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Hindered electrophoresis of nanoparticles in narrow pores

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Abstract

The hydrodynamic force (drag) on spherical and irregularly shaped particles significantly increases when the particles move close to solid and permeable boundaries. The overall effect of the increased hydrodynamic drag is to hinder the particle movement in the vicinity of boundaries and this includes the Brownian movement and electrophoresis. The Monte Carlo simulation method is used to model the Brownian movement, the resulting diffusion, and the electrophoresis of spherical particles in narrow, cylindrical pores, filled with Newtonian fluids. It is observed that the effect of the pore walls is a significant reduction of the space-averaged electrophoretic velocity of the particles, which implies reduced particle flux through the pores. The hindered electrophoresis is primarily a geometric phenomenon, caused by the increased drag and depends on the size of the particles and the pore-to-particle diameter ratio. The temperature of the fluid slightly affects the hindered electrophoresis through its effect on the viscosity, which is a determinant of the Brownian force, the diffusivity and the electrophoretic velocity. The hindered electrophoresis is almost independent of the other fluid and particle properties, such as density. Based on the simulation results a non-linear correlation for the flux of particles is derived, valid in the ranges 5 < R/α < 120, 5 nm < α < 100 nm and 273 K < T < 355 K.

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Abbreviations

D :

Particle diffusivity

E :

Electric field intensity

F :

Force

h :

Particle distance from the wall

k B :

Boltzmann constant

K :

Drag enhancement parameter

m:

Mass

NBE :

Dimensionless force

q:

Surface charge of the particle

r :

Radial coordinate

R :

Radius of the pore

\(\vec{R}\) :

Random number

Re :

Reynolds number

t :

Time

T :

Temperature

u :

Fluid velocity

v :

Particle velocity

V el :

Thermophoretic velocity

V el∞ :

Thermophoretic velocity in an infinite medium

z :

Axial coordinate

α :

Particle radius

ε :

Electric permittivity

ζ :

Zeta-potential

μ :

Dynamic viscosity

ν :

Dynamic viscosity

ρ :

Density

τ :

Characteristic time

av:

Average

el:

Electrophoretic

f:

Fluid

p:

Particle

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Acknowledgements

This research was partly supported by the W. A. “Tex” Chair of Engineering at Texas Christian University.

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  1. Department of Engineering, TCU, Fort Worth, TX, 76132, USA

    Efstathios E. Michaelides

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Correspondence to Efstathios E. Michaelides.

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Michaelides, E.E. Hindered electrophoresis of nanoparticles in narrow pores. J Therm Anal Calorim 135, 1363–1371 (2019). https://doi.org/10.1007/s10973-018-7462-x

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