Advances of capillary filling of Newtonian fluids in micro- and nanochannels

Abstract

Capillary filling is extensively involved in natural science and engineering technology, such as oil recovery, building conservation, ink printing, etc. Due to large surface to volume ratio, capillary action is very prominent at micro- and nonoscale regime, and recent years it has triggered a tremendous acceleration of research related to the capillary filling process in micro- and nanochannels. For instance, the capillary action is used to eliminate some additional accessories such as electric drive devices or syringe pumps, which can greatly simplify the design of microfluidic and nanofluidic devices. All these facts show that a thorough understanding of the kinetics of capillary-driven filling in micro- and nanochannels is of great significance. Almost a century ago, Lucas and Washburn reported an analytical solution for capillary filling of Newtonian fluids in a small cylindrical capillary tube: the filling distance is proportional to the square root of time, which is also known as the classical LW equation. Although the LW equation can well describe macroscopic capillary filling process, it’s availability at micro- and nanoscale regime is still an open question, which has attracted a lot of attention. This paper summarizes the progress of capillary filling kinetics in micro- and nanochannels in views of theoretical models, numerical simulations and experimental studies. All the three perspectives indicate that the capillary filling process should be discussed by dividing into four stages as follows: (1) purely inertial time stage, where the filling distance is proportional to the time t ; (2) visco-inertial time stage, where the inertia force, capillary force and viscous force have comparable effect on the filling kinetics; (3) purely viscous time stage, where the capillary force is balanced by viscous force and the filling distance is linearly related to the t 1/2; (4) the gravity should be considered when the pipe is vertical and there is a viscous and gravitational time stage. In purely viscous time stage, the LW equation can qualitatively describe the capillary filling process in micro- and nanochannels. Quantitatively, however, significant deviations between the experiment or simulation results and theoretical expectations have been observed in capillary filling process. Although several factors are considered to explain the deviation, such as the dynamic contact angle, bubble formation, electro-viscous effect and other factors, there is no unified understanding on the capillary filling kinetics. Finally, possible pending problems are summarized based on the results in previous work. In addition, brief introduction and prospect have been made on capillary filling of non-Newtonian fluids.