Surfactant-assisted spreading of a liquid drop on a smooth solid surface

Chan, Kit Yan; Borhan, Ali

doi:10.1016/j.jcis.2005.01.086

Cited by 25 publications

(31 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is shown clearly in figure 2(a) in which we have plotted the derivative of h; the position of its minimum value corresponds to the stationary point. This behaviour was also observed by Chan & Borhan (2005). Figure 2(c) presents the evolution of the drop thickness and surfactant concentration at the plane of symmetry.…”

Section: Resultssupporting

confidence: 72%

“…The model has two empirical constants, the so-called mobility exponent k * and n which usually takes values in the range 1 6 n 6 3. This functional dependence has been used by several researchers in the past to model contact line motion (Haley & Miksis 1991;Benintendi & Smith 1999;Chan & Borhan 2005). The power-law dependence has been verified experimentally for the spreading of uncontaminated fluids (e.g.…”

Section: Contact Line Motionmentioning

confidence: 80%

“…This is a clear indication that the adsorption of the surfactant at the substrate plays an important role in the spreading process. More recently, Chan & Borhan (2005) studied the axisymmetric spreading of a liquid drop with an insoluble surfactant and no transfer at the contact line. They focused on the effect of an equilibrium contact angle that either is fixed or depends on the surfactant concentration at the contact line.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

2011

View full text Add to dashboard Cite

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.

show abstract

Section: Resultssupporting

confidence: 72%

Section: Contact Line Motionmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

2011

View full text Add to dashboard Cite

show abstract

“…In terms of theoretical modelling, people have either considered the case of non-volatile droplets in the presence of surfactants [38][39][40][41] or evaporating droplets with particles and no surfactants.…”

mentioning

confidence: 99%

Evaporation of Sessile Droplets Laden with Particles and Insoluble Surfactants

2016

View full text Add to dashboard Cite

We consider the flow dynamics of a thin evaporating droplet in the presence of an insoluble surfactant and non-interacting particles in the bulk. Based on lubrication theory, we derive a set of evolution equations for the film height, the interfacial surfactant and bulk particle concentrations, taking into account the dependence of the liquid viscosity on the local particle concentration. An important ingredient of our model is that it takes into account the fact that the surfactant adsorbed at the interface hinders evaporation. We perform a parametric study to investigate how the presence of surfactants affects the evaporation process as well as the flow dynamics with and without the presence of particles in the bulk. Our numerical calculations show that the droplet life-time is affected significantly by the balance between the ability of surfactant to * To whom correspondence should be addressed † Department of Chemical Engineering, University of Patras, Patras 26500, Greece ‡ Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Sangareddy 502 285, Telangana, India ¶ Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK 1 enhance spreading suppressing the effect of thermal Marangoni stresses-induced motion and to hinder the evaporation flux through the reduction of effective interfacial are of evaporation, which tend to accelerate and decelerate the evaporation process, respectively. For particle-laden droplets and in the case of dilute solutions, the droplet life-time is found to be weakly-dependent on the initial particle concentration. We also show that the particle deposition patterns are influenced strongly by the direct effect of surfactant on the evaporative flux; in certain cases, the "coffee stain" effect is enhanced significantly. A discussion of the delicate interplay between the effects of capillary pressure, solutal and thermal Marangoni stresses, which drive the liquid flow inside the evaporating droplet giving rise to the observed results is provided herein.

show abstract

“…In a recent paper [5], we examined the spontaneous spreading of a liquid drop covered with an insoluble surfactant monolayer in the lubrication limit. Here, we present an extension of those results for the case of soluble surfactants in the sorption-controlled limit.Following [5], the dimensionless equations and boundary conditions governing the time-evolution of the shape of a liquid drop of density ρ and viscosity μ spreading axisymmetrically on a smooth solid surface in the lubrication limit can be written asCa ∂h ∂t = 1 r ∂ ∂r r 1 3 h 3 + αh 2 ∂ ∂r Bo h − σ r ∂ ∂r r ∂h ∂r − 1 2 h 2 + αh ∂σ ∂r , (A. Borhan).(where r is the radial coordinate, h(r, t) and R(t) represent the profile and basal radius of the drop at any time t , respectively, θ(t) denotes the dynamic contact angle, and θ a is the equilibrium advancing contact angle. Equation (1) is valid everywhere along the air-liquid interface except at the moving contact line where it is complemented by Eq.…”

mentioning

confidence: 99%