The role of the oil/water viscosity ratio kappa and the wettability (expressed as equilibrium contact angle theta(eq)) during forced imbibition in a nonplanar (two-layer) porous medium is investigated experimentally. The results show that kappa and theta(eq) act in combination not only for intermediate and large capillary numbers, but also for small values, say Ca less than or equal to 10(-6). Extensive capillary microfingering is observed, and the residual oil saturation S-or increases as theta(eq) decreases and kappa increases. This behavior becomes more significant at small contact angles and small Ca values. This phenomenon is attributed to the combined effect of the sizeable precursor wetting film and the local viscous forces. The velocity gradients that are created by the fast motion of either a meniscus in a single pore or the wetting film are sufficiently large to render viscous stresses important locally, even when the Ca value is very low, that is, even when the viscous stresses are negligible on a macroscopic scale.