Hj. Keh et Fr. Yang, BOUNDARY EFFECTS ON OSMOPHORESIS - MOTION OF A VESICLE IN AN ARBITRARY DIRECTION WITH RESPECT TO A PLANE WALL, Chemical Engineering Science, 48(20), 1993, pp. 3555-3563
The problem of the osmophoretic motion of a spherical vesicle in the p
resence of a nearby plane wall is analyzed in the quasi-steady limit o
f negligible Reynolds and Peclet numbers. The solute concentration gra
dient in the surrounding fluid is uniform in the undisturbed state and
is oriented at an arbitrary angle relative to the plane wall. The sol
ution of conservative equations for the solute species and fluid momen
tum applicable to the system is constructed by superposing solutions o
f the corresponding problems of motion normal to the plane and motion
parallel to it. Using the spherical bipolar coordinate system, the tra
nslational and angular velocities of the osmophoretic vesicle are solv
ed for various cases. Interestingly, the osmophoretic mobility of the
vesicle increases monotonically as it approaches the wall. The interac
tion between the boundary and the vesicle can be very strong when the
gap thickness gets close to zero. The direction of motion of the vesic
le is, in general, different from that of the solute concentration gra
dient. The plane wall exerts the greatest influence on the vesicle in
the case of parallel osmophoresis, and the weakest in the case of moti
on normal to it. In addition to the translational migration, the osmop
horetic vesicle rotates at the same time in the direction opposite to
that which would occur if the spherical particle sedimented parallel t
o a plane wall. The ratio of rotational-to-translational speeds of the
sphere is, in general, much larger for osmophoresis than for sediment
ation.