Eduardo O. Dias

Suppression of viscous fluid fingering: A piecewise-constant injection process

The injection of a fluid into another of larger viscosity in a Hele-Shaw cell usually results in the formation of highly branched patterns. Despite the richness of these structures, in many practical situations such convoluted shapes are quite undesirable. In this Brief Report, we propose an efficient and easily reproducible way to restrain these instabilities based on a simple piecewise-constant pumping protocol. It results in a reduction in the size of the viscous fingers by one order of magnitude.

Kinetic undercooling in Hele-Shaw flows.

A central topic in Hele-Shaw flow research is the inclusion of physical effects on the interface between fluids. In this context, the addition of surface tension restrains the emergence of high interfacial curvatures, while consideration of kinetic undercooling effects inhibits the occurrence of high interfacial velocities. By connecting kinetic undercooling to the action of the dynamic contact angle, we show in a quantitative manner that the kinetic undercooling contribution varies as a linear function of the normal velocity at the interface. A perturbative weakly nonlinear analysis is employed to extract valuable information about the influence of kinetic undercooling on the shape of the emerging fingered structures. Under radial Hele-Shaw flow, it is found that kinetic undercooling delays, but does not suppress, the development of finger tip-broadening and finger tip-splitting phenomena. In addition, our results indicate that kinetic undercooling plays a key role in determining the appearance of tip splitting in rectangular Hele-Shaw geometry.

Hamiltonian formulation towards minimization of viscous fluid fingering.

A variational approach has been recently employed to determine the ideal time-dependent injection rate Q(t) that minimizes fingering formation when a fluid is injected in a Hele-Shaw cell filled with another fluid of much greater viscosity. However, such a calculation is approximate in nature, since it has been performed by assuming a high capillary number regime. In this work, we go one step further, and utilize a Hamiltonian formulation to obtain an analytical exact solution for Q(t), now valid for arbitrary values of the capillary number. Moreover, this Hamiltonian scheme is applied to calculate the corresponding injection rate that minimizes fingering formation in a uniform three-dimensional porous media. An analysis of the improvement offered by these exact injection rate expressions in comparison with previous approximate results is also provided.