J. Ashmore(1,a), A.Q. Shen(1,b),
H.P. Kavehpour(2,c), H.A. Stone(1)
&
G.H. McKinley(2)
1: Division of Engineering and Applied Sciences,
2: Hatsopoulos Microfluidics Laboratory, Department of Mechanical Engineering,
Massachusetts Institute of Technology, Cambridge, MA 02139 (a):Current address:
TIAXLLC, 15 Acorn Park, Cambridge, MA 02140 (b):Current address: Department of Energy,
Environmental & Chemical Engineering, Washington University in St Louis, St
Louis, MO 63130 (c):Current address: Department of Mechanical and Aerospace Engineering,
University of California, Los Angeles, CA 90095
We
present an asymptotic analysis of the thickness of the liquid film that coats a
smooth solid substrate when it is withdrawn from a bath of non-Newtonian fluid,
and compare our results with experimental measurements. The film thickness is,
to a good approximation, uniform above the point where the film is withdrawn
from the fluid bath, and depends on the rotation rate, the fluid properties and
the substrate geometry. Theoretical predictions of the film thickness for a number
of different sub-strate geometries (an inclined
plate, roller and fiber) are presented, and are compared with experimental
measurements in a single roller geometry. Results are
obtained for two different limits of the Criminale-Ericksen-Filbey
constitutive equation in which the fluid rheology is
either weakly elastic and dominated by shear-thinning, or strongly elastic and
dominated by elastic stresses. A lubrication analysis yields a thin-film
equation which characterizes the film thickness as a function of spatial position.
The rheological properties of the test fluids are
measured independently using steady and oscillatory shearing deformations. The viscometric parameters are then used, in conjunction with
the governing thin-film equation, which is solved using matched asymptotics, to give a quantitative prediction of the
thickness of the fluid coating. The onset of an instability which causes the
film thickness to vary
with axial position along the roller is also observed experimentally