Effects of surfactant on droplet spreading

Abstract

The effects of surfactant and temperature on the spreading of a viscous droplet are studied. Lubrication theory is used to develop a model for the evolution of the droplet. The surfactant is assumed to be insoluble and transport onto and off of the droplet interface at the contact line is allowed. A linear temperature gradient plus a gradient in the surface energy are allowed along the substrate. We find that these effects together can increase the speed of the translation of the droplet. We also find that allowing the static contact angle to vary with the surfactant concentration and temperature, as described by Young's law, can speed up droplet motion. When contact angle hysteresis is allowed, it is possible for the droplet to stop moving when surfactant transport is allowed along the interface.

On surfactant-enhanced spreading and superspreading of liquid drops on solid surfaces

“…The adsorption of the surfactant at the substrate has already been recognized as an important factor by experimentalists and modellers in the spreading process (see e.g. Rafai et al 2002;Kumar et al 2003;Clay & Miksis 2004;Kim, Qin & Fichthorn 2006) as well as in other problems (e.g. the autophobing effect; see Craster & Matar 2007).…”

“…However, Rame (2001) noted that when one considers the transfer of the surfactant from the fluid-air interface to the solid surface directly through the contact line by advection, further complications arise; the introduction of slip makes the fluid velocity relative to the contact line equal to zero, and therefore the surfactant cannot transfer by advection alone at the contact line. Clay & Miksis (2004) also addressed the problem of transport of an insoluble surfactant at the contact line, albeit with a different mechanism, assuming a very simple model that permitted the surfactant to be adsorbed and desorbed at the contact line. Their results suggest that when the liquid-air interface is losing the surfactant to the substrate, through adsorption at the contact line, the droplet spreads faster, whereas when it is gaining the surfactant from the substrate the spreading becomes slower.…”

An explicit Eulerian method for multiphase flow with contact line dynamics and insoluble surfactant

“…A similar, but less pronounced, effect is visible on the bottom row, where the surfactant level is kept constant while the diffusion is decreased (Pe Γ increased). The velocity change at the interface is caused by the Marangoni force (14), which increases both when the surfactant concentration and its surface gradient increase. Decreasing the diffusion causes a stronger surfactant gradient on the interface (see Figure 12), hence the larger Maragoni force when Pe Γ is increased.…”

“…To illustrate the effect of Marangoni forces on a drop, we consider the case of a circular drop of unit diameter which initially has a locally high concentration of surfactant on one side, leading to tangential (Marangoni) forces (14) due to surfactant gradient. At t = 0, the Here we simulate a drop of radius R = 0.5 which is initially at rest on a solid surface, with contact angle θ = θ s,c = 80 • and a surfactant distribution that has a maximum at the right contact point.…”

“…There can also be an exchange of surfactants between the interface and the solid surface as the contact line moves, in which case additional difficulties arise in solving the contact line singularity [15,48]. A numerical study on the effects of surfactants and temperature on the spreading of a two-dimensional viscous droplet with surfactant exchange was performed by Clay & Miksis [14], using a lubrication approximation.…”