Zeta Potential using Smoluchowski Equation Solution

STEP 0: Pre-Calculation Summary
Formula Used
Zeta Potential = (4*pi*Dynamic Viscosity of Liquid*Ionic Mobility)/Relative Permittivity of Solvent
ζ = (4*pi*μliquid*μ)/εr
This formula uses 1 Constants, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Zeta Potential - (Measured in Volt) - Zeta potential is the electrical potential at the slipping plane. This plane is the interface that separates the mobile fluid from the fluid that remains attached to the surface.
Dynamic Viscosity of Liquid - (Measured in Pascal Second) - The Dynamic Viscosity of Liquid is the measure of its resistance to flow when an external force is applied.
Ionic Mobility - (Measured in Square Meter per Volt per Second) - The Ionic Mobility is described as the speed achieved by an ion moving through a gas under a unit electric field.
Relative Permittivity of Solvent - The Relative Permittivity of Solvent is defined as the relative permittivity or dielectric constant is the ratio of the absolute permittivity of a medium to the permittivity of free space.
STEP 1: Convert Input(s) to Base Unit
Dynamic Viscosity of Liquid: 10 Poise --> 1 Pascal Second (Check conversion here)
Ionic Mobility: 56 Square Meter per Volt per Second --> 56 Square Meter per Volt per Second No Conversion Required
Relative Permittivity of Solvent: 150 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ζ = (4*pi*μliquid*μ)/εr --> (4*pi*1*56)/150
Evaluating ... ...
ζ = 4.69144502936076
STEP 3: Convert Result to Output's Unit
4.69144502936076 Volt --> No Conversion Required
FINAL ANSWER
4.69144502936076 4.691445 Volt <-- Zeta Potential
(Calculation completed in 00.004 seconds)

Credits

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Amity Institute Of Applied Sciences (AIAS, Amity University), Noida, India
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7 Electrophoresis and other Electrokinetics Phenomena Calculators

Viscosity of Solvent given Zeta Potential using Smoluchowski Equation
Go Dynamic Viscosity of Liquid = (Zeta Potential*Relative Permittivity of Solvent)/(4*pi*Ionic Mobility)
Ionic Mobility given Zeta Potential using Smoluchowski Equation
Go Ionic Mobility = (Zeta Potential*Relative Permittivity of Solvent)/(4*pi*Dynamic Viscosity of Liquid)
Relative Permittivity of Solvent given Zeta Potential
Go Relative Permittivity of Solvent = (4*pi*Dynamic Viscosity of Liquid*Ionic Mobility)/Zeta Potential
Zeta Potential using Smoluchowski Equation
Go Zeta Potential = (4*pi*Dynamic Viscosity of Liquid*Ionic Mobility)/Relative Permittivity of Solvent
Drift Velocity of Dispersed Particle given Electrophoretic Mobility
Go Drift Velocity of Dispersed Particle = Electrophoretic Mobility*Electric Field Intensity
Electric Field Intensity given Electrophoretic Mobility
Go Electric Field Intensity = Drift Velocity of Dispersed Particle/Electrophoretic Mobility
Electrophoretic Mobility of Particle
Go Electrophoretic Mobility = Drift Velocity of Dispersed Particle/Electric Field Intensity

16 Important Formulas of Colloids Calculators

Surface Enthalpy given Critical Temperature
Go Surface Enthalpy = (Constant for each Liquid)*(1-(Temperature/Critical Temperature))^(Empirical Factor-1)*(1+((Empirical Factor-1)*(Temperature/Critical Temperature)))
Surface Entropy given Critical Temperature
Go Surface Entropy = Empirical Factor*Constant for each Liquid*(1-(Temperature/Critical Temperature))^(Empirical Factor)-(1/Critical Temperature)
Ionic Mobility given Zeta Potential using Smoluchowski Equation
Go Ionic Mobility = (Zeta Potential*Relative Permittivity of Solvent)/(4*pi*Dynamic Viscosity of Liquid)
Number of Moles of Surfactant given Critical Micelle Concentration
Go Number of Moles of Surfactant = (Total Concentration of Surfactant-Critical Micelle Concentration)/Degree of Aggregation of Micelle
Zeta Potential using Smoluchowski Equation
Go Zeta Potential = (4*pi*Dynamic Viscosity of Liquid*Ionic Mobility)/Relative Permittivity of Solvent
Micellar Core Radius given Micellar Aggregation Number
Go Micelle Core Radius = ((Micellar Aggregation Number*3*Volume of Hydrophobic Tail)/(4*pi))^(1/3)
Volume of Hydrophobic Tail given Micellar Aggregation Number
Go Volume of Hydrophobic Tail = ((4/3)*pi*(Micelle Core Radius^3))/Micellar Aggregation Number
Micellar Aggregation Number
Go Micellar Aggregation Number = ((4/3)*pi*(Micelle Core Radius^3))/Volume of Hydrophobic Tail
Critical Packing Parameter
Go Critical Packing Parameter = Surfactant Tail Volume/(Optimal Area*Tail Length)
Specific Surface Area for array of n Cylindrical Particles
Go Specific Surface Area = (2/Density)*((1/Cylinder Radius)+(1/Length))
Electrophoretic Mobility of Particle
Go Electrophoretic Mobility = Drift Velocity of Dispersed Particle/Electric Field Intensity
Surface Viscosity
Go Surface Viscosity = Dynamic Viscosity/Thickness of Surface Phase
Critical Chain Length of Hydrocarbon Tail using Tanford Equation
Go Critical Chain Length of Hydrocarbon Tail = (0.154+( 0.1265*Number of Carbon Atoms))
Specific Surface Area
Go Specific Surface Area = 3/(Density*Radius of Sphere)
Number of Carbon Atoms given Critical Chain Length of Hydrocarbon
Go Number of Carbon Atoms = (Critical Chain Length of Hydrocarbon Tail-0.154)/0.1265
Volume of Hydrocarbon Chain using Tanford Equation
Go Micelle Core Volume = (27.4+(26.9*Number of Carbon Atoms))*(10^(-3))

Zeta Potential using Smoluchowski Equation Formula

Zeta Potential = (4*pi*Dynamic Viscosity of Liquid*Ionic Mobility)/Relative Permittivity of Solvent
ζ = (4*pi*μliquid*μ)/εr

What is Zeta Potential?

The Zeta potential is defined as the difference in potential between the surface of the tightly bound layer {commonly known as Stern's layer (or inner Helmholtz layers)} and the electroneutral regions (of the diffuse layers) of the solutions.

Electrokinetic Potential or Zeta Potential

Zeta Potential is determined by measuring the relative movement, with respect to one another, of a solid and liquid accompanied by certain electrical phenomena which are referred to as electrokinetic effect. These phenomena are ascribed to the presence of a potential difference at the interface between any two phases at which movement occurs; this potential is known as the electrokinetic potential or, frequently, as the Zeta Potential.

How to Calculate Zeta Potential using Smoluchowski Equation?

Zeta Potential using Smoluchowski Equation calculator uses Zeta Potential = (4*pi*Dynamic Viscosity of Liquid*Ionic Mobility)/Relative Permittivity of Solvent to calculate the Zeta Potential, The Zeta Potential using Smoluchowski equation is defined as the electrical potential at the slipping plane. This plane is the interface that separates the mobile fluid from the fluid that remains attached to the surface. Zeta Potential is denoted by ζ symbol.

How to calculate Zeta Potential using Smoluchowski Equation using this online calculator? To use this online calculator for Zeta Potential using Smoluchowski Equation, enter Dynamic Viscosity of Liquid liquid), Ionic Mobility (μ) & Relative Permittivity of Solvent r) and hit the calculate button. Here is how the Zeta Potential using Smoluchowski Equation calculation can be explained with given input values -> 4.691445 = (4*pi*1*56)/150.

FAQ

What is Zeta Potential using Smoluchowski Equation?
The Zeta Potential using Smoluchowski equation is defined as the electrical potential at the slipping plane. This plane is the interface that separates the mobile fluid from the fluid that remains attached to the surface and is represented as ζ = (4*pi*μliquid*μ)/εr or Zeta Potential = (4*pi*Dynamic Viscosity of Liquid*Ionic Mobility)/Relative Permittivity of Solvent. The Dynamic Viscosity of Liquid is the measure of its resistance to flow when an external force is applied, The Ionic Mobility is described as the speed achieved by an ion moving through a gas under a unit electric field & The Relative Permittivity of Solvent is defined as the relative permittivity or dielectric constant is the ratio of the absolute permittivity of a medium to the permittivity of free space.
How to calculate Zeta Potential using Smoluchowski Equation?
The Zeta Potential using Smoluchowski equation is defined as the electrical potential at the slipping plane. This plane is the interface that separates the mobile fluid from the fluid that remains attached to the surface is calculated using Zeta Potential = (4*pi*Dynamic Viscosity of Liquid*Ionic Mobility)/Relative Permittivity of Solvent. To calculate Zeta Potential using Smoluchowski Equation, you need Dynamic Viscosity of Liquid liquid), Ionic Mobility (μ) & Relative Permittivity of Solvent r). With our tool, you need to enter the respective value for Dynamic Viscosity of Liquid, Ionic Mobility & Relative Permittivity of Solvent and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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