數學有意思

2007年5月24日 星期四

2007年5月22日 星期二

Electrohydrodynamic (EHD) flow

Electrohydrodynamic (EHD) flow around a charged spherical colloid near
an electrode was studied theoretically and experimentally to understand the
nature of long-range particle–particle attraction near electrodes. Numerical
computations for finite double-layer thicknesses confirmed the validity of an
asymptotic methodology for thin layers. Then the electric potential around the
particle was computed analytically in the limit of zero Peclet number and thin
double layers for oscillatory electric fields at frequencies where Faradaic
reactions are negligible. Streamfunctions for the steady component of the EHD
flow were determined with an electro-osmotic slip boundary condition on the
electrode surface. Accordingly, it was established how the axisymmetric flow
along the electrode is related to the dipole coefficient of the colloidal
particle. Under certain conditions, the flow is directed toward the particle and
decays as r?4, in accord with observations of long-range particle aggregation.
To test the theory, particle-tracking experiments were performed with
fluorescent 300 nm particles around 50μm particles over a wide range of
electric field strengths and frequencies. Treating the particle surface
conductivity as a fitting parameter yields velocities in excellent agreement
with the theoretical predictions. The observed frequency dependence, however,
differs from the model predictions, suggesting that the effect of convection on
the charge distribution is not negligible as assumed in the zero Peclet number
limit.