Hydrodynamic Mapping of Two-Dimensional Electric Fields in Monolayers

We have measured the 2D dipolar electric fields generated by surface density fluctuations in Langmuir monolayers using optical microscopy to monitor the motion of micron-size, electrically charged, particles trapped at the air-water interface. The particle velocity is directly proportional to the local electric field gradient. Quantitative agreement with the theory is demonstrated for charged polystyrene latex particles interacting with liquid condensed domains of pentadecanoic acid. Typical velocities are of order $0.1--10\mu \mathrm{m}/\mathrm{s}$, corresponding to forces in the ${10}^{-15\mathrm{}}--{10}^{-12\mathrm{}}\mathrm{N}$ range.