Numerical simulations of cell sorting through inertial microfluidics

The dynamics of a cell suspended in a Newtonian liquid subjected to a pressure-driven flow at non-negligible inertia in cylindrical and square cross section microfluidic channels is studied through three-dimensional arbitrary Lagrangian-Eulerian finite-element numerical simulations. The cell is modeled through the neo-Hookean hyper-elastic constitutive equation, which can describe biological particles undergoing moderate deformations. The cell-to-channel relative dimension is fixed to 0.2, whereas the Reynolds number Re, measuring the relative importance of liquid inertial and viscous forces, and the elastic capillary number Ca e, measuring the relative importance of liquid viscous stress and solid elastic stress, are varied by several orders of magnitude. In a cylindrical tube, the cell migrates transversally to the flow direction until reaching a radial equilibrium position depending on Re and Ca e. Given Re, the softer the cell (i.e., the larger Ca e) the closer its equilibrium position to the tube axis, thus allowing for the separation of healthy and diseased cells which have similar dimensions but different mechanical properties. In a channel with a square cross section, a much more complex dynamics is found. Depending on Re and Ca e, the cell can either migrate to the channel centerline, to the closest median of the channel cross section (thus, four equilibrium positions can be identified due to symmetry), to the closest diagonal (again, four equilibrium positions), or to an intermediate position in between the median and the diagonal (eight equilibrium positions).