379038 Control and Stabilization of Radial Viscous Fingering Using Time-Dependent Strategies

Wednesday, November 19, 2014: 8:30 AM
M304 (Marriott Marquis Atlanta)
Zhong Zheng, Hyoungsoo Kim and Howard A. Stone, Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ

Control and stabilization of the immiscible viscous fingering has attracted great research interests recently. In this paper, we report a general form of the time-dependent control strategies, which either completely stabilize the fluid displacement process or maintain a constant number of viscous fingers during the fluid displacement process. We first derive the general form of the control strategies based on linear perturbation theory. The strategies include manipulation of the injection rate, the gap-thickness between the two parallel plates, the viscosity of the injecting fluid, and the interfacial tension between the two immiscible fluids. We then demonstrate the effectiveness of these time-dependent strategies by manipulating the gap thickness in the power-law form $b(t) propt t^{1/7}$ as an example. Experimental results show very good agreement with the predictions of linear perturbation theory, both qualitatively and quantitatively. From the value of a single time-independent control parameter $J$, we are able to either stabilize the fluid displacement process or maintain a series of non-splitting viscous fingers.

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