Numerical simulations of interfacial instabilities on a rotating miscible droplet in a time-dependent gap Hele–Shaw cell with significant Coriolis effects

✍ Scribed by Chen-Hua Chen; Ching-Yao Chen

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 260 KB
• Volume: 51
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/fld.1142

✦ Synopsis

Abstract

Interfacial instability of a rotating miscible droplet with significant Coriolis force in a Hele–Shaw cell is simulated numerically. The influences of the relevant control parameters are first discussed qualitatively by fingering patterns. More vigorous fingerings are found at higher rotational effects, a lower viscosity contrast and a weaker effective surface tension (Korteweg constant). For a time‐dependent gap Hele–Shaw cell, a higher cell lifting rate makes the rotating droplet bear an inward straining flow, which leads to fingering enhancement. On the contrary, a higher pressing rate provides more stable effects by additional squeezing outward flow. A quantitative analysis between the Coriolis effects and tilting angles of fingers is addressed. For arbitrary combinations of all relevant control parameters, the values of tilting angles follow a nearly linear relationship with the Coriolis effects. We estimate the correlation between the relevant control parameters (dimensionless Coriolis factor Re, viscosity parameter R, cell lifting rate a) and tilting angles (θ) of fingers that can be approximated as $\theta = (0.0047\sqrt {Pe/R} + 18.2a)Re$ for significant Korteweg stresses. Copyright © 2005 John Wiley & Sons, Ltd.