A fluid--peridynamic structure model of deformation and damage of microchannels

Abstract

Soft-walled microchannels arise in many applications, ranging from organ-on-a-chip platforms to soft-robotic actuators. However, despite extensive research on their static and dynamic response, the potential failure of these devices has not been addressed. To this end, we explore fluid--structure interaction in microchannels whose compliant top wall is governed by a nonlocal mechanical theory capable of simulating both deformation and material failure. We develop a one-dimensional model by coupling viscous flow under the lubrication approximation to a state-based peridynamic formulation of an Euler--Bernoulli beam. The peridynamic formulation enables the wall to be modeled as a genuinely nonlocal beam, and the integral form of its equation of motion remains valid whether the deformation field is smooth or contains discontinuities. Through the proposed computational model, we explore the steady and time-dependent behaviors of this fluid--peridynamic structure interaction. We rationalize the wave and damping dynamics observed in the simulations through a dispersion (linearized) analysis of the coupled system, finding that, with increasing nonlocal influence, wave propagation exhibits a clear departure from classical behavior, characterized by a gradual suppression of the phase velocity. The main contribution of our study is to outline the potential failure scenarios of the microchannel's soft wall under the hydrodynamic load of the flow. Specifically, we find a dividing curve in the space spanned by the dimensionless Strouhal number (quantifying unsteady inertia of the beam) and the compliance number (quantifying the strength of the fluid--structure coupling) separating scenarios of potential failure during transient conditions from potential failure at the steady load.

Figures (10)

• Figure 1: Schematic of the problem geometry and the mathematical notation.
• Figure 2: Steady state (a) deformed channel wall $H(X)$ and (b) pressure load $P(X)$ along the beam computed using classical continuum mechanics by Inamdar et al. inamdar2020unsteady (solid curves) and the fluid--peridynamic structure solver developed in this work (dashed curves), for three horizon sizes: $\Delta = 1/100$ and $\Delta = 1/20$. The simulation parameters are $\beta = 556$ and $Re = 0.5$.
• Figure 3: Nonlinear dynamics of the coupled problem illustrated by the time evolution of the channel height, $H(X,T)$. Darker curves represent later times, while lighter curves correspond to earlier times. The arrows indicate the direction of temporal evolution of the channel height. The simulation parameters are $St = 10$, $\beta = 20$, $Re = 0.5$, and $\Delta = 1/120$.
• Figure 4: Effect of the horizon size $\Delta$ on the damping behavior of the channel height oscillations at an early time of $T = 0.02$, showing the stronger wave damping as $\Delta$ increases. The simulation parameters are $St = 10$, $\beta = 10^5$, and $Re = 10^{-5}$.
• Figure 5: Dimensionless phase velocity $|v_{p}|$ versus $k/\pi$ for the classical Euler--Bernoulli beam (CBT) and the nonlocal PD beam with three horizon lengths $\Delta_{1}=0.02$, $\Delta_{2}=0.04$, and $\Delta_{3}=0.08$; $\beta=0$. Dashed horizontal lines show the large-$k$ asymptotes given in Eq. \ref{['eq:k_limit']}.