Coupling state-based peridynamics and lubrication theory to understand flow-induced deformation and damage of microchannels

The purpose of this study is to deepen our understanding of the interaction between a fluid flow and the soft walls of a microchannel, a multiphysics problem that arises in applications ranging from microfluidics to biomedical engineering and chemical synthesis. A one-dimensional model is developed to analyze the coupled fluid-structure interaction (FSI) between a 2D soft-walled microchannel and the viscous fluid flow within it. Unlike previous works on the subject, this study employs a peridynamic state-based formulation of the Euler-Bernoulli beam theory to model the bending and damage of the soft wall of the microchannel. The fluid dynamics problem is simplified by cross-sectionally averaging the 2D Navier-Stokes equations, under the lubrication approximation, to yield a one-dimensional description. Notably, the peridynamic theory employed in this study is capable of simulating the onset and progression of damage to the elastic wall, specifically the incipience of fracture. We demonstrate how our approach offers an understanding of the timing and location of the failure of the soft wall. Specifically, we examine how these outcomes are influenced by the key dimensionless numbers of the problem: the Reynolds number of the flow, a Strouhal number associated with the wall inertia, a compliance number capturing the FSI, and a nonlocality number arising from peridynamics. These parameters are systematically varied to study the conditions under which a 2D soft-walled channel can fail under both static and dynamic loading conditions, showing that the potential failure location shifts when the beam is two-way coupled to the flow. Thus, our modeling approach provides new insights into the mechanical resilience of microfluidic devices under various conditions, which can aid in the design and optimization of devices made of soft polymeric materials.