Short and long time drop dynamics on lubricated substrates

Abstract

I. DETERMINING MASTER CURVES FOR THE INERTIAL AND VISCOUS REGIMEFig. S 1: Time history of drop shapes as a function of film viscosity (µo), indicated to the left. At the point of detachment from the needle the drop shape is independent of the film viscosity.An inertial (τ ρ ) and a viscous (τ µ ) time scale are found to describe the drop deformation after contact with the oil film ( Fig. 5), where Fig. S1 shows the time history of the drop shapes. A similar scaling law is also expected for the apparent radius (r). By scaling r with the initial drop size (R) and time (t) with τ ρ or τ µ two distinct spreading regimes appear (Fig. S2). The inertial scaling ( Fig. S2a) shows that the data for Oh < 0.2 follows nearly the same curve, where as Oh > 0.2 the data remains scattered. If r is instead scaled with τ µ the data for Oh < 0.2 is reduced to nearly a single curve (Fig. S2b). The data in the transitional regime (0.2 < Oh < 2) follows neither of the two scaling laws.A log-log plot of the non-dimensional apparent radius (r/R) in Figs. S2a,b shows that it follows a power-law like behavior (Figs. S3, S4). We fit a master curve through each data set to determine the range of the exponents and the pre-factors for the two regimes. Since the experimental data show that these two regimes are bounded within a certain time span we only use the data in these regions for the fitting, which is illustrated by dashed square in Figs. S3a, S4a. Each data set inside the dashed area is fitted onto a curve of the form r/R = a(t/τ ρ ) b or r/R = a(t/τ µ ) b , where a and b are constants determined by the best fit. For clarity, the data in the transitional regime (0.2 < Oh < 2) has been omitted below.The inertial regime is defined before drop detachment from the needle (t/τ ρ < 2). Each data set is fitted by a single curve (Fig. S3), which is represented by the dashed line. We find the the inertial regime to be represented by a curve r/R ≈ 1.1( t τρ ) 0.45 , where the pre-factor varies between 1.09 -1.13 and the exponent is ≈ 0.45.

How droplets nucleate and grow on liquids and liquid impregnated surfaces

“…58 The spreading rate of this nanolm is dictated by the capillary forces opposed either by inertial or viscous forces. Although the spreading of oil around a droplet is expected to be greater compared to spreading of oil in a plane, the latter can be used as an approximation for the spreading velocity around a droplet.…”

Air-stable droplet interface bilayers on oil-infused surfaces

“…When a water droplet was deposited onto an oil-infused surface, an oil meniscus rapidly formed around the droplet to balance its three-phase contact line:γ oa +γ wo +γ wa = 0. It should be noted that because γ wo + γ oa < γ wa for all oils used here (except hexadecane; SI Appendix, Table S2), a thin film of oil is cloaked about the water-air interface, andγ wa is actually replaced bỹ γ wo +γ oa (21,56). For brevity, the oil-cloaked droplet interface will henceforth be referred to simply as the water-air interface.…”

Stability of Surface-Immobilized Lubricant Interfaces under Flow

“…1,26,27,28 These investigations have shown the surface-immobilized liquid layer to remain stable upon introduction of the droplets; however, the appearance of a thin cloaking or wrapping layer of lubricant covering the droplets has been sometimes observed. 26,27 The origin of this wrapping layer has been ascribed to the differences in surface energy between the surface-immobilized liquid, the liquid being repelled (water), and the air: the low surface energy of the lubricant makes a lubricant-air interface more energetically favorable than an air/water interface. The result is formation of a thin layer of lubricant over the droplet upon introduction of the droplet to the surface.…”

“…The result is formation of a thin layer of lubricant over the droplet upon introduction of the droplet to the surface. 26,27 Nevertheless, the amount of lubricant necessary to cover the droplet has generally not appeared to be enough to noticeably disrupt the underlying lubricant layer.…”