PhD

Simulation of multi-component flows by the lattice Boltzmann method and application to the viscous fingering instability

The lattice Boltzmann method (LBM) is a specific discrete formulation of the Boltzmann equation. Since its first premises, thirty years ago, this method has gained some popularity and is now applied to almost all standard problems encountered in fluid mechanics including multi-component flows.

Simulation of multi-component flows by the lattice Boltzmann method and application to the viscous fingering instability

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Multi-component flows

In nature, chemical compounds commonly mix each other. One of the elemental material in fluid mechanics, air, is predominantly composed of two components: nitrogen ($\text{N}_2$, $\approx 78\%$) and oxygen ($\text{0}_2$, $\approx 21\%$). Mass transfer seems at first sight not something too complicated: a species should move down its concentration gradient. This is known as the first Fick's law, which can be written for two components as \[ \mathbf{J}_1=-\mathcal{D}\frac{dc_1}{dz}, ~ \text{and } J_2=-J_1\]

Viscous Fingering Instability

Viscous fingering is an ubiquitous instability that occurs when a less viscous fluid displaces a more viscous fluid in a porous medium. The interface between the two fluids starts to deform, and finger-like patterns emerge and grow. This phenomenon can either increases the mixing in porous media, which is incredibly difficult because of the absence of turbulence that can actively stir the flow or be dramatic to some processes. The typical example is secondary oil recovery, for which fingering from the injected aqueous solution pushing the more viscous oil in underground reservoirs of porous rocks reduces the sweep efficiency severely.