Droplet Sliding and Spray Retention

Several authors [119] have tried to relate the resistance to movement of liquid drops on a tilted surface to the surface tension and the contact angles (advancing and receding) of liquid droplets with the solid surface. The detailed analysis given by Furmidge [119] is summarized below. 

The above force is opposed by the surface force resulting from wetting and dewetting of the leaf surface as the droplet slides downwards. In moving down, an area w dl of the leaf is wetted by the droplet and a similar area is dewetted by the trailing edge. The work of wetting per unit area of the surface is equal to + 1)j 

If the impaction of the spray is uniform and the spray droplets are reasonably homogeneous in size, the total volume of spray retained in an area of surface is proportional to the time of spraying until the time when the first droplet runs off the surface. Also, the volume v of spray retained per unit area, R, at the moment of incipient run-off is given by 

Combining Eqs. (14.64) and (14.65), it is possible to obtain an expression for w, the diameter of adhering droplet in terms of the surface forces given above, i.e. la and 0, 

The value of k depends on the droplet spectrum, since it relates to the rate of buildup of critical droplets and their distribution. However, Eq. (14.67) does not take into account the flattening effect of the droplet on impact, which results in reduction of 6 and increase of w above the value predicted by Eq. (14.66). Thus, Eq. (14.67) is only likely to be valid under conditions of small impaction velocity. In this case, retention is governed by the surface tension of the spray liquid, the difference between 6 and Or (i.e. the contact angle hysteresis) and the value of 0a-Equation (14.67) can be further simplified by removing the constant terms and standardizing sin a as equal to 1. A further simplification is to replace the second term between square brackets on the right-hand side of Eq. (14.67) by 0m the arithmetic mean of 0a and 0r. In this way a retention factor, F, may be defined by the simple expression 

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