Series solution and its extension for the nonlinear flow response of soft hair beds

Abstract

In nature and engineering applications, flexible fiber beds covering biological surfaces can play a role in reducing resistance. These fibers deform under the action of fluids, and this deformation affects the fluid flow state, forming a complex fluid–solid interaction phenomenon. To quantitatively analyze these issues, the physical model is simplified. We focus on the deformation of a soft hair bed caused by Stokes flow. Additionally, we study the deformation of a single hair under Stokes flow in greater detail. The deformation problem of an elastic single fiber in a channel caused by Stokes flow can be described by a nonlinear integral equation. We have obtained a new series solution, which has been compared with the previous perturbation method to verify the accuracy and effectiveness of the series solution. Meanwhile, we have further provided an extended form of flexible fiber deformation through experimental fitting. This fluid–solid interaction problem involves multiple fields and is very important in many natural and engineering systems. The research in this paper can not only help us better understand complex phenomena in nature but also delve into the interaction mechanism between fluids and solids, providing a theoretical basis for future scientific research and engineering applications.