Roughness exponents of the liquid/vapor/solid contact line on surfaces with dilute random Gaussian defects: numerical...

We study here the roughness exponents of the averaged contact line width of a liquid in contact with flat, weakly heterogeneous substrates containing dilute, randomly distributed Gaussian-type defects. For this purpose, we employ the full capillary model. The obtained results for the magnitude of the averaged root-mean-square width of the contact line show that there is only one interval in which the width scales with length as a power function. The numerical studies and analysis indicate that this interval should be regarded as a length scale smaller than the jog length. The roughness exponent found is not a universal constant independent of the apparent contact angle formed by the liquid on the solid surface. It closely approaches the theoretically predicted value of 1/2 [M. O. Robbins, and J. F. Joanny, Europhys. Lett. 3, 729 (1987)] only within the contact angle ranges of ${10}^{\circ }$ to ${30}^{\circ }$ and ${150}^{\circ }$ to ${170}^{\circ }$ . Furthermore, it can be considered that there is still a significant range of contact angles, from ${55}^{\circ }$ up to ${125}^{\circ }$ , in which the roughness exponent remains practically constant, however, having a value of 0.8.