Problem 12.2 Consider that a viscous liquid containing small, spherical glass beads of uniform size (10 vol \%) is injected into a position somewhere between the tube wall and the centerline of a long cylindrical tube. Assume that the diameter dp of the glass beads is very small compared with the diameter D of the tube (i.e., dpD ). Will there be a radial migration of the glass beads as they move along the tube axis? If so, in which direction will the glass beads migrate (i.e., toward the tube wall or toward the centerline of the tube)? In answering the question, consider the following situations: (1) the suspending medium is a Newtonian liquid, (2) the suspending medium may be represented by the ZFD model (see Chapter 3 ), (3) the suspending medium may be represented by the Coleman-Noll second-order fluid (see Chapter 3). Assume that the viscosity of the suspension is so large that the inertia effect is negligible compared with the viscous force. +1Dt=20d which is referred to as the Zaremba-Fromm-DeWitt (ZFD) model (DeWitt 1955; Fromm 1947; Zaremba 1903), 3 For steady-state simple shear flow, Eq. (3.15) Substituting Eq. (3.75) into (3.74) and neglecting certain high-order terms resulting from the double integral terms yields (Coleman and Noll 1961b) =0A(1)+A(1)2+A(2) where