Analysis and simulations of droplet generation regimes in a coaxial microfluidic device

TL;DR

The paper develops and validates a Basilisk-based framework for predicting microdroplet generation by segmentation in coaxial microfluidic devices, spanning squeezing, dripping, and jetting regimes. It couples a sharp interface VOF method with CSF surface tension, height-function curvature, and embedded boundary geometry to solve the incompressible Navier–Stokes equations for two immiscible fluids, and introduces comprehensive regime maps and new scaling laws that incorporate viscosity-ratio effects. Through validation against Bretherton theory, Taylor-bubble dynamics, and literature experiments, the study demonstrates Basilisk’s accuracy and offers practical guidance for device design, including regime prediction and droplet-diameter scaling. The findings highlight the importance of viscosity ratio in regime transitions and size control, and suggest avenues for extending to 3D geometries and more advanced boundary conditions for broader microfluidic applications.

Abstract

The generation of microdroplets via segmentation in microfluidic devices is of interest in many applications, from biochemical to pharmaceutical. This technique permits indeed much higher control on the droplet size, uniformity and generation rate than in standard batch generation processes. In this work we have evaluated the suitability of the open-source software Basilisk to accurately predict microdroplet generation by segmentation. We have validated the numerical tool with analytical solutions for the dynamics of droplets in confined flows, namely with Bretherton theory, and by comparison with literature experimental results. We have then performed several campaigns of numerical simulations for a coaxial device, analyzing the different regimes of droplet generation, and evaluating how the physical and flow parameters affect the production mechanisms and {the diameters of the generated droplets}. Finally we have proposed new scaling laws for the prediction of droplet diameters in the dripping and jetting regimes, refining existing ones by taking into account additional physical effects, like the viscosity ratio.

Figures (14)

• Figure 1: Example of grid adaptivity for the Taylor bubble at $Re=0.1$. Left panel $Ca = 0.1$, maximum resolution $H/\Delta = 204$, right panel $Ca = 0.001$, maximum resolution $H/\Delta = 410$.
• Figure 2: (a) Grid convergence for $Ca=0.001$ and $Re=0.1$: droplet terminal velocity at different grid resolution and for different adaptivity thresholds. The red line represents the steady state value obtained with the semi-empirical relations aussillous2000quick. (b) Temporal evolution of the droplet terminal velocity with different tolerance for the multigrid Poisson equation resolution. (c) Droplet terminal velocity at different Capillary numbers compared to Bretherton theory bretherton1961motion and literature semi-empirical relations aussillous2000quick. (d) Droplet shapes for different Capillary numbers, at different times.
• Figure 3: Sketch of the coaxial device.
• Figure 6: Thread length: minima represents pinchoff position. (a): dripping case. (b): jetting case. Evaluation of different maximum level of refinement and different adaptivity threshold criteria.
• Figure 7: Maps of droplet generation regimes as a function of $Ca_c$ and $We_d$. Blue squares denotes squeezing, red circles dripping, and green triangles jetting. Black lines are the transition zones of Utada et al.utada2007dripping Fig. 4. Each panel represents a different campaign of simulations.