Langmuir 1986,2, 155-160
155
Deformation of Droplets Suspended in Viscous Media in an Electric Field. 1. Rate of Deformation Satoru Moriya,? Keiichiro Adachi, and Tadao Kotaka* Department of Macromolecular Science, Faculty of Science, Osaka University, Toyonaka, Osaka 560, J a p a n Received August 6, 1985. I n Final Form: October 24, 1985 Deformation of droplets suspended in viscous media in an electric field was investigated. Under a low field, a spherical droplet of radius b deformed into an ellipsoid with the major and minor semiaxes Y and X , respectively. From the force balance among the electric force, the interfacial free energy y, and the Y + X)as a function viscous drags acting on the droplet, we derived the degree of deformation D = (Y - X)/( of time t in the low field of strength E as D(t) = D,[1 - exp(-t/~)] with D, = 9q,K2bF/(16y)and T = (ql + q p ) b / ~where , D,, identical with that given by OKonski and Thacher and by Torza et al., is the equilibrium degree of deformation under the given field, eo is the dielectric constant of the vacuum, Kz is the relative dielectric constant of the medium, T is the characteristic time of the droplet deformation, and q1 and qz are the shear viscosities of the droplet and medium, respectively. Tests of these equations were made on droplets of poly(vinylpyrro1idone) solutions and pure water suspended in nonpolar media such as di-n-butyl phthalate solutions of polystyrene under a 60-Hz alternating current field of below 0.5 MV/m. The droplets and media were adjusted so that the one phase is far more viscous than the other; i.e., either q1 >> q, or q1 > v2. The full line represents eq 14. y was examined on all the systems according to our eq 14. To do this, we cast the observed T data into the form T
= (am + P172)b/Y
(16)
with CY and /? as adjustable constants. Since we have deliberately chosen the systems in such a way that they have either ql >> q2 or q1
