  A self-consistent model is developed to investigate attachment / detachment
kinetics of two soft, deformable microspheres with irregular surface and coated
with flexible binding ligands. The model highlights how the microscale binding
kinetics of these ligands as well as the attractive/repulsive potential of the
charged surface affects the static deformed configuration of the spheres. It is
shown that in the limit of smooth, neutral charged surface (i.e., the Debye
length, $\kappa \rightarrow \infty $), interacting via elastic binders (i.e.,
the stiffness coefficient, $\lambda \rightarrow 0$) the adhesion mechanics
approaches the regime of application of the JKR theory, and in this particular
limit, the contact radius scales with the particle radius, according to the
scaling law, $R_c\propto R^{\frac{2}{3}}$. We show that adhesion dominates in
larger particles with highly charged surface and with resilient binders. Normal
stress distribution within the contact area fluctuates with the binder
stiffness coefficient, from a maximum at the center to a maximum at the
periphery of the region. Surface heterogeneities result in a diminished
adhesion with a distinct reduction in the pull off force, larger separation
gap, weaker normal stress and limited area of adhesion. These results are in
agreement with the published experimental findings.
