Hydrodynamic focusing in porous media and its ramifications on the critical penetration depth

The effect of hydrodynamic focusing through porous media is analytically investigated to ascertain the critical thickness such that liquids do not completely penetrate the media. The flow field of a single drop impacting a surface with any number of pores is established by solving the Laplace equation resulting from an instantaneous pressure impulse as prescribed by impact dynamics. Complex analysis is utilized to transform the drop into the complex plane via conformal mapping in order to determine the liquid velocity penetrating into the pores. The critical penetration of the drop into the porous media occurs when the kinetic energy of the drop, known as a function of the penetration velocity, is dissipated by viscous friction. It was found that hydrodynamic focusing in multi-pore surfaces occurs, and the liquid penetration velocity rapidly diminishes as the number of pores increases. Moreover, the critical thickness of a porous media also rapidly diminishes as the number of pores increases and importantly, plateaus. Implications for liquids splashing onto garments is discussed.