Ionic Mobility Formula:
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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.
The calculator uses the Smoluchowski equation:
Where:
Explanation: The zeta potential and relative permittivity determine the driving force, while viscosity provides the resistance to ion movement.
Details: Ionic mobility is crucial for understanding electrochemical processes, designing batteries, electrophoresis applications, and studying colloidal systems.
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.
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.