Multiscale modelling in the numerical computation of isothermal non-wetting

Abstract

A state of permanent, isothermal non-wetting of a solid surface by a normally wetting liquid may be achieved if the surface moves tangentially to a liquid drop that is pressed against it. Surrounding gas is swept into the space between the liquid and solid creating a lubricating film that prevents wetting. The length scales of the drop and the film are typically three or more orders of magnitude different, making numerical simulation difficult from a resolution standpoint. The present paper focuses on a hybrid approach employing lubrication theory for the thinnest portions of the gas film and numerical simulation for the liquid and outer gas phases.

Droplet levitation over a moving wall with a steady air film

“…Isothermal non-coalescence phenomena between a droplet and a wall or a liquid surface can occur under various conditions. Examples include droplet levitation over moving solid walls (Neitzel et al 2001;Smith & Neitzel 2006;Lhuissier et al 2013;Saito & Tagawa 2015;Gauthier et al 2016), atomically smooth horizontal walls (de Ruiter et al 2015), inclined walls (Hodges, Jensen & Rallison 2004;Gilet & 262 E. Sawaguchi, A. Matsuda, K. Hama, M. Saito and Y. Tagawa 1 mm U FIGURE 1. Side view of a levitating droplet over a moving wall.…”

Dynamic wetting failure in surfactant solutions

“…The model is evaluated using three approaches: (i) a one-dimensional (1D) lubrication-type approach, (ii) a novel hybrid of a 1D description of the receding phase and a 2D description of the advancing phase, and (iii) an asymptotic theory of Cox (1986b). Although similar 1D/2D hybrid approaches have previously been used to study single-phase (Stay & Barocas 2003) and two-phase (Smith & Neitzel 2006;Lavalle et al 2015) flows, this is the first work, to the best of the authors' knowledge, that presents a hybrid model for fluid displacement with dynamic contact lines.…”

Numerical simulation of isothermal nonwetting

“…The counter-clockwise flow motion of the major vortex is induced by the increased air velocity within the interstitial film. The streamlines for the flow field from the multiscale model of Smith and Neitzel [11] computed for V = 300 mm/s, D = 1.01 mm and q = 2.491 mm 2 /s are similar to those seen in Figure 3(e). Figure 4 exhibits the resultant speed (V s = √ u 2 + v 2 ), and pressure-difference ( P = P a − P l ) distribution on the silicone-oil drop's free surface, when the wall's distance is fixed (D = 1.01 mm) and the moving-wall velocity is varied (V = 300, 400, and 500 mm/s).…”

“…Figure 12 shows the behaviour of D − S(x) versus x for different wall velocities for both silicone-oil and water; the results show the free surface being depressed upstream and bulging downstream, compared with the undeformed profile. For V = 300 mm/s, the minimum interstitial film is 0.012 mm at x = −0.05 mm, while Smith and Neitzel [11] reported minimum film being 0.0122 mm at x = −0.073 mm. The Weber number is the ratio of inertial force to surface-tension force, defined for the present situation as W e l = l V 2 R/ l , and is indicative the degree of surface deformation.…”

“…The positive value of resultant velocity is defined for the counter-clockwise flow motion along the free surface, and the negative one for the clockwise flow motion. The speed distribution (Figure 4(a)) shows two stagnation points (V s = 0) located near x = 0.35 mm and x = −0.6 mm when V = 300 mm/s, while those of Smith and Neitzel [11] are located at x = −0.4 mm and x = 0.75 mm. In this case, the maximum speed is V s = 11.61 mm/s located at x = −0.06 mm, while Smith and Neitzel [11] show V s = 12.57 mm/s at x = −0.069 mm, an 8.3% resultant velocity difference.…”