Dilute suspensions of length-changing rods in various domains.

摘要

Several biological and physical phenomena feature rod-like filaments that can change in length, including bundles of cytoskeletal filaments driven by motor proteins, elongating rodlike cells, and liquid-crystal filaments. Motivated by these examples, we studied hydrodynamic interactions of suspensions of rods which can change in length. Filament length changes exert stress on the fluid, causing long-range hydrodynamic coupling between filaments. In the first part, we restrict ourselves to periodic domains. We discuss in details the kinetic modeling of a suspension of rods in the dilute limit. We use linear-stability analysis and numerical solution of the PDEs to explore the linearized system for growing/shrinking filaments in a nearly isotropic state and a nematically aligned state. Eigenvalue, eigenfunction, and related non-linear analysis are demonstrated. Although the filaments are active only through their length changes (they otherwise move passively with the fluid flow), the induced fluid flow for growing filaments is similar to that of a swimming "pusher" which induces an extensional stress dipole on the fluid. At the end of this first part, we discuss some potential applications like synchronization of flagella motion from our linear theory. In the second part, we consider more realistic domains with boundaries in 2 dimensions like disks or annuluses. We use the previously developed kinetic model to demonstrate, mostly by numerical simulation, how the boundary shape, and differing Neumann and Dirichlet boundary condition on the orientation of rods, can change the behavior of the system. For example, we find that non-homogenous Dirichlet boundary condition could lead to flows in a steady direction. We also find that the boundaries serve as friction forces in these systems. We also find there is phase transition phenomenons in the case of annuluses.