Viscosity of Solvent given Zeta Potential using Smoluchowski Equation Calculator

Dynamic Viscosity Formula:

\[ \mu_{liquid} = \frac{\zeta \times \varepsilon_r}{4 \times \pi \times \mu} \]

Dynamic Viscosity of Liquid (Pa·s):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Viscosity of Solvent given Zeta Potential?

Definition: This calculator determines the dynamic viscosity of a liquid solvent using the Smoluchowski equation, which relates viscosity to zeta potential, relative permittivity, and ionic mobility.

Purpose: It's used in electrokinetic phenomena studies, particularly in colloid chemistry and surface science to analyze liquid properties.

2. How Does the Calculator Work?

The calculator uses the Smoluchowski equation:

\[ \mu_{liquid} = \frac{\zeta \times \varepsilon_r}{4 \times \pi \times \mu} \]

Where:

\( \mu_{liquid} \) — Dynamic viscosity of liquid (Pa·s)
\( \zeta \) — Zeta potential (V)
\( \varepsilon_r \) — Relative permittivity of solvent (dimensionless)
\( \mu \) — Ionic mobility (m²/V·s)
\( \pi \) — Archimedes' constant (~3.14159)

Explanation: The equation relates the electrokinetic potential at the slipping plane to the liquid's resistance to flow.

3. Importance of Viscosity Calculation

Details: Accurate viscosity determination is crucial for understanding fluid behavior in electrokinetic processes, designing microfluidic devices, and studying colloidal systems.

4. Using the Calculator

Tips:

Enter zeta potential in volts (typically 10-200 mV for colloidal systems)
Relative permittivity is dimensionless (78.5 for water at 25°C)
Ionic mobility in m²/V·s (typical range 5×10⁻⁸ to 8×10⁻⁸ for common ions)

5. Frequently Asked Questions (FAQ)

Q1: What is zeta potential?
A: Zeta potential is the electric potential at the slipping plane, the boundary between the stationary layer of fluid attached to a particle and the mobile fluid.

Q2: When is the Smoluchowski equation valid?
A: It's valid for thin double layers (κa ≫ 1) where κ is the Debye length and a is the particle radius.

Q3: What affects ionic mobility?
A: Ionic mobility depends on ion charge, size, solvent viscosity, and temperature.

Q4: How does temperature affect the calculation?
A: Temperature affects all parameters - zeta potential, permittivity, and mobility are all temperature-dependent.

Q5: What are typical viscosity values for common solvents?
A: Water at 20°C: ~0.001 Pa·s; Ethanol: ~0.0012 Pa·s; Glycerol: ~1.5 Pa·s (all at 20°C).