(409g) Spontaneous Imbibition and Forced Wetting in Closed Square Capillaries and Open Rectangular Grooves

Spontaneous imbibition and forced wetting in closed capillaries and open grooves with corners impact fluid movement in microfluidic devices and porous media. The bulk capillary flows in both cornered capillaries and rectangular grooves with sizes on the order of the capillary length of the fluid are similar to that in cylindrical capillaries. However, the fluid interface is forced to attain a tight radius near the interior corners, enhancing capillary effects which result in the formation of rivulets rising in the corners.

In this computational study, we investigate the capillary driven flows in square capillaries and rectangular grooves under gravity. The flow is modelled using Volume-of-Fluid method and the free surface is accurately tracked using adaptive mesh refinement. The influence of the parameters such as liquid viscosity, gravity, contact angle and the capillary size are investigated. The bulk flows are compared with experiment for both spontaneous imbibition and forced wetting.

As predicted by theoretical analysis of capillary rise in isolated corners, results of the computations show that the rivulets are formed in interior corners of the capillaries and grooves only when the contact angle is less than 45 degrees. In capillaries and grooves with widths smaller than the capillary length, at long times, the rivulet height grows proportional to the one-third power of time (h ~ t^1/3)as predicted for isolated corners. For open grooves, the meniscus forms a cusp on the outer corner which is removed when the lateral face of the groove becomes small.