Laplace pressure driven drop spreading

Abstract

This work concerns the spreading of viscous droplets on a smooth rigid horizontal surface, under the condition of complete wetting (spreading parameter S > 0) with the Laplace pressure as the dominant force. Owing to the self-similar character foreseeable for this flow, a self-similar solution is built up by numerical integration from the center of symmetry to the front position to be determined, defined as the point where the free-surface slope becomes zero. Mass and energy conservation are invoked as the only further conditions to determine the flow. The resulting fluid thickness at the front is a small but finite (Z lo-') fraction of the height at the center. By comparison with experimental results the regime is determined in which the spreading can be described by this solution with good accuracy. Moreover, even within this regime, small but systematic deviations from the predictions of the theory were observed, showing the need to add terms modifying the Laplace pressure force.

Mathematical modelling of surface tension effects in liquid wall films

“…The reason behind this phenomenon is that only relevant force is capillary pressure, which produces fairly small spreading velocities whose effects on the droplet spreading are visible only after 1 ms. Further time evolution shows that droplet shape does not change much between 0.25 s and 0.4 s, since the wall film thickness gradients on the edge of the droplet tend to zero. On the same picture could also be noticed that the behaviour of the droplet during the whole period of the simulation remains symmetrical, which is qualitatively in agreement with analytical results of Diez et al (1994). Quantitative comparison of simulation results and non-dimensional analytical droplet profile given in Figure 5 shows that the present numerical predictions are in good agreement with the analytical expression from Diez.…”

“…The droplet is driven with Laplace (capillary) pressure as dominant force and other forces being absent or negligible. Similar tests were obtained by Diez et al (1994), who proposed analytical solution using lubrication theory, which neglects convective terms in momentum equation, and compared the proposed solution with experimental results. The problem can be observed as two dimensional because of axial symmetry.…”

“…Diez et al (1994) showed that the droplet assumes parabolic non-dimensional profile, which is conserved during all stages of the spreading process. This way it is reasonable to begin validation of the implemented model by assuming initial droplet shape of rotational paraboloid to see if non-dimensional profile of Diez et al (1994) is conserved during the numerical simulation of droplet spreading. Further confirmation of the model comes from the initialisation of some artificial droplet shape that is highly unlikely to be encountered in nature.…”

Numerical modeling of urea water based selective catalytic reduction for mitigation of NOx from transport sector

“…The droplet is driven with a Laplace (capillary) pressure as dominant force and other forces being absent or negligible. Similar tests were obtained by Diez et al (1994). He proposed an analytical solution using lubrication theory, which neglects convective terms in the momentum equation, and confirmed it experimentally.…”

“…The problem can be observed as a two-dimensional because of axial symmetry. Diez et al (1994) showed that the normalized film thickness h/h 0 can be expressed as a single function of the scaled radial position r/r f , irrespective of the time level.…”