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

Abstract

The mechanisms driving the surfactant-enhanced spreading of droplets on the surface of solid substrates, and particularly those underlying the superspreading behaviour sometimes observed, are investigated theoretically. Lubrication theory for the droplet motion, together with advection-diffusion equations and chemical kinetic fluxes for the surfactant transport, leads to coupled evolution equations for the drop thickness, interfacial concentrations of surfactant monomers and bulk concentrations of monomers and micellar, or other, aggregates. The surfactant can be adsorbed on the substrate either directly from the bulk monomer concentrations or from the liquid-air interface through the contact line. An important feature of the spreading model developed here is the surfactant behaviour at the contact line; this is modelled using a constitutive relation, which is dependent on the local surfactant concentration. The evolution equations are solved numerically, using the finite-element method, and we present a thorough parametric analysis for cases of both insoluble and soluble surfactants with concentrations that can, in the latter case, exceed the critical micelle, or aggregate, concentration. The results show that basal adsorption of the surfactant plays a crucial role in the spreading process; the continuous removal of the surfactant that lies upon the liquid-air interface, due to the adsorption at the solid surface, is capable of inducing high Marangoni stresses, close to the droplet edge, driving very fast spreading. The droplet radius grows at a rate proportional to t a with a = 1 or even higher, which is close to the reported experimental values for superspreading. The spreading rates follow a non-monotonic variation with the initial surfactant concentration also in accordance with experimental observations. An accompanying feature is the formation of a rim at the leading edge of the droplet. In some cases, the drop spreads to form a 'pancake' or creates a 'secondary' front separated from the main droplet.

Fluid-dynamical model for antisurfactants

“…We follow many well-established fluid-dynamical models of coupled flow and surfactant transport [4][5][6][7][8] by distinguishing between the surface region of the fluid, taken to have a notional thickness η of the order ofångströms, and the remaining bulk region of the fluid. The bulk region may include a 'subsurface' region of high concentration gradients, which mediates solute exchange between the surface and the deeper regions of the fluid [9]; for simplicity we assume that such a region may be described by the same governing equations as the rest of the bulk.…”

“…4] and subsequently extended to soluble surfactants [e.g. [5][6][7]. However, as we shall see, in general σ also depends on the bulk concentration c b evaluated at the top of the bulk region, or, equivalently, on the surface excess Γ, defined as…”

“…Incorporating other effects, such as a maximum surface concentration due to packing effects or a critical micelle concentration in the bulk [7], is straightforward in principle but in practice it introduces distracting complications and so is not discussed further here. Similarly, we do not attempt to represent the underlying molecular or ionic interactions that control the surface excess and its effects [13], but in the spirit of established surfactant models [4][5][6][7][8] we subsume these into a simple kinetic description.…”

“…Since this anti-surfactant behaviour may play a significant role in the flow of solutions with free surfaces, it is perhaps surprising that it has not yet been incorporated into fluid-dynamical models, especially as corresponding models for both soluble and insoluble surfactants are now well established and have been widely studied [4][5][6][7][8]. It should be noted that, in general, a model for an antisurfactant cannot be obtained from one for a surfactant simply by reversing the dependence of the surface tension on the surface concentration of solute, because, as we shall explain below, this is not in general consistent with the underlying physical mechanisms by which solutes affect surface tension.…”

On the microhydrodynamics of superspreading

“…How the superspreaders facilitate this rapid spreading and complete wetting is a puzzle as the interfacial energetics, self-assembly and transport at the contact line of the superspreaders must be fundamentally different relative to the conventional surfactants to account for this dramatic difference. Karapetsas et al (2011) present a new framework and numerical calculations for the interfacial transport of the superspreaders at the contact line, which provides both a starting point for rationalizing their superwetting behaviour and a clue towards understanding how their unique molecular architecture drives the superspreading process.…”