A two-angle model of dynamic wetting in microscale capillaries under low capillary numbers with experiments.

OBJECTIVES: An accurate model of the dynamic contact angle θd is critical for the calculation of capillary force in applications like enhanced oil recovery, where the capillary number Ca ranges from 10-10 to 10-5 and the Bond number Bo is less than 10-4 . The rate-dependence of the dynamic contact angle under such conditions remains blurred, and is the main target of this study.

EXPERIMENTS: Featuring with pressure control and interface tracking, the innovative experimental system presented in this work achieves the desired ranges of Ca and Bo, and enables the direct optical measurement of dynamic contact angles in capillaries as tiny as 40 × 20 (width × height) μm and 80 × 20 μm. The advancing and receding processes of wetting and nonwetting liquids were tested.

FINDINGS: The dynamic contact angle was confirmed velocity-independent with 10-9  < Ca < 10-5 (contact line velocity V = 0.135-490 μm/s) and it can be described by a two-angle model with desirable accuracy. A modified two-angle model was developed and an empirical form was obtained from experiments. For different liquids contacting the same surface, the advancing angle θadv approximately equals the static contact angle θo . The receding angle θrec was found to be a linear function of θadv , in good agreement with our and other experiments from the literature.