Lab-on-a-Chip Part 1 – Cell & Molecule Techniques

Accessible Equation Supplement

Prof. Steven S. Saliterman
University of Minnesota

1. Young’s Equation

Equation 1.1 — Young’s Contact Angle Relationship

$$\gamma_{LG}\cos\theta + \gamma_{SL} = \gamma_{SG}$$

• \(\gamma_{LG}\): Liquid–gas interfacial tension (N/m)
• \(\gamma_{SL}\): Solid–liquid interfacial tension (N/m)
• \(\gamma_{SG}\): Solid–gas interfacial tension (N/m)
• \(\theta\): Contact angle (degrees)

2. Electrowetting

Equation 2.1 — Contact Angle Under Applied Voltage

$$\cos\theta(V) - \cos\theta_0 = \frac{2\gamma_{LG}}{\varepsilon_r \varepsilon_0}\frac{t}{V^2}$$

• \(\theta(V)\): Contact angle under applied voltage
• \(\theta_0\): Equilibrium contact angle
• \(V\): Electric potential (V)
• \(\varepsilon_r\): Relative dielectric constant
• \(\varepsilon_0\): Permittivity of free space
• \(t\): Dielectric thickness (m)
• \(\gamma_{LG}\): Liquid–gas interfacial tension (N/m)