Interdisciplinary Applied Mathematics

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n-Hexane


20


18.4


51.1


n-Octane


20


21.8


50.8


Olive Oil


20


20


Silicone Oil (PDMS)


25


20

TABLE 8.1. Surface tension values for some liquids ( 1 mN/m = 1 dyn/cm).


When в > 90°, the liquid is nonwetting, and thus the solid is called hydrophobic.


When в = 0, we have complete wetting.


A schematic is shown in Figure 8.4. In the following we will present a more general version of this equation.

8.2 General Form of Young’s Equation


The triple-line force balance expressed in equation (8.6) is valid for simple cases, but it is inadequate in describing situations in which internal bulk forces in    the    droplet    are present,    e.g.,    due    to gravity or    electric    fields.    In


such cases these bulk forces have to be balanced against the interfacial forces. An effective approach to obtaining the governing equations is to consider the total energy of the system and minimize it in order to obtain equilibrium solutions. Such procedures have been developed and applied in (deGennes, 1985; Dussan, 1979; Digilov, 2000), and also in (Shapiro et al., 2003a); here    we    follow    the    analysis    of    (Shapiro    et    al.,    2003a),    which is


directly applicable to microfluidic problems.


The starting point is to assume that the droplet is spherical, characterized fully by its radius R and the contact angle в. Other system parameters will depend on the specific application, e.g., gravity, temperature, voltage. Having the energy E = E(R, в) as a function of two independent variables, at equilibrium we have that dE(R, 9) = 0, and thus

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