In this article, we propose a numerical model based on the equation to simulate the dynamics of a front inside a microchannel that features an imperfection at a sidewall to different flow rates. The micro-front displays pinning–depinning phenomena without damped oscillations in the aftermath. To model this behavior, we propose a model with a localized external force and a damping coefficient. Numerical simulations with a constant damping coefficient show that the front displays pinning–depinning phenomena showing damped oscillations once the imperfection is overcome. Replacing the constant damping coefficient with a parabolic spatial function, we reproduce accurately the experimental front–defect interaction.
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