(378c) Capillary Driven Flow in Axially Interacting Multi-Capillary System

Impregnation of a liquid in an empty capillary follows Washburn’s diffusive dynamics. Washburn’s dynamics also state that larger radius capillary fills faster due to less resistivity, even though the capillary pressure is less. However, if two capillaries are axially interacting, the smaller radius capillary fills faster. If the three interacting capillaries are used, the largest radius capillary will have slowest imbibition of the liquid, while the fastest moving meniscus can be in either of the other two capillaries. This is because, in the three interacting capillary system, we can have different relative radii of the capillaries and their position with respect to each other can be shuffled. Therefore, in a multi-capillary system the imbibition behavior is complex. We develop a generalized one-dimensional lubrication approximation model to predict the impregnation behavior in an interacting multi-capillary system. It is observed that, the flow dynamics is governed by the contrast in the radii of the capillaries and their arrangement within the multi-capillary system. the radius of the capillary through which the fluid reaches the exit and time it takes the liquid to reach the exit (breakthrough time) change significantly with the change in the arrangement of capillaries. We take example of a 20 capillary system of capillary radii ranging between 10 µm and 200 µm and observe that the dimensionless breakthrough time ranges between 0.31 and 0.42 and the radius of the capillary through which the impregnating fluid breaks through can be between 10 µm and 100 µm. The multi-capillary system which does not interact is used to find flow properties of a porous medium. Here we show that for the cases where capillary pressure is significant and pores interact with each other we need to take into account the behavior of interacting capillary system.