Unresolved Mathematical Issues in Coating Flow Mechanics

Author(s):  
Avner Friedman
Keyword(s):  
Author(s):  
Steffen Schirrmeister

Pilot-scale micro-process technology for heterogeneously catalyzed gas phase reactions is generally highly demanding towards the methods of catalyst coating, flow distribution, reactor manufacturing and assembly, safety issues and other factors. Yet, first cost analysis have shown that economical processes can be developed using micro-technology. For this matter, it is necessary to improve and simplify the laboratory set-up, meaning that the stacked architectures at the meter-scale must be brought down to the micron-scale. This in return calls for specific methods of catalyst coating and a particularly precise assembly of the operation unit.


1999 ◽  
Vol 66 (1) ◽  
pp. 197-203 ◽  
Author(s):  
P. J. Schall ◽  
J. P. McHugh

The linear stability of two-layer flow over an infinite elastic substraw is considered. The problem is motivated by coating flow in a printing press. The flow is assumed to be inviscid and irrotational. Surface tension between the fluid layers is included, but gravity is neglected. The results show two unstable modes: one mode associated with the interface between the elastic layer and the fluid (mode 1), and the other concentrated on the interface between the two fluids (mode 2). The behavior of the unstable modes is examined while varying the elastic parameters, and it is found that mode 1 can be made stable, but mode 2 remains unstable at small wavenumber, similar to the classic Kelvin—Helmholtz mode.


2015 ◽  
Vol 26 (5) ◽  
pp. 647-669 ◽  
Author(s):  
M. A. LAM ◽  
L. J. CUMMINGS ◽  
T.-S. LIN ◽  
L. KONDIC

We consider a coating flow of nematic liquid crystal (NLC) fluid film on an inclined substrate. Exploiting the small aspect ratio in the geometry of interest, a fourth-order nonlinear partial differential equation is used to model the free surface evolution. Particular attention is paid to the interplay between the bulk elasticity and the anchoring conditions at the substrate and free surface. Previous results have shown that there exist two-dimensional travelling wave solutions that translate down the substrate. In contrast to the analogous Newtonian flow, such solutions may be unstable to streamwise perturbations. Extending well-known results for Newtonian flow, we analyse the stability of the front with respect to transverse perturbations. Using full numerical simulations, we validate the linear stability theory and present examples of downslope flow of nematic liquid crystal in the presence of both transverse and streamwise instabilities.


2004 ◽  
Vol 16 (5) ◽  
pp. 1818-1821 ◽  
Author(s):  
Tauqeer Muhammad ◽  
Roger E. Khayat

2016 ◽  
Vol 32 (5) ◽  
pp. 643-651 ◽  
Author(s):  
C.-K. Chen ◽  
M.-C. Lin

AbstractThis paper investigates the weakly nonlinear stability of a thin axisymmetric viscoelastic fluid with hydromagnetic effects on coating flow. The governing equation is resolved using long-wave perturbation method as part of an initial value problem for spatial periodic surface waves with the Walter's liquid B type fluid. The most unstable linear mode of a film flow is determined by Ginzburg-Landau equation (GLE). The coefficients of the GLE are calculated numerically from the solution of the corresponding stability problem on coating flow. The effect of a viscoelastic fluid under an applied magnetic field on the nonlinear stability mechanism is studied in terms of the rotation number, Ro, viscoelastic parameter, k, and the Hartmann constant, m. Modeling results indicate that the Ro, k and m parameters strongly affect the film flow. Enhancing the magnetic effects is found to stabilize the film flow when the viscoelastic parameter destabilizes the one in a thin viscoelastic fluid.


AIChE Journal ◽  
2015 ◽  
Vol 61 (5) ◽  
pp. 1745-1758 ◽  
Author(s):  
Semi Lee ◽  
Jaewook Nam
Keyword(s):  

2008 ◽  
Vol 97 (2) ◽  
pp. 1030-1038 ◽  
Author(s):  
Bonnie E. Lai ◽  
Yao Quan Xie ◽  
Michael L. Lavine ◽  
Andrew J. Szeri ◽  
Derek H. Owen ◽  
...  

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