Electroconvection in a layer of liquid subjected to unipolar
injection is characterized
by two stability criteria, a linear and a nonlinear one, with an
associated hysteresis
loop. Experimentally it is found that the velocity field fluctuates
around its mean value.
A temporal analysis of the measured current, which is directly related
to the velocity,
revealed the existence of a well-defined frequency correlated to the
mean rotation time
of a fluid particle in the convective cell, thus indicating
that these fluctuations are not
stochastic but related to the intrinsic dynamics of the system. Here a
method of
superparticles is used to solve the problem of the non-stationary
electroconvection of
the liquid. A good agreement between theoretical and experimental
results is obtained.