The Interpretation of Dynamic Contact Angles Measured by the Wilhelmy Plate Method

We present an analysis for properly interpreting apparent dynamic contact angles measured using the Wilhelmy plate method at low capillary numbers, Ca. This analysis removes the ambiguity in current dynamic measurements which interpret data with the same formula as static measurements. We properly account for all forces, including viscous forces, acting on the plate as it moves into or out of a liquid bath. Our main result, valid at O(1) as Ca --> 0, relates the apparent dynamic contact angle to material-dependent, geometry-independent parameters necessary for describing dynamic wetting of a system. The special case of the apparent contact angle = pi/2 was solved to O(Ca). This O(Ca) solution can guide numerical work necessary for higher Ca's and arbitrary values of the apparent contact angle. These results make the Wilhelmy plate a viable method for determining material parameters for dynamic spreading.