Electrokinetics

⚡️	Electrogravitics	Electrokinetics
🧲	Magnetogravitics	Magnetokinetics

Electrokinetics

Electrokinetics is a branch of physics and chemistry that investigates the electrically induced motion of charged particles, fluids, or interfaces, encompassing a range of interfacial phenomena driven by electric fields or generating them through mechanical means. Key effects include electrophoresis (motion of dispersed particles in a fluid under an electric field), electroosmosis (bulk fluid motion through a porous medium or capillary due to an applied electric field), streaming potential (electric potential generated by fluid flow over a charged surface), and sedimentation potential (electric field from settling charged particles). These phenomena originate from the electrical double layer (EDL) at solid-liquid interfaces, where fixed surface charges are balanced by mobile counterions, leading to tangential forces under external fields. Electrokinetics plays a crucial role in colloid science, with theoretical foundations linking electrostatics, fluid dynamics, and transport processes, and has been quantitatively described since the 19th century. Modern extensions incorporate nonlinear effects, AC fields, and nanoscale considerations for advanced applications.

History

• The discovery of electrokinetic phenomena dates back to 1809 when Ferdinand Friedrich Reuss observed electroosmotic flow through porous clay diaphragms under an applied voltage, marking the first documented electrokinetic effect.
  • Reuss's experiments demonstrated water movement from anode to cathode, attributing it to electrical forces on charged interfaces.
• In 1859, Georg Quincke discovered the streaming potential, establishing the reciprocal nature of electroosmosis and streaming effects.
• Theoretical advancements began in 1879 with Hermann von Helmholtz's model of the electrical double layer and the introduction of the zeta potential $\zeta$.
  • Marian Smoluchowski (1903) derived the Helmholtz–Smoluchowski equation for thin double layers.
  • Gouy (1910) and Chapman (1913) developed the diffuse double-layer model, followed by Stern's 1924 combination of fixed and diffuse layers.
• The 20th century saw widespread application in colloid chemistry, geophysics, and, from the 1990s onward, microfluidics and nanotechnology.
  • Induced-charge electrokinetics (ICEK) was formalized by Bazant et al. in 2004–2010.

Theoretical Basis

Electrokinetics couples the Poisson equation for the electric potential with the Navier–Stokes equations and ion transport (Nernst–Planck).

• Poisson equation (electrostatics in the EDL):

$\nabla ^{2}\psi =-{\frac {\rho _{e}}{\varepsilon }}$

where $\psi$ is the electric potential and $\rho _{e}=F\sum z_{i}c_{i}$ is the charge density.

• Helmholtz–Smoluchowski electroosmotic velocity (thin EDL limit, $\kappa a\gg 1$):

$v_{\mathrm {EO} }=-{\frac {\varepsilon \zeta }{\eta }}\mathbf {E}$

• Electrophoretic velocity (Hückel–Onsager limit for thick EDL, $\kappa a\ll 1$):

$v_{\mathrm {EP} }={\frac {2\varepsilon \zeta }{3\eta }}\mathbf {E}$

Henry's function $f(\kappa a)$ interpolates between 1 (Hückel) and 1.5 (Smoluchowski).

• Streaming potential coefficient:

$\left({\frac {\Delta \phi }{\Delta P}}\right)_{I=0}=-{\frac {\varepsilon \zeta }{\eta \sigma }}$

• Full Poisson–Nernst–Planck–Navier–Stokes (PNP–NS) system for nonlinear and transient electrokinetics:

${\frac {\partial c_{i}}{\partial t}}+\nabla \cdot \left(-D_{i}\nabla c_{i}-{\frac {z_{i}D_{i}F}{RT}}c_{i}\nabla \psi +c_{i}\mathbf {v} \right)=0$

$\rho \left({\frac {\partial \mathbf {v} }{\partial t}}+\mathbf {v} \cdot \nabla \mathbf {v} \right)=-\nabla p+\eta \nabla ^{2}\mathbf {v} +\rho _{e}\mathbf {E}$

• Induced-charge electroosmosis (ICEO) slip velocity on polarizable surfaces:

$\mathbf {v} _{\mathrm {slip} }=-{\frac {\varepsilon }{\eta }}\langle \mathbf {E} _{t}\rangle \Delta \mathbf {E} _{t}$

• Dukhin number (surface vs. bulk conduction):

$\mathrm {Du} ={\frac {K^{s}}{K^{b}a}}$

Applications

• Soil and groundwater remediation (electrokinetic remediation) – removal of heavy metals and organic pollutants from low-permeability clays.
• Microfluidics – electroosmotic and electrophoretic pumping in lab-on-a-chip devices; capillary electrophoresis for DNA/protein separation.
• Biomedical – transdermal drug delivery (iontophoresis), electrophoretic displays (e-ink), cell sorting via dielectrophoresis.
• Geophysics – streaming potential surveys for fracture mapping and hydrocarbon exploration.
• Energy harvesting – reverse electrodialysis and pressure-driven streaming currents in nanochannels.
• Industrial – electrokinetic dewatering of slurries, food processing, and nanoparticle self-assembly.

Discipline	Relevant Mainstream Object/Equation	Role in Electrokinetics
Fluid Dynamics	$\rho \left({\frac {\partial \mathbf {v} }{\partial t}}+\mathbf {v} \cdot \nabla \mathbf {>} \mathbf {v} \right)=-\nabla p+\eta \nabla ^{2}\mathbf {v} +\rho _{e}\mathbf {E}$	Navier–Stokes with body force from electric double layer
Electrochemistry	$\nabla ^{2}\psi =-{\frac {\rho _{e}}{\varepsilon }}$	Poisson equation for potential in the EDL
Colloid Science	$v_{\mathrm {EP} }={\frac {\varepsilon \zeta }{\eta }}\mathbf {E} \cdot f(\kappa a)$	Henry’s equation for particle mobility
Environmental Engineering	$v_{\mathrm {EO} }=-{\frac {\varepsilon \zeta }{\eta }}\mathbf {E}$	Helmholtz–Smoluchowski electroosmotic flow
Microfluidics	$\mu _{\mathrm {ep} }={\frac {\varepsilon \zeta }{\eta }}$	Electrophoretic mobility in capillary electrophoresis
Geophysics	$C_{s}={\frac {\Delta \phi }{\Delta P}}=-{\frac {\varepsilon \zeta }{\eta \sigma }}$	Streaming potential coefficient for subsurface imaging
Biomedical Engineering	$J_{\mathrm {drug} }=-\mu _{\mathrm {EO} }C_{\mathrm {drug} }E$	Iontophoretic flux across skin
Nanotechnology	$\mathbf {F} _{\mathrm {DEP} }=2\pi \varepsilon _{m}r^{3}\mathrm {Re} [K(\omega )]\nabla E^{2}$	Dielectrophoretic force for nanoparticle manipulation
Chemical Engineering	$\mathbf {J} _{i}=-D_{i}\nabla c_{i}-{\frac {z_{i}D_{i}Fc_{i}}{RT}}\nabla \psi +c_{i}\mathbf {v}$	Nernst–Planck flux equation for ion transport
Nonlinear Electrokinetics	$\mathrm {Du} ={\frac {K^{s}}{K^{b}a}},\ \ \mathrm {Wi} ={\frac {\beta Ea}{2D}}$	Dimensionless numbers governing surface-conduction and field-enhanced dissociation effects