Numerical solution of the dip coating process with insoluble surfactants: Langmuir or a linear approximation for surface tension? (original) (raw)
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The thickening effect of interfacial surfactant in the drag-out coating problem
Journal of Statistical Mechanics: Theory and Experiment, 2009
In experiments involving dip coating flows on an infinite flat substrate which is withdrawn from an infinite liquid bath, the thin film deposited far up on the plate usually thickens in the presence of insoluble interfacial surfactant. Using perturbation analysis within the lubrication approximation we prove that the film thickens in the presence of interfacial surfactant for low capillary numbers if surface tension away from the transition and meniscus regions increases in the direction of withdrawal of the plate, a condition that should truly emerge from the solution of the full problem. Thus, we essentially show that fine scale properties of the interfacial dynamics and the dynamics in the bulk of the fluid near the transition and meniscus regions are, in fact, not important. We show that it is only the surface tension gradient far away from the transition and meniscus regions that matters. This result is arrived at by first deriving upper and lower bounds on the film thickness in terms of Marangoni and capillary numbers. An estimate based on these results and interfacial surfactant dynamics also yields a qualitative profile of the interfacial surfactant concentration that results in an increase in film thickness.
Dynamical thickening transition in plate coating with concentrated surfactant solutions
2011
We present a large range of experimental data concerning the influence of surfactants on 15 the well-known Landau-Levich-Derjaguin experiment where a liquid film is generated by pulling 16 a solid plate out of a bath. The thickness h of the film was measured as a function of the pulling 17 velocity V for different kind of surfactant and at various concentrations. Measuring the thickening 18 factor =h/h LLD , where h LLD is obtained for a pure liquid, in a wide range of capillary 19 (Ca=V/), two regimes of constant thickening can be identified: at small capillary number, is 20 large due to a confinement and surface elasticity (or Marangoni) effects and at large Ca, is 21 slightly higher than unity, due to surface viscous effects. At intermediate Ca, decreases as Ca 22
Numerical Modelling of the Dip Coating Problem
Volume 7: Fluids and Heat Transfer, Parts A, B, C, and D, 2012
Flow behavior of Newtonian and Bingham fluids flow in a dip coating process was numerically analyzed using finite element and finite volume techniques. To capture the free surface location, two techniques have been considered; the remeshing technique embedded in the finite element code Polyflow and the Volume of Fluid model incorporated in the finite volume code FLUENT. In contrast to the first technique, the later does not require a prior approximate knowledge of the final free surface shape and requires less resource. A fairly good agreement is observed for both techniques with numerical results available in the literature for both Newtonian and Bingham fluid cases.
Industrial & Engineering Chemistry Research, 2014
Dip coating is a simple, straightforward, and economical technique used in many food industrial applications. The objective of this work was to validate a mathematical model (presented by the authors in a companion paper as Part 1) of the fluid-dynamic variables in a dip-coating process considering that the film-forming fluid behaves as a generalized Newtonian fluid, with data obtained from literature, and to perform a sensitivity analysis. A validation process was carried out using experimental data of average film thickness of different film-forming fluids (commercial milk chocolate, commercial deep-fat frying batters, glycerol/water solutions, sugar/syrup solutions, glycerine/water solutions, mineral oil, and Carbopol solutions). On the basis of the low errors obtained, predictions were considered satisfactory. An extensive examination of the effect of the main process variables, such as τ 0 , K, n, m, U p , ρ, θ and h, on the velocity profile and the characteristics of the local and average film thickness was established.
The behavior of thin liquid films is known to be strongly affected by the presence of surfactants at the interfaces. The detailed mechanism by which the latter enhance film stability is still a matter of debate, in particular concerning the influence of surface elastic effects on the hydrodynamic boundary condition at the liquid/air interfaces. In the present work, "twin" hydrodynamic models neglecting surfactant transport to the interfaces are proposed to describe the coating of films onto a solid plate (Landau-Levich-Derjaguin configuration) as well as soap film pulling (Frankel configuration). Experimental data on the entrained film thickness in both configurations can be fitted very well using a single value of the surface elasticity, which is in good agreement with independent measurements by mean of surface expansion experiments in a Langmuir through. The analysis shows how and when the soap films or dip coating experiments may be used to precisely and sensitively measure the surface elasticity of surfactant solutions.
Surfactant-induced rigidity of interfaces: a unified approach to free and dip-coated films
Soft matter, 2015
The behavior of thin liquid films is known to be strongly affected by the presence of surfactants at the interfaces. The detailed mechanism by which the latter enhance film stability is still a matter of debate, in particular concerning the influence of surface elastic effects on the hydrodynamic boundary condition at the liquid/air interfaces. In the present work, "twin" hydrodynamic models neglecting surfactant transport to the interfaces are proposed to describe the coating of films onto a solid plate (Landau-Levich-Derjaguin configuration) as well as soap film pulling (Frankel configuration). Experimental data on the entrained film thickness in both configurations can be fitted very well using a single value of the surface elasticity, which is in good agreement with independent measurements by mean of surface expansion experiments in a Langmuir through. The analysis thus shows that soap films or dip coating experiments may be used to measure the surface elasticity of s...
Plate Coating: Influence of Concentrated Surfactants on the Film Thickness
Langmuir, 2012
We present a large range of experimental data concerning the influence of surfactants on 13 the well-known Landau-Levich-Derjaguin experiment where a liquid film is generated by pulling 14 a plate out of a bath. The thickness h of the film was measured as a function of the pulling 15 velocity V for different kinds of surfactants (C 12 E 6 , which is a non-ionic surfactant, and DeTAB 16 and DTAB, which are ionic) and at various concentrations near and above the critical micellar 17 concentration (cmc). We report the thickening factor α=h/h LLD , where h LLD is the film thickness 18 obtained without a surfactant effect, i.e. as for a pure fluid but with the same viscosity and 19 surface tension as the surfactant solution, over a wide range of capillary numbers (Ca = ηV/γ 20 with η the surfactant solution viscosity and γ its surface tension), and identify three regimes: (i) 21 at small Ca, α is large due to confinement and surface elasticity (or Marangoni) effects, (ii) for