Investigation of the dynamic behavior of liquid transfer between two flat surfaces

Volume partitioning during liquid-bridge stretching and pinch-off between solid surfaces is controlled by dynamic wetting competing with hydrodynamic forcing arising from viscous extensional stresses and inertia generated during plate separation. Previous studies have focused on liquid transfer between parallel surfaces and suggest three distinct regimes: quasi-static, transitional, and dynamic. Here we test whether these regimes remain valid for slightly tilted (non-parallel) geometries relevant to roll-based processes, and whether tilting modifies transfer primarily through contact-line physics.

Liquid bridges of glycerol-water mixtures were stretched between parallel and slightly tilted 0^°-10^° plates while varying separation velocity, viscosity, and surface wettability. High-speed imaging quantified the transfer ratio ϕ (fraction of volume transferred from donor to acceptor surface). Complementary phase-field simulations incorporating contact-angle hysteresis were performed to resolve realistic contact-line motion during bridge stretching and breakup.

The same three regimes are observed for both parallel and tilted plates. In the quasi-static regime, ϕ is primarily determined by the differences in receding contact angles between two surfaces; in the dynamic regime, contact lines become effectively pinned, yielding an approximately constant ϕ≈43%. In the transitional regime, liquid transfer dynamics is governed by a dimensionless withdrawal number Π_w=μV³/ρg²ℓ_c³. Transfer ratios reveal the scaling ϕ∼Π_w^1/6and collapse onto a single master curve ϕΠ_w. Notably, the alteration to the lateral contact-line slip resulting from a tilt between the two surfaces affects the transfer ratio only when both surfaces have comparable wettability; surfaces with highly disparate wettability exhibit negligible sensitivity to such tilting.