A generalized analytical model for investigating flow dynamics influenced by wall wettability in capillary-driven microfluidics

Capillarity is a key mechanism for fluid control in microfluidic devices, enabling, for example, liquid movement without external pumps. This study develops and validates an analytical model to describe the velocity and displacement of the liquid meniscus in three-dimensional microfluidic channels with walls exhibiting different wettability. Particular focus is placed on the transient behavior of the meniscus during the initial phases of channel filling, a critical yet often overlooked aspect for optimizing flow control. This is especially relevant given the growing adoption of capillary pumps and valves in microfluidic systems. To evaluate the validity and reliability of the proposed model under diverse operating conditions, channels with different geometries and dimensional ratios were fabricated using various materials and techniques. Experimental results confirm the model’s accuracy, even in complex configurations, with relative errors ranging from 7\(\%\) to 10\(\%\).