Dense emulsions, colloidal gels, microgels, and foams all display a solid-like behavior at rest characterized by a yield stress, above which the material flows like a liquid. Such a fluidization transition often consists of long-lasting transient flows that involve shear-banded velocity profiles. The characteristic time for full fluidization, $tau_text{f}$, has been reported to decay as a power-law of the shear rate $dot gamma$ and of the shear stress $sigma$ with respective exponents $alpha$ and $beta$. Strikingly, the ratio of these exponents was empirically observed to coincide with the exponent of the Herschel-Bulkley law that describes the steady-state flow behavior of these complex fluids. Here we introduce a continuum model, based on the minimization of a free energy, that captures quantitatively all the salient features associated with such textit{transient} shear-banding. More generally, our results provide a unified theoretical framework for describing the yielding transition and the steady-state flow properties of yield stress fluids.
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