= Adhesive-cell rolling threshold
{title2=$\dot\gamma_c\sim J^{4/3}/(\eta G^{1/3}R^{4/3})$}
For a weakly adhering elastic sphere, balancing elastic contact energy $Ga^5/R^2$ against adhesion $Ja^2$ gives contact radius $a\sim(JR^2/G)^{1/3}$. If peeling the rear contact dissipates work of order $J$ per unit area, its rolling moment is $M_r\sim JaR$. Balancing this with a fluid shear moment $\eta\dot\gamma R^3$ gives the displayed estimate. A perfectly reversible elastic contact has no such net rolling-energy barrier; adhesive hysteresis or bond kinetics must justify a finite threshold, and the corresponding dissipative adhesion energy replaces $J$.
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