Marangoni-enhanced capillary wetting in surfactant-driven superspreading

Abstract

Superspreading is a phenomenon such that a drop of a certain class of surfactant on a substrate can spread with a radius that grows linearly with time much faster than the usual capillary wetting. Its origin, in spite of many efforts, is still not fully understood. Previous modelling and simulation studies (Karapetsas et al. J. Fluid Mech., vol. 670, 2011, pp. 5–37; Theodorakis et al. Langmuir, vol. 31, 2015, pp. 2304–2309) suggest that the transfer of the interfacial surfactant molecules onto the substrate in the vicinity of the contact line plays a crucial role in superspreading. Here, we construct a detailed theory to elaborate on this idea, showing that a rational account for superspreading can be made using a purely hydrodynamic approach without involving a specific surfactant structure or sorption kinetics. Using this theory it can be shown analytically, for both insoluble and soluble surfactants, that the curious linear spreading law can be derived from a new dynamic contact line structure due to a tiny surfactant leakage from the air–liquid interface to the substrate. Such a leak not only establishes a concentrated Marangoni shearing toward the contact line at a rate much faster than the usual viscous stress singularity, but also results in a microscopic surfactant-devoid zone in the vicinity of the contact line. The strong Marangoni shearing then turns into a local capillary force in the zone, making the contact line in effect advance in a surfactant-free manner. This local Marangoni-driven capillary wetting in turn renders a constant wetting speed governed by the de Gennes–Cox–Voinov law and hence the linear spreading law. We also determine the range of surfactant concentration within which superspreading can be sustained by local surfactant leakage without being mitigated by the contact line sweeping, explaining why only limited classes of surfactants can serve as superspreaders. We further show that spreading of surfactant spreaders can exhibit either the $1/6$ or $1/2$ power law, depending on the ability of interfacial surfactant to transfer/leak to the bulk/substrate. All these findings can account for a variety of results seen in experiments (Rafai et al. Langmuir, vol. 18, 2002, pp. 10486–10488; Nikolov & Wasan, Adv. Colloid Interface Sci., vol. 222, 2015, pp. 517–529) and simulations (Karapetsas et al. 2011). Analogy to thermocapillary spreading is also made, reverberating the ubiquitous role of the Marangoni effect in enhancing dynamic wetting driven by non-uniform surface tension.

Molecular Dynamics Simulation of the Superspreading of Surfactant-Laden Droplets. A Review

“…The Karapetsas et al [25] model predicted values of spreading exponents α = 1 or even higher, while the non-monotonic variation of the spreading rate with surfactant concentration was captured by the model in agreement with experimental observations [2]. Recently, computational fluid dynamics and theoretical models [23] have been employed to study superspreading confirming these predictions [24]. While numerical simulation and theory have contributed significantly to unveiling the superspreading mechanism, both are unable to describe the microscopic behaviour of the systems.…”

“…Another way of studying superspreading is with numerical simulation [23][24][25]. For example, Karapetsas et al have studied the superspreading of surfactant-laden droplets by using continuum simulation based on lubrication theory, advection-diffusion equations and chemical kinetic fluxes for the surfactant transport [25].…”

“…Nowadays, the existence of reliable force-fields for water-surfactant systems based on all-atom [39][40][41][42] and coarse-grained (CG) models [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60] enable the genuine simulation of such systems. For example, recent simulations of aqueous solutions with surfactants [21,22,[61][62][63][64][65][66][67] have established the connection between the behaviour of surfactants in the bulk and spreading [68][69][70][71], while the superspreading mechanism and the main characteristics of superspreading surfactants have been the focus of recent studies [5,[19][20][21][22][23][24]68,[70][71][72]. In view of these important advances in the superspreading arena, this review will highlight what we believe a...…”

“…Superspreading is important for many applications in a wide range of different areas, such as coating technology, drug and herbicides delivery, and enhanced oil recovery [3,[7][8][9][10], manifested as enhanced fluid flow and efficient spreading. In view of the large spectrum of applications, superspreading has motivated a wide range of experimental [11][12][13][14][15][16][17][18], as well as numerical and simulation research in the recent years [19][20][21][22][23][24][25][26]. The main focus of these studies has been the underlying mechanisms of this phenomenon and identifying key features that distinguish superspreaders from other common (or conventional) surfactants.…”

Superspreading on Hydrophobic Substrates: Effect of Glycerol Additive

“…One of the proposed mechanisms explains superspreading due to Marangoni flow at the leading edge [6,[24][25][26]. When a surfactant solution spreads over a substrate surface, both liquid/air and liquid/solid interfacial areas expand.…”