Hydrodynamic resistance and mobility of deformable objects in microfluidic channels

This work reports experimental and theoretical studies of hydrodynamic behaviour of deformable objects such as droplets and cells in a microchannel. Effects of mechanical properties including size and viscosity of these objects on their deformability, mobility, and induced hydrodynamic resistance are investigated. The experimental results revealed that the deformability of droplets, which is quantified in terms of deformability index (D.I.), depends on the droplet-to-channel size ratio $ρ$ and droplet-to-medium viscosity ratio $λ$⁠. Using a large set of experimental data, for the first time, we provide a mathematical formula that correlates induced hydrodynamic resistance of a single droplet $ΔRd$ with the droplet size $ρ$ and viscosity $λ$⁠. A simple theoretical model is developed to obtain closed form expressions for droplet mobility $ϕ$ and $ΔRd$⁠. The predictions of the theoretical model successfully confront the experimental results in terms of the droplet mobility $ϕ$ and induced hydrodynamic resistance $ΔRd$⁠. Numerical simulations are carried out using volume-of-fluid model to predict droplet generation and deformation of droplets of different size ratio $ρ$ and viscosity ratio $λ$⁠, which compare well with that obtained from the experiments. In a novel effort, we performed experiments to measure the bulk induced hydrodynamic resistance $ΔR$ of different biological cells (yeast, L6, and HEK 293). The results reveal that the bulk induced hydrodynamic resistance $ΔR$ is related to the cell concentration and apparent viscosity of the cells.