Remarks by Jonathan D. Blake

Theory of Wetting-Induced Fluid Entrainment by Advancing Contact Lines on Dry Surfaces

“…This asymmetry can be used to rationalize the gap in magnitudes between U adv and U rec ; upon retreating, the gas offers a smaller viscous friction than the liquid, and thus the destabilization threshold should be larger for the advancing configuration. Although a similar scaling, U adv ∼ Bγ(π − θ e ) 3 /η L [9], has been suggested for advancing contact lines on hydrophobic surfaces (where B ≫ A depends on the gas viscosity, η G ), this relation does not capture the experimentally reported dependence of U adv on the wider θ e range [8][9][10].…”

“…Increasing experimental evidence supports the important role of surface specificity on entrainment [8][9][10]. A non-monotonic dependence of U adv as θ e is varied was observed when forcing water films on wafers covered with dry gelatin containing different surfactants [8]. However, careful measurements displayed a dramatic saturation of U adv on hydrophilic substrates made of glass, and a rapid decay with θ e on hydrophobic solids (treated with silane chains) [9].…”

“…Introduction.-The entrainment of a fluid by a solid raises fundamental questions on the hydrodynamics of moving contact lines [1], which are the intersection of fluid and solid boundaries, and is relevant to a wide variety of practical situations in materials science [2,3] and microfluidics [4,5]. Fluid entrainment gives rise to rich phenomena such as bubble entrainment in solid plate immersion [6,7], gas intrusion in coating [8] and solid-liquid splashing [9], drop emission from forced liquid microfilaments [10], the ejection of drops and rivulets from forced running drops [11,12] and the more familiar film deposition on withdrawn solid plates [13,14].…”

“…In Ref. [8], water films were forced on surfactant-treated, dry aqueous gelatin surfaces, where U adv was found to increase on hydrophilic surfaces to reach a maximum at θ e ≈ 60 − 80 • . In Ref.…”

“…In agreement with a previous analysis [9], in the hydrophobic limit Eq. (7) reduces to (π − θ e ) 2 − (π − θ) 2 ≃ c L Ca + ηL(π − θ) −1 Ca, (8) where L ∼ O(10) is a numerical pre-factor that depends on the scale separation, ξ/h o . In this regime the critical advancing speed obeys η L U adv γ ∼ (π − θ e ) 3 , as indicated by the scaling of the capillary (l.h.s.)…”