3D computational modeling and simulation are presented on adhesion, deformation, rolling and detachment of a liquid capsule on adhesive surfaces in shear flow with an objective to understand the adhesive rolling motion of biological cells, such as leukocyte and cancel cells, and the coupling between cell deformation and biophysics of adhesive bonds. The computational model is based on an immersed boundary method for deformable capsules, and a finite difference-Fourier transform technique for solving the complete Navier-Stokes equations. The flow solver is coupled with a Monte Carlo simulation representing random process for bond formation and breakage between the capsule and the adhesive surface. Four sets of simulations are presented. In the first set, we cosider initial capture of a capsule by a single bond. The ratio of forward to reverse reaction rates for bond formation is set to infinity with an objective to understand the role between the adhesion force and capsule deformability. Under this condition, the capsule reaches a steady state with a tear-drop shape and a flattened contact area with the surface. The timescale to attain the steady state is computed as a function of adhesion strength and capillary number. It is observed that the timescale drops sharly with increasing adhesion strength and quickly reaches an asymptotic value. At a low adhesion bond strength, the timescale is independent of capillary number. But at a higher adhesion strength, the timescale increases with increasing capillary number. We then consider the second set of simlations where finite values of reaction-rate ratios are considered which allows the bond to sustain or break. Here we btain the critical bond strength that would be needed for complete adhesion of the capsule on to the surface. The compete adhesion is posible when the lifetime of the bond is greater than the steady-sate timescale obtained from the first set of simulations. The capsule lifts off from the surface if the bond strength is below the critical bond strength due to the presence of the hydrodynamic lift force that acts on a deformable particle in wall-bounded shear flow. Nextwe consider the rolling motion of the adherent capsule. Becuase of the stochastic process of bond formation and breakage, the roling motion is comprised of intermittent `stops-and-runs' which is well-known for biological cells such as leukocytes. We then present detail sttistical analysis, such as probability density functions of velocity fluctuations, of the stochastic process. In the fourth set of simulations, we consoder lift-off of an adherent capsule. These results enable us to develop state diagrams for leukocyte adhesion in presence of cell deformation. Our results suggest that the regimes of firm adhesion, stable rolling, and no-adhesion are governed by the hydrodynamic lift force that is present for a deformable cell, but not for a rigid capsule. The range of bond strength over which stable rolling can occur decreases with increasing capillary number. The critical bond strength for the firm adhesion is lower for a deformable capsule than that for a rigid capsule. The critical bond strength for the detachment of an adherent cell first increases but then decreases with increasing cell deformability.

Supported by NSF grants BES-0603035 and CTS-0625936.