Shear Deformation of the Spherical Shell Acted on by an External Alternating Electric Field: Possible Applications to Cell Deformation Experiments

Shape deformation of the thin, area non-compressible spherical shell separating two differ­ ent media, subjected to an external, alternating, homogeneous electric field is considered. The function relating shape deformation of the shell to the shear stress in its plane is presented. Shear stress develops as a result of Maxwell stress acting on both shell surfaces. All media are considered as lossy. The theoretical model predicts that the shear stress reaches its maximal value at the shell “equator” in relation to the field direction. The magnitude of the shear stress depends on the strength and frequency of the electric field, on the geometric parameters of the shell, and on the electric parameters of the system studied. The foregoing was applied to an analysis of cell deformation, e.g., an erythrocyte in an elec­ tric field. The analysis predicts that the maximal shear stress in the membrane develops at field frequencies close to f = 107 Hz. This is comparable to the electrocompression stress of the same membrane, maximal at the cell “pole”. At lower frequencies, compression predominates over shear stress.