Depinning regimes and contact angle hysteresis of a drop on doubly periodic microtextured surfaces

We investigate numerically the drop shape evolution under quasistatic drop volume change on doubly periodic microtextured surfaces in the framework of the capillary model. Taking into account the symmetries of the periodic lattice of defects, we study the drop contact line (CL) motion along all lines of symmetry, allowing us to get a more complete view of the CL behavior. Four CL depinning regimes for a liquid drop are distinguished related to the stick, slip, and jump motion of the CL. The distinction of the different regimes is made based on the region of the CL where the process starts and on whether the start of the depinning is related to detaching from a defect or to the CL reaching a new row of defects. For every type of depinning regime we study the advancing and receding apparent contact angles (CAs) as functions of the defect concentration. We established a relation between the results for the CL depinning and the CA hysteresis (CAH) for a drop on hydrophilic and hydrophobic heterogeneous surfaces. A comparison of the obtained numerical results for the CAH is made with the existing theoretical, experimental, and numerical data.