Microfluidics Part 2 – Basic Fluid Mechanics

Accessible Equation Supplement

Prof. Steven S. Saliterman
University of Minnesota

1. Viscosity

Equation 1.1 — Dynamic Viscosity

$$\tau = \mu \frac{du}{dy}$$

• \(\tau\): Shear stress
• \(\mu\): Dynamic viscosity
• \(\frac{du}{dy}\): Velocity gradient

Equation 1.2 — Kinematic Viscosity

$$\nu = \frac{\mu}{\rho}$$

• \(\nu\): Kinematic viscosity
• \(\mu\): Dynamic viscosity
• \(\rho\): Density

2. Specific Weight and Gravity

Equation 2.1 — Specific Weight

$$\gamma = \rho g$$

• \(\gamma\): Specific weight
• \(\rho\): Density
• \(g\): Gravity

Equation 2.2 — Specific Gravity

$$SG = \frac{\rho}{\rho_{\text{water}}}$$

3. Reynolds Number

Equation 3.1 — Reynolds Number

$$Re = \frac{\rho V D}{\mu}$$

• \(Re\): Reynolds number
• \(\rho\): Density
• \(V\): Velocity
• \(D\): Diameter
• \(\mu\): Dynamic viscosity

4. Poiseuille Flow

Equation 4.1 — Velocity Profile

$$v_z = \frac{1}{4\mu}\frac{\partial p}{\partial z}(r^2 - R^2)$$

Equation 4.2 — Poiseuille’s Law

$$Q = \frac{\pi R^4 \Delta p}{8\mu l}$$

5. Diffusion

Equation 5.1 — Diffusion Distance

$$x^2 = 2Dt$$

Equation 5.2 — Diffusion Coefficient

$$D = \frac{RT}{6\pi r \eta N_A}$$