We examine the dynamics of a miscible displacement in a capillary, calculating the nonequilibrium capillary pressure of a moving (and slowly diffusing) miscible meniscus. During the displacement, the capillary pressure varies with time following stretching and smearing of a miscible interface. The capillary pressure remains different from zero for a long time (on a diffusion time scale), slowing the displacement. This capillary pressure is however completely ignored by all theories currently available for practical modeling of miscible displacements in capillaries and porous matrices.
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