The role of a pre-wetting layer in resolving the contact line paradox of thin films in infinite elastic domains

Abstract

Hydraulic fracturing for oil and gas production from shale formations, as well as natural geological phenomena, involve the propagation of thin viscous films within elastic media. For viscous fluids, stress diverges as the thickness of the film tends to zero, arresting the propagation of the film, and thus implying the contact line paradox. For free-surface films, this paradox is resolved by considering a precursor film, leading to Tanner's law. This approach was extended recently for viscous films between a thin elastic plate and a rigid solid, allowing calculation of the film propagation rate. In this work, we examine the effect of a pre-wetting layer on the rate of propagation of a viscous flow within an infinitely deep and long domain. We analyse the linear and nonlinear dynamic problems, and perform a self-similarity analysis. We find that peeling front propagation scales as time to the power of $1/9$ and $1/3$ for thin and thick pre-wetting layer limits, respectively. Our results contribute to the understanding of the contact line paradox in elastic media and the crucial role of the pre-wetting layer in resolving it.