1. What is Ionic Mobility given Zeta Potential?

Definition: This calculator determines the ionic mobility using the Smoluchowski equation based on zeta potential, relative permittivity of the solvent, and dynamic viscosity.

Purpose: It helps in electrochemistry and colloid science to understand the movement of ions in a liquid medium under an electric field.

2. How Does the Calculator Work?

The calculator uses the Smoluchowski equation:

Where:

• \( μ \) — Ionic mobility (m²/V·s)
• \( ζ \) — Zeta potential (V)
• \( ε_r \) — Relative permittivity of solvent (dimensionless)
• \( μ_{liquid} \) — Dynamic viscosity of liquid (Pa·s)
• \( \pi \) — Archimedes' constant (~3.14159)

Explanation: The zeta potential and relative permittivity determine the driving force, while viscosity provides the resistance to ion movement.

3. Importance of Ionic Mobility Calculation

Details: Ionic mobility is crucial for understanding electrochemical processes, designing batteries, electrophoresis applications, and studying colloidal systems.

4. Using the Calculator

Tips: Enter zeta potential in volts, relative permittivity (150 for water at 20°C), and dynamic viscosity in Pa·s (1 for water at 20°C). Viscosity must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is typical zeta potential range?
A: Typically between ±100 mV, with most colloidal systems in the range of ±10 to ±50 mV.

Q2: Why is relative permittivity important?
A: It determines how much the solvent reduces the electric field between ions compared to vacuum.

Q3: How does temperature affect the calculation?
A: Temperature affects both viscosity and permittivity. Higher temperature generally decreases viscosity and slightly decreases permittivity.

Q4: What are typical ionic mobility values?
A: For small ions in water at 25°C, typically 5-10 × 10⁻⁸ m²/V·s.

Q5: When is the Smoluchowski equation valid?
A: For thin double layers (high ionic strength) where the particle radius is much larger than the Debye length.