Role of solutal free convection on interdiffusion in a horizontal microfluidic channel

Jean-Baptiste Salmon (1) , Laurent Soucasse (2) , Frédéric Doumenc (3, 4)

1 LOF - Laboratoire du Futur
2 EM2C - Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion
3 FAST - Fluides, automatique, systèmes thermiques
4 UFR 919 - Sorbonne Université - UFR d'Ingénierie

We theoretically studied the role of solutal free convection on the diffusion of a buoyant solute at the microfluidic scales, ~5–500 μm. We first considered a horizontal microfluidic slit, one half of which is initially filled with a binary solution (solute and solvent) and the other half with pure solvent. The buoyant forces generate a gravity current that couples to the diffusion of the solute. We performed numerical resolutions of the 2D model describing the transport of the solute in the slit. This study allowed us to highlight different regimes as a function of a single parameter, the Rayleigh number Ra which compares gravity-induced advection to solute diffusion. We then derived asymptotic analytical solutions to quantify the width of the mixing zone as a function of time in each regime and established a diagram that makes it possible to identify the range of Ra and times for which buoyancy influences the transport of solute. Interestingly, we recovered the same succession of regimes as in the case of a 2D porous layer, with the same scaling laws but significantly different numerical prefactors. In a second step, we performed numerical resolutions of the same model but for a 3D microfluidic channel with a square cross section using an in-house made software, specifically optimized for the simulation of free convection in cavities on parallel architectures and based on a multidomain spectral method. We observed the same regimes as in the 2D case and focused on the dispersion regime at long timescales. We then derived analytically the expression of the 1D dispersion coefficient for a channel with a rectangular section and analyzed the role of the transverse flow in the particular case of a square section. Finally, we showed that the impact of this transverse flow on the solute transport can be neglected for most of the microfluidic experimental configurations. References: J.-B. Salmon, L. Soucasse, F. Doumenc, Phys. Rev. Fluids 6, 034501 (2021)

Mots clés: free convection; dispersion; microfluidic

Domaines: Mécanique des fluides [physics.class-ph]

Jean-Baptiste Salmon, Laurent Soucasse, Frédéric Doumenc. Role of solutal free convection on interdiffusion in a horizontal microfluidic channel. 2nd Fluids and complexity Conference, Nov 2021, Nice, France. . ⟨hal-04402169⟩