Fingering patterns on an expanding miscible drop in a rotating Hele-Shaw cell

We perform a detailed numerical study for the evolution of an expanding miscible drop in a rotating Hele-Shaw cell. Two mathematical formulations applied to model the coating layer expansion during practical spin-coating process, such as thinning of the layer by cell pressing and drop spreading outward due to injection, are investigated. Including miscible interfacial stresses, we focus on the investigation of dynamical and morphological influences of two different stabilizing parameters: the gap width parameter for the pressing cell and the injecting strength. In the case of a pressing cell, the fingering features of the expanding miscible drop, such as the critical radius, are distinct from those ones in the experiments of spin coating due to the different distributions of the inherent radial velocity. On the other hand, the global interfacial evolutions of an expanding drop with an additional injection bear remarkable resemblances to their immiscible counterparts. The better agreement for an injecting model suggests its appropriateness when we simulate the emerging fingering instabilities in the spin-coating process. Moreover, we investigate the effects of Coriolis force at higher miscible Bond numbers. Coriolis force affects significantly the onset of fingering instability and the tilting angles of fingers. These stable effects are in line with the results from the previous studies for miscible and immiscible flow fields. Copyright (c) 2007 John Wiley & Sons, Ltd.