Four Modes of Droplet Permeation Through a Micro-pore with a T-Shaped Junction During Spreading

Abstract

Permeation accompanying droplet spreading is a well-known phenomenon in additive manufacturing, for example in inkjet printing and coating, where the extremely dynamic evolution of the free surface influences printing accuracy and uniformity. It is exceedingly difficult to track the permeation interface and dynamically deformed surface by experimental methods alone. In the work reported here, we adopted a meshless computational method to investigate the dynamic behavior of the permeable fluid passing through a T-shaped junction to elucidate the permeation phenomenon. Four permeation modes—retraction, suspension or capture (SOC), asymmetric transverse penetration (ATP), and symmetrical transverse penetration (STP)—have been studied under different forces and wettability. Regime maps between the Weber number and the wetting conditions are presented to reveal the mechanisms of the permeation modes and the transitions from one to another. The retraction pattern that dominates the permeation behavior on a hydrophobic substrate is already well known (and called the Cassie–Baxter state). For the hydrophilic condition, the permeation pattern is determined by the ratio of the inertia force to the capillary force. The SOC, ATP, and STP modes emerge sequentially as the inertia force rises. The ATP mode occurs when the maximal amplitude of the meniscus interface reaches the bottom wall, and the STP mode depends on the inertia force overcoming the capillary force. These two permeation mechanisms result in different tendencies of mode transition. A porous model of arrayed T-junctions is also presented to investigate the combined process of permeation and spreading. It is found that various combinations of permeation modes during droplet spreading play an important role in the permeation dynamics, and that inhibition of transverse creeping enhances the spreading on a highly porous substrate.