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Wetting

The spreading of a liquid over a solid depends on the components of the interfacial tensions acting parallel to the solid surface at the line of contact, of which the net force per unit length of the triple interface along the solid surface will then be ${\mathrm{F}}_{\mathrm{h}}(\theta )={\gamma }_{\mathrm{VS}}-{\gamma }_{\mathrm{LS}}-{\gamma }_{\mathrm{VL}}\cos (\theta )$. The triple interface will move in the direction dictated by ${\mathrm{F}}_{\mathrm{h}}$ until a value of $\theta$ is reached at which ${\mathrm{F}}_{\mathrm{h}}=0$, giving equilibrium, or, if such a position is not possible, the liquid spreads completely, and then ${\theta }^{\prime }=0,\cos {\theta }^{\prime }=1$, and the equation becomes:

It is convenient to define a spreading coefficient, ${\mathrm{S}}_{\mathrm{LS}}$, by

If ${\mathrm{S}}_{\mathrm{LS}}>0$, the liquid spreads completely, whereas if ${\mathrm{S}}_{\mathrm{LS}}\le 0$ the drop does not spread completely and it finds an equilibrium contact angle ${\theta }_{\mathrm{eq}}$ where ${\mathrm{F}}_{\mathrm{h}}=0$.