APPLICATION OF THE THEORY OF SIMILARITY TO DESCRIBE THE ELECTROOSMOTIC FLOW OF LIQUIDS THROUGH POROUS MEMBRANES

A physical model of the stationary electroosmotic fluid motion in a closed spherical shell is considered, inside of which a disk membrane with transverse cylindrical pores filled with liquid is placed. A constant electric field is applied to the faces of the membrane by means of porous electrodes. As a mathematical model, the Navier-Stokes system of equations for the stationary electroosmotic flow of a viscous incompressible fluid inside a closed solid spherical shell under the influence of an external constant electric field is used. A simplified nonlinear system of Navier-Stokes equations is considered for the case of stationary motion of an incompressible viscous fluid under the condition of constant fluid pressure. This system of equations is reduced to a dimensionless form. During the procedure of reducing the equations to a dimensionless form, the real fluid velocity was normalized relative to the electroosmotic sliding velocity determined by the Helmholtz-Smoluchowski formula. As a result of the analysis of the obtained system, it was shown that in the case under consideration, in addition to the standard similarity criterion in the form of the Reynolds number, one more similarity criterion arises due to the electroosmotic nature of the fluid flow. The obtained dimensionless system of equations contains, in addition to similarity criteria, also functions of dimensionless arguments that describe the behavior of the electric potential in a double electric layer. The dimensionless system of equations of fluid motion can be used in cases of shells and membranes of arbitrary shape, as well as liquids with different physicochemical nature in the design and manufacture of electro-acoustic transducers that use the phenomenon of electroosmosis. The results obtained make it possible to optimize the design of the considered electroacoustic transducers operating on the use of electrokinetic phenomena on models.