QUASI-SELF-SIMILARITY FOR WETTING DROPS

We develop and experimentally test a quasi-self-similar solution for t he spreading of viscous nonvolatile droplets over a dry and horizontal solid substrate, under the condition of complete wetting (spreading p arameter S > 0) with both gravity and Laplace pressure as driving forc es. The problem does not admit a self-similar solution because two dim ensional characteristic parameters, namely, the slipping length lambda and the capillary distance a cannot be ruled out. Therefore, we appro ximate the solution by the members of a family of self-similar solutio ns, each one corresponding to different values of the ratios x(f)/a an d h(0)/lambda, where x(f) and h(0) are the instantaneous drop extensio n and central thickness, respectively. This treatment of the problem a lso produces an explicit formula (which must be integrated) to predict the drop radius. The excellent agreement with our own and other autho rs' experimental data suggests that the approach can be considered as an interesting tool for solving problems where strict self-similarity fails.