Synergistic effects of geometry, inertia, and dynamic contact angle on wetting and dewetting of capillaries of varying cross sections

Understanding the role of geometry, inertia, and dynamic contact angle on wetting and dewetting of capillary tubes has theoretical and practical aspects alike. The specific and synergistic effects of these factors were studied theoretically using a mathematical model that includes inertial and dynamic contact angle terms. After validating the model for capillaries of uniform cross section, the model was extended to capillaries with sinusoidal modulations of the radius, since in practice, capillaries rarely have uniform cross-sections. The height of the meniscus during wetting and dewetting was significantly affected by the relations between the local slope of the capillary surface and the Young contact angle. Non-dimensional variables were defined using viscous effects and gravity as the scaling parameters. Simulations using the dimensionless model showed that the inertial and dynamic contact angle terms can be neglected for narrow capillaries of uniform cross-section but not for uniform, wide cross-section capillaries. Moreover, nonuniformity in cross-sectional area induced hysteresis, deceleration, blocking, and metastable equilibrium locations. An increase in contact angle further amplified the effect of geometry on wetting and dewetting processes. These results enable characterization and modeling of fluid retention and flow in porous structures that inherently consist of capillaries of varying cross section.