Numerical analysis of the deformation of an adherent drop under shear flow

The adhesion of leukocytes to substrates is an important biomedical problem and has drawn extensive research. In this study, employing both single and compound drop models, we investigate how hydrodynamics interacts with an adherent liquid drop in a shear flow. These liquid drop models have recently been used to describe the rheological behavior of leukocytes. Numerical simulation confirms that the drop becomes more elongated when either capillary number or initial contact angle increases. Our results show that there exists a thin region between the drop and the wall as the drop undergoes large stretching, which allows high pressure to build up and provides a lift force. In the literature, existing models regard the leukocyte as a rigid body to calculate the force and torque acting on the drop in order to characterize the binding between cell receptors and endothelial ligands. The present study indicates that such a rigid body model is inadequate and the force magnitude obtained from it is less than half of that obtained using the deformable drop models. Furthermore, because of its much higher viscosity, the cell nucleus introduces a hydrodynamic time scale orders of magnitude slower than the cytoplasm. Hence the single and compound drops experience different dynamics during stretching, but exhibit very comparable steady-state shapes. The present work offers a framework to facilitate the development of a comprehensive dynamic model for blood cells.