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Nonlinear electrokinetic phenomena, where electrically driven fluid flows depend nonlinearly on the applied voltage, are commonly encountered in aqueous suspensions of colloidal particles. A prime example is the induced-charge electro-osmosis, driven by an electric field acting on diffuse charge induced near a polarizable surface. Nonlinear electrohydrodynamic flows also occur in non-polar fluids, driven by the electric field acting on space charge induced by conductivity gradients. Here, we analyse the flows about a charge-neutral spherical solid particle in an applied uniform electric field that arise from conductivity dependence on local field intensity. The flow pattern varies with particle conductivity: while the flow about a conducting particle has a quadrupolar pattern similar to induced-charge electro-osmosis, albeit with opposite direction, the flow about an insulating particle has a more complex structure. We find that this flow induces a force on a particle near an electrode that varies non-trivially with particle conductivity: while it is repulsive for perfectly insulating particles and particles more conductive than the suspending medium, there exists a range of particle conductivities where the force is attractive. The force decays as the inverse square of the distance to the electrode and thus can dominate the dielectrophoretic attraction due to the image dipole, which falls off with the fourth power with the distance. This electrohydrodynamic lift opens new possibilities for colloidal manipulation and driven assembly by electric fields.
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Capacitance of a conducting hollow cylindrical shell in a closed form
The charge distribution within a hollow conducting cylinder with zero-thickness walls is calculated from the minimum potential energy (𝑈) consideration. The surface charge density consists of a diverging term (Jackson, 1975) and a sum of Legendre polynomials with the coefficients determined from the minimum 𝑈 approach. The sum converges. This allows to express the capacitance in closed form. It is in agreement with Butler (1980). We present electric field lines inside and outside of the cylinder. An electric field pattern can be studied in detail. Most of the numerical analysis is done for the conducting cylinder of the length equal to ten radii. The surface charge density near the edges diverges; and in the middle, it is twenty five percent less than that of a uniformly distributed charge. The self-energy of the conducting cylinder is about 5 percent lower than that of uniformly distributed surface charge.
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- Award ID(s):
- 2230363
- PAR ID:
- 10538990
- Editor(s):
- Lacks, Daniel
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Journal of Electrostatics
- Edition / Version:
- 1
- Volume:
- 126
- Issue:
- C
- ISSN:
- 0304-3886
- Page Range / eLocation ID:
- 103866
- Subject(s) / Keyword(s):
- Electrostatic potential Electrostatic energy
- Format(s):
- Medium: X Size: 1MB Other: pdf
- Size(s):
- 1MB
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.elstat.2023.103866
