D. Poncelet et al., Theory of electrostatic dispersion of polymer solutions in the production of microgel beads containing biocatalyst, ADV COLL IN, 79(2-3), 1999, pp. 213-228
The theory of electrostatic dispersion of polyelectrolyte solutions is elab
orated in order to describe the effect of the applied electric potential U
and different physico-chemical factors on the droplet size. It has been sho
wn that the droplet diameters d gradually decrease with increasing U as d(U
) congruent to d(o)[1 - (U/U-cr)(2)](1/3) up to some critical value U-cr (r
anging between similar to 2 kV and similar to 10 kV). In the region U> U-cr
unstable liquid jets begin to form which disaggregate in multiple droplets
with diameters smaller than 0.1 mm. The analytical expression for the crit
ical electric potential U-cr as a function of internal diameter d(c) of a n
eedle, distance h between electrodes, surface tension gamma(o) of a polymer
solution, as well as of viscosity eta and now rate j(v) of polymer solutio
ns, diffusion coefficients D of surface active species, polarity of applied
electric potential and geometry of dropping set-up, and so on, have been o
btained. Particularly, it has been shown that the viscosity eta as well as
the surface tension gamma(o) have little influence on U-cr when droplets fo
rm in non-equilibrium conditions, i.e. when the characteristic time tau(ad)
of adsorption of surface active species at the surface of droplets is much
greater than the droplet formation time tau(v). On the other hand, the sig
n of the applied electric potential greatly influences the droplets size an
d U-cr, which is explained by the difference in the diffusion coefficients
D and consequently in the time tau(ad) of adsorption at the droplets surfac
e of bulky negatively charged macroions of alginate and small counter ions
(e.g. Na+). (C) 1999 Elsevier Science B.V. All rights reserved.