Advanced Electrophoretic Force Calculator
Formula Used
Here F is force, q is charge, E is electric field, μ is mobility, η is viscosity, r is particle radius, ε is permittivity, ζ is zeta potential, and f(κa) is the Henry factor.
How to Use This Calculator
Select the model that matches your available data. Use the direct charge model when net particle charge is known. Use the mobility model when measured electrophoretic mobility is available. Use the zeta potential model for colloids or particles with known surface potential.
Enter the electric field directly, or enter applied voltage and distance. Add particle radius, viscosity, and correction factors. Press calculate. The result appears above the form. Download CSV or PDF when you need records for a report.
Example Data Table
| Case | Model | Key Inputs | Expected Use |
|---|---|---|---|
| Charged bead | F = qE | q = 1e-18 C, E = 1000 V/m | Particle tracing force entry |
| Measured mobility | v = μE | μ = 3e-8 m²/(V·s), r = 100 nm | Steady drag estimate |
| Zeta particle | Henry model | ζ = -25 mV, εr = 78.5 | Colloid migration setup |
Electrophoretic Force Modeling Guide
Why Electrophoretic Force Matters
Electrophoretic force describes how a charged particle responds to an electric field. It is important in microfluidics, colloids, gels, membranes, and lab on chip devices. In a simulation model, this force can move ions, beads, cells, droplets, or charged contaminants. The basic idea looks simple. A charge feels force when the field is present. Real systems are often harder. Fluid drag, particle size, surface charge, viscosity, and double layer effects can change the motion. This calculator gives a fast design check before a detailed multiphysics study.
Main Physical View
The direct model uses F equals qE. It is useful when net charge is known. The mobility model uses measured electrophoretic mobility. It estimates steady Stokes drag from the velocity produced by the field. The zeta model uses permittivity, viscosity, zeta potential, and a Henry factor. This path is helpful for suspended particles where surface potential drives motion. The result should be treated as an engineering estimate. It should not replace a resolved electric double layer model when gradients are strong.
Using Results in a Simulation
In a particle tracing study, the force can be entered as a domain force. The direction follows the sign of charge or mobility. A negative value moves opposite to the electric field. In creeping flow, steady motion is usually limited by drag. That is why the calculator reports velocity, Stokes drag, effective charge, and Debye length. These outputs help compare force based and velocity based setups. They also help spot unit mistakes before solving.
Important Modeling Notes
Use consistent units for every input. Electric field may come from voltage divided by distance. Mobility is commonly reported in square meters per volt second. Zeta potential is often entered in millivolts. Viscosity may use milli pascal seconds for water like fluids. Particle radius should be a real radius, not diameter. Ionic strength affects screening and Debye length. High salt gives a thin double layer. Low salt gives longer range electrostatic effects.
Best Practice Checks
Start with a known test case. Compare the calculator force with a simple hand calculation. Then use the same sign convention in the simulation. Keep mesh, solver, and boundary conditions separate from this estimate. Large particles, high fields, and non Newtonian liquids need extra care. Temperature changes viscosity and permittivity. Brownian motion may matter for nanoscale particles. Use this output as a clean reference for setup checks, scaling studies, and documentation.
Limitations to Remember
Electrophoresis can couple with electroosmosis, pressure flow, diffusion, and particle wall interactions. This calculator does not solve those coupled fields. It assumes a simple spherical particle and a representative field value. Use lower fields when heating or electrochemical reactions may occur. Check material data for your exact liquid. Record each assumption beside the result. Clear documentation makes later model calibration easier. Use final values as screening guides, not certified laboratory measurements for regulated design reports.
FAQs
What is electrophoretic force?
Electrophoretic force is the force on a charged particle caused by an electric field. In the simplest form, it equals charge multiplied by field strength. In liquids, drag and surface charge effects also shape the final motion.
Which model should I choose?
Choose the direct charge model when net charge is known. Choose the mobility model when measured mobility is available. Choose the zeta model when surface potential, viscosity, and permittivity describe your suspended particle.
Can I use voltage instead of field?
Yes. Select the voltage and distance option. The calculator divides voltage by the electrode gap or path length. This gives an average electric field for quick setup checks.
Why does sign matter?
The sign tells the migration direction. A positive force follows the electric field direction. A negative force moves opposite to it. This is important when defining domain forces or particle motion settings.
What is the Stokes drag check?
The Stokes drag check estimates resistance on a small spherical particle in viscous flow. It uses radius, viscosity, and velocity. At steady motion, drag can balance electrophoretic driving force.
What does zeta potential mean here?
Zeta potential is an estimate of electrical potential near the slipping plane of a particle. It helps estimate electrophoretic mobility when direct mobility data is not available.
What is the Henry factor?
The Henry factor adjusts mobility for double layer thickness. Smoluchowski is often used for thin double layers. Hückel is often used for thick double layers around small particles.
Why include Debye length?
Debye length estimates electrostatic screening distance in an electrolyte. It helps judge whether double layer effects are thin or thick compared with the particle radius.
Can this replace a full simulation?
No. It is a setup and scaling calculator. A full simulation is still needed for complex fields, wall effects, nonlinear fluids, electroosmosis, diffusion, reactions, or resolved double layers.
What units are safest?
SI units are safest for final checks. Use volts per meter, meters, pascal seconds, coulombs, and square meters per volt second when comparing with equations or model variables.
Why can force and drag differ?
Direct charge force uses qE. Drag uses velocity from mobility. They match only when the effective charge implied by mobility equals the entered net charge. Differences can reveal modeling assumptions.