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State diagram for adhesion dynamics of deformable capsules under shear flow.

Due to the significance of understanding the underlying mechanisms of cell adhesion in biological processes and cell capture in biomedical applications, we numerically investigate the adhesion dynamics of deformable capsules under shear flow by using a three-dimensional computational fluid dynamic model. This model is based on the coupling of the front tracking-finite element method for elastic mechanics of the capsule membrane and the adhesion kinetics simulation for adhesive interactions between capsules and functionalized surfaces. Using this model, three distinct adhesion dynamic states are predicted, such as detachment, rolling and firm-adhesion. Specifically, the effects of capsule deformability quantified by the capillary number on the transitions of these three dynamic states are investigated by developing an adhesion dynamic state diagram for the first time. At low capillary numbers (e.g. Ca < 0.0075), whole-capsule deformation confers the capsule a flattened bottom in contact with the functionalized surface, which hence promotes the rolling-to-firm-adhesion transition. It is consistent with the observations from previous studies that cell deformation promotes the adhesion of cells lying in the rolling regime. However, it is surprising to find that, at relatively high capillary numbers (e.g. 0.0075 < Ca < 0.0175), the effect of capsule deformability on its adhesion dynamics is far more complex than just promoting adhesion. High deformability of capsules makes their bottom take a concave shape with no adhesion bond formation in the middle. The appearance of this specific capsule shape inhibits the transitions of both rolling-to-firm-adhesion and detachment-to-rolling, and it means that capsule deformation no longer promotes the capsule adhesion. Besides, it is interesting to note that, when the capillary number exceeds a critical value (e.g. Ca = 0.0175), the rolling state no longer appears, since capsules exhibit large deviation from the spherical shape.