Contact angle measurements are often performed on smooth surfaces to gain information about the wettability of a surface. The interfacial tensions between solid-liquid, liquid-air, and air-solid are $\gamma_{SL}$, $\gamma_{LA}$, and $\gamma_{AS}$, respectively. Which of the following expressions describes the contact angle, $\Theta$?
Contact angle measurements are often performed on smooth surfaces to gain information about the wettability of a surface. The interfacial tensions between solid-liquid, liquid-air, and air-solid are $\gamma_{SL}$, $\gamma_{LA}$, and $\gamma_{AS}$, respectively. Which of the following expressions describes the contact angle, $\Theta$?
Show Hint
- $\cos \Theta = \dfrac{\gamma_{AS}-\gamma_{SL}}{\gamma_{LA}}$
- $\cos \Theta = \dfrac{\gamma_{SL}-\gamma_{AS}}{\gamma_{LA}}$
- $\cos \Theta = \dfrac{\gamma_{LA}-\gamma_{AS}}{\gamma_{SL}}$
- $\cos \Theta = \dfrac{\gamma_{LA}-\gamma_{SL}}{\gamma_{AS}}$
The Correct Option is A
Solution and Explanation
The equilibrium of interfacial tensions at the contact line is: \[ \gamma_{AS} = \gamma_{SL} + \gamma_{LA}\cos \Theta \] Step 2: Rearrange.
\[ \cos \Theta = \frac{\gamma_{AS}-\gamma_{SL}}{\gamma_{LA}} \] Step 3: Match with options.
This exactly corresponds to option (A).
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