Dynamics of droplet migration in oscillatory and pulsating microchannel flows and prediction and uncertainty quantification of its lateral equilibrium position using multifidelity Gaussian processes

The dynamics of a droplet in oscillatory and pulsating flows of a Newtonian fluid in a microchannel has been studied numerically. The effects of oscillation frequency, surface tension, and channel flow rate have been explored by simulating the drop within a microchannel. These types of flows introduce new equilibrium positions for the drop compared to steady flows with similar conditions. The simulation results are very sensitive to the grid resolution due to the unsteady behavior of the base flow. Therefore, a set of fine grids have been used in this study to capture the physics of this problem more accurately. However, these fine grids make the computations significantly expensive. Therefore, a multifidelity Gaussian processes method with two levels of fidelity has been used to predict the results of the remaining fine-grid simulations along with their uncertainties based on their correlations with those of the coarse-grid cases over a wide range of input parameters.