Theory of electrostatic dispersion of polymer solutions in the production of microgel beads containing biocatalyst

The theory of electrostatic dispersion of polyelectrolyte solutions is elaborated in order to describe the effect of the applied electric potential U and different physico-chemical factors on the droplet size. It has been shown 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 (ranging 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 critical electric potential U-cr as a function of internal diameter d(c) of a needle, 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 solutions, diffusion coefficients D of surface active species, polarity of applied electric potential and geometry of dropping set-up, and so on, have been obtained. 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 form 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 sign of the applied electric potential greatly influences the droplets size and 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 surface of bulky negatively charged macroions of alginate and small counter ions (e.g. Na+). (C) 1999 Elsevier Science B.V. All rights reserved.