Slow motion of a slip spherical particle through a viscoelastic Giesekus fluid in a peristaltic tube

Abstract

The slow motion of a spherical body along the centerline of a peristaltic tube filled with a viscoelastic Giesekus fluid is studied analytically. The slip condition between the spherical surface and the fluid is considered. The stress components are obtained in both the cylindrical and spherical coordinates with applying the perturbation technique due to the small values of the Deborah number. The longwave assumption is applied in both coordinate systems. Then, the stream function is determined, for the general solution, as a combination of the stream function of the cylindrical and spherical coordinates. The radial and axial velocity components, the pressure rise per wavelength, the skin friction coefficients at both the cylindrical and spherical surfaces are obtained. The drag force on the spherical particle is calculated numerically and compared with the exact form of the drag force for a special choice of the parameters. According to the restriction of the viscosity coefficients, the exerted drag force is enhanced for the viscoelastic fluids rather than the Newtonian one. Also, the trapping bolus is represented graphically. The graphical results illustrate that the trapping bolus appears for the viscoelastic fluid and disappears with reducing the peristaltic motion of the tube wall.