Reactive spreading and recoil of oil on water

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Original entry: Scott Tsai, APPHY 226, Spring 2009

"Reactive spreading and recoil of oil on water" Ernst A. van Nierop, Armand Ajdari, and Howard A. Stone

Physics of Fluids 18, 038105 (2006)

Soft Matter Keywords

Droplets, spreading, surface tension, flow, chemical reaction, recoil, liquid lens.

Overview

Refer to abstract of paper

Soft Matter Examples

By chemical reactions at the interface between a immiscible drop and immiscible thin film, the surface tension between the two fluids can be changed. The authors of this paper demonstrate this and see that the drop spreads rapidly, then recoils slowly to its equilibrium shape.

Fig.1
Fig.2
Fig.3

In their experiments, the authors used 0.1 microliter droplets of white heavy mineral oil containing oleic acid with a petri dish of a weak aqueous solution of sodium hydroxide to perform this experiment. They describe the problem using a balance of surface tensions at the interface of the two fluids (Fig. 1).

They saw taht after the drop falls onto the thin film, the oleic acid at the interface reacts with the sodium hydroxde in the thin film to create surfactants that help to decrease surface tension. This kind of surface-tension reduction is characterized by the following equation, where k is a concentration-dependent factor.

<math> \sigma_{ow,\infty} = \sigma_{ow,\infty}-\sigma_{ow,0}e^{-kt} </math>

The authors found spreading and recoiling data for four experiments (Fig. 2 and 3). In each experiment, there were different combinations of acid/base for the droplet/film. The initial slopes of spreading increased with increasing concentrations of each solution. It was determined in a seperate experiment that with no reagents or surfactant present, teh oil spread slowly and reached the equilibrium shape without recoil. With the reagents in the solutions (Fig. 3), the oil drop radii recoil occurs.

From a scaling point of view, the authors saw local areas of power-law spreading of the droplets.

<math> R(t) \propto t^{\alpha} </math>

After fitting, they found average <math> \alpha </math> to be <math> 0.64 < \alpha_{spread} < 0.89 </math>. This is different than the spreading of a regular drop on a thin film, where <math> \alpha </math> is approximately <math> 1 \over 2 </math>. The authors also fitted the recoil as a power law, and saw that <math> -0.34<\alpha_{recoil}<-0.14 </math>. They saw that the slope of the recoil was steepest when the reagent concentration of the thin film was lower (Fig. 3).

The authors explain their observations by saying that when teh drop first contacts the thin film, only a few oleic acid molecules are near the interface. They react with the sodium hydroxide in teh film to produce surfactant, which reduces the local oil-water surface tension, causing the drop to spread. The spreading is a result of the dynamic equilibrium of the triple line as the oil-water surface tension is being reduced. At the time when all the oleic acid in teh drop have reacted, the maximum radius is reached, and the drop begins to recoil. Recoil is a result of the diffusion of the surfactants at the interface away from the interface. As they diffuse away, the surface tension begins to go back to its original value. And the triple-line equilibrium dictates that the drop shape will have to change - causing the drop to recoil.