Decoupled rolling, sliding and sticking of a viscoplastic drop on a superhydrophobic surface

Abstract

While the dynamics of Newtonian fluid drops on an inclined non-wettable surface has been widely reported, that of viscoplastic drops is less well known. Combining experimental and theoretical analysis, we reveal unique behaviours of viscoplastic drops on an inclined superhydrophobic surface: (i) decoupled rolling, sliding and sticking motions and (ii) two distinct rolling modes, i.e. viscous rolling and rigid-body rolling. First, determined by the relative magnitudes of gravitational, yield and adhesive stresses, a viscoplastic drop rolls, slides or sticks on a superhydrophobic surface. To the best of our knowledge, this is the first distinct differentiation of viscoplastic drop motions on a superhydrophobic surface, which is a clear departure from the previous observations of Newtonian drops on superhydrophobic surfaces and viscoplastic drops on hydrophilic/hydrophobic surfaces. We subcategorized two types of rolling as liquid-like viscous rolling and solid-like rigid-body rolling. With a low Deborah number (i.e. dimensionless viscoplastic relaxation time), the viscoplastic drop shows a viscous rolling as a Newtonian drop does on an inclined surface. With a high Deborah number, however, the viscoplastic drop does not have enough time to be 'fluid'. Consequently, the ellipsoidal drop deforms to be more spherical as it goes down the inclined surface, and tumbles, as if a solid body initiates its rolling by 'tipping'.