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The drag-out problem in film coating
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10.1063/1.2079927
/content/aip/journal/pof2/17/10/10.1063/1.2079927
http://aip.metastore.ingenta.com/content/aip/journal/pof2/17/10/10.1063/1.2079927

Figures

Image of FIG. 1.
FIG. 1.

Sketch of the computational domain for the drag-out problem and the corresponding coordinates.

Image of FIG. 2.
FIG. 2.

For the vertical withdrawal case and , the flow rate across the film increases monotonically with the capillary number and, as , approaches asymptotically 0.582. The points are the results obtained by solving numerically the Stokes equations and the solid line represents the prediction given by Eq. (2).

Image of FIG. 3.
FIG. 3.

The air-liquid interfacial profiles obtained by solving numerically the Stokes equations for different values of the capillary number in the vertical withdrawal case with . The profiles for are indistinguishable.

Image of FIG. 4.
FIG. 4.

(a) The normal stress along the air-liquid interface (i.e., along the whole curve in Fig. 1) for the vertical withdrawal case with and . (b) The normal stress at the stagnation point on the air-liquid interface decreases monotonically with the capillary number and approaches asymptotically zero for the vertical withdrawal case with .

Image of FIG. 5.
FIG. 5.

The flow rate across the film increases with the capillary number at , 1, 10, 100, and 1000 for the vertical withdrawal case. The points are the results obtained by solving the Navier-Stokes equations and the solid line represents the prediction given by Eq. (2).

Image of FIG. 6.
FIG. 6.

(a) The air-liquid interfacial profiles at , 0.20, 0.45, and 0.95 for the vertical withdrawal case with . The points are the experimental data given by Lee and Tallmadge (Ref. 4), while the lines represent the results obtained by solving numerically the full Navier-Stokes equations. (b) The air-liquid interfacial profiles obtained by solving numerically the full Navier-Stokes equations at , 2.0, 3.5, 4.5, and 8.3 for the vertical withdrawal case with . Note that the simulation domain here ( and ) is much larger than the typical one we used for at the whole range of or for but at low values of because, as shown later [cf. Fig. 6(c)], the interfacial profiles were found to be sensitive to the size of the simulation domain for at higher values . (c) The air-liquid interfacial profiles obtained by solving numerically the full Navier-Stokes equations with different sizes of the simulation domain (cf. Fig. 1) for the vertical withdrawal case with and .

Image of FIG. 7.
FIG. 7.

The flow rate increases monotonically with (a) the capillary number and (b) the combined parameter for the inclined withdrawal cases with at angles of inclination , , , and 0. The points are the results obtained by solving numerically the Stokes equations and the lines represent the corresponding prediction given by Eq. (8).

Image of FIG. 8.
FIG. 8.

The maximum flow rate increases monotonically with the angle of inclination and approaches when .

Image of FIG. 9.
FIG. 9.

The value of is a monotonically decreasing function of . The points are the results obtained by solving the Stokes equations and the solid line represents the prediction given by Eq. (9).

Image of FIG. 10.
FIG. 10.

The values of for and given by solving Wilson’s model equation (B6) are in good agreement with these obtained by solving the full Stokes equations as long as . However, the prediction given by Wilson’s formula [i.e., Eq. (8)] is accurate only if .

Image of FIG. 11.
FIG. 11.

The sketch of flat front and the corresponding coordinates for the stability analysis.

Tables

Generic image for table
Table I.

Comparison, at , of the flow rates as well as the corresponding asymptotic film thicknesses measured experimentally (Ref. 4) and those computed from the numerical solution of the full Navier-Stokes equations.

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/content/aip/journal/pof2/17/10/10.1063/1.2079927
2005-10-17
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The drag-out problem in film coating
http://aip.metastore.ingenta.com/content/aip/journal/pof2/17/10/10.1063/1.2079927
10.1063/1.2079927
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