(24b) Subphase Depth and Surfactant-Driven Marangoni Transport
The flow fields produced by surface tension gradients on a thin liquid film, bounded above by a vapor interface and below by a solid surface are dependent on the depth of the subphase. Expanding on prior theoretical and experimental proof of this phenomena1, this work quantitatively examines the effects of subphase depth on the fluid flow patterns, the speed of the Marangoni front, and the transport of a non-surface active dye across the fluid subphase, as well as looking at the effects of film rupture at smaller subphase thicknesses.
We have developed a simple, sensitive optical method to measure the evolution of the subphase surface height as a function of time within the first second after a surfactant solution is deposited on the subphase. The experimental setup consisted of a flat bottomed petri dish containing aqueous films ranging from 0.3 mm to 2.4 mm in thickness on a light table. For one set of experiments the erythrosine dye (which is not surface active) is include in the surfactant solution and in the subphase at the same concentration. A narrow bandpass filter is mounted in front of a camera to record transmitted light intensity pixel-by-pixel across the subphase. Determination of the surface height profile is achieved by calculating the local optical density and applying a pre-determined Beerâs law-based calibration curve, enabling the instantaneous quantitative measurement of subphase depth with a time resolution of 33 ms. For a second set of experiments, dye is only included in the surfactant solution, so that transport of the non-surface active materials of the drop can be tracked. Subphases were either water or 1 wt% polyacrylamide.
Three distinct regimes become apparent from these experiments. First, at depths under 0.9 mm, material from the deposition region is depleted so quickly, it results in a stranded sessile drop separated from the rest of the fluid by a ring where the underlying solid surface has been completely de-wetted. This flow behavior severely limits the amount of dye that spreads by trapping a portion of it inside the stranded drop. There is a transitional regime between 0.9 mm and 1.5 mm, where the fluid thins in a ring around the region of deposition, but does not de-wet the underlying solid surface. At these depths the spreading Marangoni ridge achieves a maximum height compared to thicker or thinner depths; and transport of dye, while slowed, is surpressed. For depths greater than 1.5 mm, recirculation flows occur, allowing fluid to reenter the region of deposition during spreading. This leads to no thinned ring region, and the most rapid transport of dye.
Subphase depth has a significant effect on Marangoni flow behavior. These behaviors can be separated in two three distinct regimes based on the fluid flow behavior. For the thinnest films, the fluid flow isolates the majority of the dye from the bulk subphase, limiting its transport. On intermediate films the transport of the dye is slowed but not cut off, and on thicker films dye spreads the fastest. The effects of the subphase depth on Marangoni transport must be taken into account for the purposes of pulmonary drug delivery so that transport of the drugs is not unintentionally hindered by the aerosol formulation.
1 Gaver DP, Grotberg JB. Droplet spreading on a thin viscous film. J Fluid Mech 1992;235:399â414.