Hydrodynamics of a disk in a thin film of weakly nematic fluid subject to linear friction

Abstract

To make progress towards the development of a theory on the motion of inclusions in thin structured films and membranes, we here consider as an initial step a circular disk in a two-dimensional, uniaxially anisotropic fluid layer. We assume overdamped dynamics, incompressibility of the fluid, and global alignment of the axis of anisotropy. Motion within this layer is affected by additional linear friction with the environment, for instance, a supporting substrate. We investigate the induced flows in the fluid when the disk is translated parallel or perpendicular to the direction of anisotropy. Moreover, expressions for corresponding mobilities and resistance coefficients of the disk are derived. Our results are obtained within the framework of a perturbative expansion in the parameters that quantify the anisotropy of the fluid. Good agreement is found for moderate anisotropy when compared to associated results from finite-element simulations. At pronounced anisotropy, the induced flow fields are still predicted qualitatively correctly by the perturbative theory, although quantitative deviations arise. We hope to stimulate with our investigations corresponding experimental analyses, for example, concerning fluid flows in anisotropic thin films on uniaxially rubbed supporting substrates.

arXiv comment14 pages, 5 figures

References in corpus (24)

• Director Field Configurations around a Spherical Particle in a Nematic Liquid Crystal
• Effect of collective molecular reorientations on Brownian motion of colloids in nematic liquid crystal
• Active colloids in liquid crystals
• Dynamics of rigid and flexible extended bodies in viscous films and membranes
• On the mobility of extended bodies in viscous films and membranes
• Long-lived anomalous thermal diffusion induced by elastic cell membranes on nearby particles
• Microrheological Characterisation of Anisotropic Materials
• Brownian motion near a liquid-like membrane
• Non-reciprocal response of a two-dimensional fluid with odd viscosity
• State diagram of a three-sphere microswimmer in a channel
• Mobility of an axisymmetric particle near an elastic interface
• Particle mobility between two planar elastic membranes: Brownian motion and membrane deformation
• Hydrodynamic interaction between particles near elastic interfaces
• Hydrodynamic lift of a two-dimensional liquid domain with odd viscosity
• A parallel Newton multigrid framework for monolithic fluid-structure interactions
• Stokes-Einstein diffusion of colloids in nematics
• Hydrodynamics of an odd active surfer in a chiral fluid
• Hydrodynamic coupling and rotational mobilities near planar elastic membranes
• Flow of a viscous nematic fluid around a sphere
• Mediated interactions between rigid inclusions in two-dimensional elastic or fluid films
• Three-disk microswimmer in a supported fluid membrane
• Hydrodynamic aggregation of membrane inclusions due to non-Newtonian surface rheology
• Hydrodynamic efficiency limit on a Marangoni surfer
• The role of boundaries for displacements and motion in two-dimensional fluid or elastic films and membranes

Cited by in corpus (3)

• Analytical solution for the hydrodynamic resistance of a disk in a compressible fluid layer with odd viscosity on a rigid substrate
• Hydrodynamic flow field and frictional resistance coefficient of a disk rotating steadily in a compressible fluid layer with odd viscosity on a rigid substrate
• Rotational dynamics of a disk in a thin film of weakly nematic fluid subject to linear friction