Spreading of droplet with insoluble surfactant on corrugated topography

Abstract

The flow of microscale fluid on a topography surface is a key to further development of MEMS, nanoscience and technology. In the present paper, a theoretical model of the droplet spreading with insoluble surfactant over corrugated topography is established with the lubrication theory, and the evolution equations of film thickness and surfactant concentration in base state and disturbance state are formulated. The droplet dynamics, the nonlinear stability based on nonmodal stability theory, and the effects of topography structure and Marangoni stress are numerically simulated with PDECOL scheme. Results show that the impact of topographical surface is strengthened apparently while the Marangoni stress driven by surfactant concentration is weakened in the mid-late stages of the spreading. The droplet radius on the topography advances faster and the lowest height of liquid/gas interface near the droplet edge reduces remarkably in the intermediate stage compared with those on the flat wall. The quantity of the wavelet similar to the topography increases gradually, with the characteristics of wavelet crest height with time exhibiting a single-hump feature. The spreading stability is enhanced under the disturbance wavenumber of 4, however, is to deteriorate and even to transform into instability when wavenumber increases further. In addition, the reductive Marangoni number, enhancive capillary number, modest Peclet number, the low height of the topography as well as small wavenumber of topography can make contributions to the evident stability of droplet spreading.