Spontaneous fingering between miscible fluids

Abstract

Diffusion-initiated interfacial dynamics between two miscible fluids are investigated. Heptane is diffused into viscous crude oil in a microscale Hele-Shaw cell. No external pressure gradients are applied; hence, the imposed Peclet number is zero. Surprisingly, the diffusive/dispersive process is dictated by a two-stage dispersive mechanism owing to the multicomponent character of the crude oil. Stage I is distinguished by the spontaneous fractal-like fingering of heptane into the crude oil phase due to diffusive preferential light components extraction from the crude oil. Stage II is characterized by diffusive miscible fluid-pair mixing between the heptane and the heavy components in the crude oil. Preferential diffusive extraction of light components exceeds the diffusion between heptane and heavy components in stage I, thereby allowing a distinct interface to form between heptane and the crude oil. Compositional gradients induce dynamic interfacial tension gradients that lead to convection. Convection cells at the finger tips dictate local mass exchange and drive the self-similar fractal-like finger splitting. Fractal analysis of the fingering process shows increasing fractal dimensionality during the early diffusively-dominant fingering regime approaching that of diffusion-limited aggregation (Df ∼ 1.67), and a drastic decrease in fractal dimensionality thereafter due to small-scale convection (Df ∼ 1.55). We characterize the fractal finger growth and mass exchange, and calculate the local dynamic interfacial tension. We find that spontaneous fingering, i.e., the occurrence of stage I, requires gap spacing less than 15 μm in the current system and the presence of light extractable components in the crude oil.