Direct numerical simulation of deformable droplets motion with uncertain physical properties in macro and micro channels

The lateral migration rate, equilibrium position of droplets and their final distribution determine the main characteristics of multiphase flows within channels such as total flow rate and pressure drop. Since the performance of inertial microfluidics in the context of classification and sorting of cells relies deeply on migration rate as well as the distribution of particles suspended in the carrier fluid moving within a micro-channel, the subject becomes more critical when we move toward micro-scale problems . The main parameters dominate the flow field are viscosity ratio, density ratio, drops deformability, Reynolds number (Re) and the ratio of drops diameter to channel height. Changes in these parameters result in new and different flow conditions, and therefore lead to different migration rates and particle distribution patterns. In order to understand the effect of uncertainty in material properties such as viscosity, we conduct numerical simulations on deformable droplets motion within two-dimensional macro and micro-scale channels using combination of front tracking method and a newly proposed Uncertainty Quantification (UQ) model. The deformable droplet motion in both macro and micro-scale channels are studied in two separate sections of this paper. In each section, the deterministic case is investigated using front tracking method and the accuracy of the results is verified by comparison with the available data in the literature. Next, along with Monte-Carlo methods, the proposed stochastic particle tracking (SPT) approach is applied to propagate the uncertainties associated with droplet physical properties to flow variables. Numerical experiments indicate a faster convergence rate for this approach with respect to the number of samples in comparison with Monte Carlo and Quasi-Monte Carlo simulations.