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A variational approach has been recently employed to determine the idealtime-dependent injection rate Q(t) that minimizes fingering formation when afluid is injected in a Hele-Shaw cell filled with another fluid of much greaterviscosity. However, such a calculation is approximate in nature, since it hasbeen performed by assuming a high capillary number regime. In this work, we goone step further, and utilize a Hamiltonian formulation to obtain an analyticalexact solution for Q(t), now valid for arbitrary values of the capillarynumber. Moreover, this Hamiltonian scheme is applied to calculate thecorresponding injection rate that minimizes fingering formation in a uniformthree-dimensional porous media. An analysis of the improvement offered by theseexact injection rate expressions in comparison with previous approximateresults is also provided.

Hamiltonian formulation towards minimization of viscous fluid fingering