Droplet Spreading Dynamics

Deposit a small drop of octane on very clean glass and record the radius R,(t) as a function of time (see Fig. 1.17). Plot Tl t) on log/log paper. Check that TZ t, where a 0.1. If we replace the octane with a silicone oil, or even water, provided only that it can wet the glass, we find that all these liquids spread according to a universal law which does not depend on the liquid. If V = 7/ 7 is the characteristic speed and 17 the volume deposited, it is found that 

How can the spreading law V dd) be explained The macroscopic force pulling on the droplet is the unbalanced Young s force 

This force includes two terms S (very large) and 7 d/2 (very small indeed, 10 times smaller than S for angles 6 1°). We will neglect S We shall assume that the frictional force 

One of the majour contributions of de Gennes to wetting dynamics is the demonstration that the frictional force in the precursor film exactly balances S  

It is for this reason that, on a nanoscopic scale, S plays no role whatever in the spreading. On the other hand, the greater S is, the more the precursor film spreads out. 

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To find a rate, one must generally identify the driving force and the resistauice against flow. We elaborated this for a number of examples in sec. 1.6.4. All these examples involved macroscopic amounts of fluid, moving under the influence of external forces and having a resistance of a viscous nature. Under such conditions solution of the Navier-Stokes equation [1.6.1.15] or variants thereof, suffices to describe the fluid dynamics. For a droplet, spreading on a (Fresnel) surface, the situation is more complicated. Flow in the bulk of the drop obeys Navier-Stokes... 

Figure 19. Glycerin droplet spreading on the wax substrate. Time evolution of (a) the spread factor and (b) the dynamic contact angle.

Oliver and Mason [292] have used replica methods to assess the effect of surface roughness on the spreading of liquids and to measure contact angles. For stationary studies, small beads of poly(methyl methacrylate) (PMMA) were melted and the molten droplets spread and solidified on the surfaces. Dynamic studies involved polymer melts mounted on a remotely controlled hot stage stub in the SEM and the experiments were video recorded. 

De Ruijter, M. J. D., Blake, T. D., and Coninck, J. D. 1999. Dynamic Wetting Studied by Molecular Modeling Simulations of Droplet Spreading. Langmuir 15 7836. 

Consequences are remarkable, both on the shape and on the dynamics of a macroscopic nematic droplet spreading spontaneously on a solid substrate. When spreading proceeds, the initial spherical cap profile evolves progressively toward a characteristic bell shape, while the dynamics is accelerated with respect to the one of a simple spreading liquid. Tanner s law is no longer obeyed. 

The effect of surfactants on spray retention efficiency is influenced by droplet size and velocity, leaf angle, and surfactant type and concentration. Examination of spray retention and surface spreading on a range of outdoor-grown crop plants was examined by Anderson et Retention was determined by dynamic surface tension, whereas droplet spreading was related to equilibrium values. They concluded that the basis of selection could be determined by cost, lack of phytotoxicity, and ability to solubilize or aid penetration of the a.i. this would not prejudice the retention properties of the formulation. 

Ruijter MJ, Blake TD, De Coninck J (1999) Dynamic wetting studies by molecular modeling simulations of droplet spreading. Langmuir 15 7836-7847... 

FIGURE 1.3 Complete wetting case the droplet spreads out completely, and only the dynamic contact angle can be measured, which tends to become zero over time. 

It should be noted that the dynamic conditions of droplet impact processes discussed above cover a large range of the actual conditions in many industrial processes, such as spray forming, thermal spray, spray combustion, spray cooling, and aircraft flight. Under these conditions, the spreading behavior of droplets on a flat surface is essentially governed by inertia and viscous effects (Fig. 

If the fluid dynamic conditions of a droplet are within the spreading regime, i.e., below the threshold curve in the We-Oh map, liquid splashing and ejection from the impact surface can be eliminated. The corresponding threshold velocity can be written as ... 

Molecular dynamics has been used extensively to explore the solid-liquid interface. In one such study, a modified Lennard-Jones potential has been used to model this interaction in the spreading of a droplet [4], of the form... 

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