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Side wall effects in thin gravity-driven film flow – steady and draining flow
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Image of FIG. 1.
FIG. 1.

(Color online) Channel geometry illustrating side wall effects on the flow.

Image of FIG. 2.
FIG. 2.

(Color online) Measurement setup for the free surface shape detection.

Image of FIG. 3.
FIG. 3.

Cross-sectional velocity field (darkest shade = fastest, lightest shade = slowest) and flow domain visualizations for different types of side wall influence.

Image of FIG. 4.
FIG. 4.

(Color online) Decrease of the dimensionless flow rate due to the no-slip boundary condition (without capillarity).

Image of FIG. 5.
FIG. 5.

(Color online) Influence of capillary elevation at the side walls on the dimensionless flow rate.

Image of FIG. 6.
FIG. 6.

(Color online) Transition film thickness, , where the competing influence of the no-slip boundary condition and the capillary elevation on the flow rate equalize each other.

Image of FIG. 7.
FIG. 7.

(Color online) LDV measurements (points) for different film and measurement heights , respectively, compared with the theoretical prediction (lines).

Image of FIG. 8.
FIG. 8.

(Color online) Influence of the film thickness on the velocity overshoot.

Image of FIG. 9.
FIG. 9.

(Color online) Dependence of the critical film thickness on the contact angle.

Image of FIG. 10.
FIG. 10.

(Color online) Comparison of the steady free surface shapes obtained experimentally and theoretically for two different static contact angles in the proximity of the side walls.

Image of FIG. 11.
FIG. 11.

(Color online) Comparison of the free surface shape associated with experiments of steady and draining flow () in the proximity of the side walls, revealing a decrease of the resulting contact angle for the draining flow.

Image of FIG. 12.
FIG. 12.

(Color online) Numerical simulation of the free surface shape for draining flow over one half of the channel , with inlaid subviews to show the local impact on the free surface shape in the proximity of the side walls, cf., Fig. 11.

Image of FIG. 13.
FIG. 13.

(Color online) Measured surface shape in the vicinity of an outflow edge (Ref. 32).

Image of FIG. 14.
FIG. 14.

(Color online) Computed trailing edge shapes of the draining flow. Left hand side corresponds to and right hand side to . The contact angle at the substrate is .


Generic image for table
Table I.

Physical properties of silicone oil at .

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Table II.

Reynolds numbers.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Side wall effects in thin gravity-driven film flow – steady and draining flow