Coarse-graining the dynamics of immersed and driven fiber assemblies

Abstract

An important class of fluid-structure problems involve the dynamics of ordered arrays of immersed, flexible fibers. While specialized numerical methods have been developed to study fluid-fiber systems, they become infeasible when there are many, rather than a few, fibers present, nor do these methods lend themselves to analytical calculation. Here, we introduce a coarse-grained continuum model, based on local-slender body theory, for elastic fibers immersed in a viscous Newtonian fluid. It takes the form of an anisotropic Brinkman equation whose skeletal drag is coupled to elastic forces. This model has two significant benefits: (1) the density effects of the fibers in a suspension become analytically manifest, and (2) it allows for the rapid simulation of dense suspensions of fibers in regimes inaccessible to standard methods. As a first validation, without fitting parameters, we achieve very reasonable agreement with 3D Immersed Boundary simulations of a bed of anchored fibers bent by a shear flow. Secondly, we characterize the effect of density on the relaxation time of fiber beds under oscillatory shear, and find close agreement to results from full numerical simulations. We then study buckling instabilities in beds of fibers, using our model both numerically and analytically to understand the role of fiber density and the structure of buckling transitions. We next apply our model to study the flow-induced bending of inclined fibers in a channel, as has been recently studied as a flow rectifier, examining the nature of the internal flows within the bed, and the emergence of inhomogeneous permeability. Finally, we extend the method to study a simple model of metachronal waves on beds of actuated fibers, as a model for ciliary beds. Our simulations reproduce qualitatively the pumping action of coordinated waves of compression through the bed.

References in corpus (7)

• A boundary element regularised Stokeslet method applied to cilia and flagella-driven flow
• A fast platform for simulating flexible fiber suspensions applied to cell mechanics
• Gaussian-Like Immersed Boundary Kernels with Three Continuous Derivatives and Improved Translational Invariance
• The boundary integral formulation of Stokes flows includes slender-body theory
• A general formulation of Bead Models applied to flexible fibers and active filaments at low Reynolds number
• Immersed Boundary Smooth Extension (IBSE): A high-order method for solving incompressible flows in arbitrary smooth domains
• Lubricated Immersed Boundary Method in Two Dimensions

Cited by in corpus (7)

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• Collective stiffening of soft hair assemblies
• Operating Principles of Peristaltic Pumping through a Dense Array of Valves
• Hydraulic resistance of channels obstructed by a dense array of elastic fibers