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.

中文翻译：

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液滴在扩散过程中通过具有 T 形结的微孔的四种渗透模式

伴随液滴扩散的渗透是增材制造中众所周知的现象，例如在喷墨印刷和涂层中，自由表面的极端动态演变会影响印刷精度和均匀性。仅通过实验方法很难跟踪渗透界面和动态变形表面。在这里报道的工作中，我们采用无网格计算方法来研究可渗透流体通过 T 形接头的动态行为，以阐明渗透现象。在不同的力和润湿性下研究了四种渗透模式——收缩、悬浮或捕获 (SOC)、不对称横向渗透 (ATP) 和对称横向渗透 (STP)。韦伯数和润湿条件之间的状态图被呈现出来，以揭示渗透模式的机制以及从一种到另一种的转变。主导疏水基材渗透行为的回缩模式已经众所周知（并称为 Cassie-Baxter 状态）。对于亲水条件，渗透模式由惯性力与毛细管力的比值决定。随着惯性力的增加，SOC、ATP 和 STP 模式依次出现。当弯月面界面的最大振幅到达底壁时出现ATP模式，而STP模式依赖于克服毛细力的惯性力。这两种渗透机制导致模式转换的不同趋势。还提出了阵列 T 型接头的多孔模型，以研究渗透和扩散的组合过程。发现液滴扩散过程中渗透模式的各种组合在渗透动力学中起着重要作用，并且横向蠕变的抑制增强了在高度多孔基材上的扩散。