Primary electroviscous effect in a dilute suspension of charged spherical colloidal particles with a slip surface
- PDF / 486,270 Bytes
- 7 Pages / 595.276 x 790.866 pts Page_size
- 25 Downloads / 219 Views
ORIGINAL CONTRIBUTION
Primary electroviscous effect in a dilute suspension of charged spherical colloidal particles with a slip surface Hiroyuki Ohshima 1 Received: 10 March 2020 / Revised: 8 August 2020 / Accepted: 28 August 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The theory of Watterson and White (J Chem Soc Faraday Trans II, 77: 1115, 1981) on the primary electroviscous effect in a dilute suspension of charged spherical colloidal particles in an electrolyte solution is extended to cover the case where liquid slip occurs on the particle surface on the basis of the Navier boundary condition suitable for a hydrophobic surface. The general expressions for the effective viscosity and the primary electroviscous coefficient of the suspension as well as their low-zeta potential approximate expressions are derived. Keywords Effective viscosity . Primary electroviscous coefficient . Zeta potential . Spherical particle . Slip surface . Hydrophobic surface
Introduction A suspension of colloidal particles in a liquid has an effective viscosity ηs that is greater than the viscosity η of the original liquid. Einstein [1] derived the following expression for ηs of a dilute suspension of uncharged spherical colloidal particles: 5 ð1Þ ηs ¼ η 1 þ ϕ 2 where ϕ is the particle volume fraction. Taylor [2] obtained an expression for ηs of a dilute suspension of uncharged liquid drops of viscosity ηd, which is given by 5ηd þ 2η ϕ ð2Þ ηs ¼ η 1 þ 2 ð η d þ ηÞ As ηd → ∞, Eq. (2) reduces back to Eq. (1). When the liquid contains an electrolyte and the particles are charged, ηs is further increased due to the presence of the electrical double layer around the particles. For a dilute particle suspension, this phenomenon is called primary electroviscous effect and we may write
* Hiroyuki Ohshima [email protected] 1
Faculty of Pharmaceutical Sciences, Tokyo University of Science, 2641 Yamazaki Noda, Chiba 278-8510, Japan
5 ηs ¼ η 1 þ ð1 þ pÞϕ 2
ð3Þ
where p is the primary electroviscous coefficient. A number of authors [3–26] have proposed theoretical treatments of the primary electroviscous effect in a suspension of charged particles or the effective viscosity of the suspension. The standard theory for this effect and the governing electrokinetic equations (which are similar to those for the electrokinetic problems) were given by Watterson and White [7]. The primary electroviscous effect in a dilute suspension of liquid drops was discussed in Ref. [18] and the following expression for ηs as well as approximate expressions for the electroviscous coefficient p was derived: 5η þ 2η ηs ¼ η 1 þ d ð1 þ pÞϕ ð4Þ 2 ð η d þ ηÞ which becomes Eq. (2) as the primary electroviscous coefficient p → 0. The theories of the electrokinetic phenomena in a suspension of colloidal particles in an aqueous electrolyte solution including the electroviscous effect usually assume that no liquid slip occurs on the particle surface [27–45]. The no-slip boundary condition, however, can be applied only to a h
Data Loading...