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Fluid Flow Induced Deformation of a Boundary Hair
- Publication Year :
- 2022
-
Abstract
- The deformation of a dense carpet of hair due to Stokes flow in a channel can be described by a nonlinear integro-differential equation for the shape of a single hair, which possesses several solutions for a given choice of parameters. While being posed in a previous study and bearing resemblance to the pendulum problem from mechanics, this equation has not been analytically solved until now. Despite the presence on an integral with a nonlinear functional dependence on the dependent variable, the system is integrable. We compare the analytically obtained solution to a finite-difference numerical approach, identify the physically realizable solution branch, and briefly study the solution structure through a conserved energy-like quantity. Time-dependent fluid-structure interactions are a rich and complex subject to investigate and we argue that the solution discussed herein can be used as a basis for understanding these systems.
- Subjects :
- Physics - Fluid Dynamics
Nonlinear Sciences - Pattern Formation and Solitons
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2203.04169
- Document Type :
- Working Paper