear viscosity of the liquid crystal medium. Such effective shear viscosity increases linearly with the area fraction of particles, similar to Einstein formula but with a different prefactor. We provide explicit asymptotic formulas for the dependence of this prefactor on the material parameters of the solvent. Finally, we identify a case of decreasing the effective viscosity by increasing the magnitude of the shear-flow alignment coefficient of the liquid crystal solvent.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
