Elasto-capillary modulated filling dynamics in deformable microchannels

Surface tension mediated fluid–structure interactions, or elasto-capillarity, play a pivotal role in a wide range of micro-fluidic applications, as well as in physiological flows. In this study, we analyze the capillary-driven transport of a Newtonian fluid in a thin, cylindrical, deformable microchannel. Through a reduced order model, we rigorously study the dynamics of capillary rise in the channel, highlighting the importance of wall elasticity. Both horizontal and vertical channels, as well as closed and open-ended capillaries are considered. The long-time oscillations in the capillary penetration length are studied through a linearized model. Elasto-capillary instabilities are demonstrated by means of a full-order computational model, whose results compare favorably with that of the analytical model. We showcase that the capillary walls deflect inwards on account of the Laplace pressure drop across the liquid–gas interface. Through a scaling estimate, we report that this deflection does not alter the scaling in both the initial inviscid as well as in the viscous Washburn regime, although it does decrease the Washburn coefficient. Additionally, we report a giant augmentation of the equilibrium (or Jurin) height with elasticity of the channel wall. Finally, we delineate parametric regimes that dictate the occurrence of near-Jurin height oscillations, highlighting a distinct suppression of the oscillations for softer channel walls. Our findings offer an alternative method of controlling both the dynamics of capillary-driven transport at the micro- and nano-scales, by fine-tuning the interplay between the surface tension induced deformability of the channel walls, fluid viscosity, and gas pressure.