The Physics of Microdroplets Chapter 4

This page contains Evolver datafiles for Chapter 4 images. The data files contain evolution scripts (always named "gogo") and scripts for producing EPS files for the book images (always named "run").

The image scripts set the viewing angle with the "view_matrix := ..." command. The particular view matrix used was generated by moving the surface by mouse by hand and then printing out the view matrix with the "print view_matrix" command, and cutting and pasting the result into the "run" command.

Fig. 4-1 Sessile drop.
Fig. 4-5 Drop moving toward hydrophilic side.
Fig. 4-7 Drop moving uphill.
Fig. 4-9 Drop sliding downhill.
Fig. 4-10 Drop climbing step.
Fig. 4-16 Defect pinning a drop.
Fig. 4-17 Drop sliding around a defect
Fig. 4-21 Drop on hydrophilic strip.
Fig. 4-22 Cases for drop on hydrophilic strip.
Fig. 4-23 End views of the four cases.
Fig. 4-28 Bulging between square rods.
Fig. 4-29 Drop on ridge.
Fig. 4-30 Drop in valley.
Fig. 4-37 Drop on top of pillars.
Fig. 4-40 Drop on pillars, sagging.
Fig. 4-41 Drop over hole.
Fig. 4-42 Drop on sparse pillars.
Fig. 4-43 Drop on close-set pillars.

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Fig. 4-1 Sessile drop.

Basically the same as the mound.fe example in the Evolver distribution.

Datafile: Fig_4_1.fe

Fig. 4-5 Drop moving toward hydrophilic side.

The two different sides of the substrate have contact angles of 100 and 60 degrees respectively. The contact angles are implemented with two level-set constraints with energy integrands, one for each side. Where the contact line crosses between sides, there are contact line vertices constrained to lie on the dividing line. It is important that whenever there is a sharp transition in contact angle that there are contact line vertices constrained to lie on the dividing line, so each edge is fully in one region or the other, and cannot get confused as to what its contact angle is.

Datafile: Fig_4_5.fe

Fig. 4-7 Drop moving uphill.

	The energy advantage of a lower contact angle can overcome gravity. This is basically the same datafile as figure 4-5, but with the substrate level-set constraints tilted. But that does require the addition of "content" integrands to those constraints to subtract off the volume below the substrate from the volume of the drop. Datafile: Fig_4_7.fe

Fig. 4-9 Drop sliding downhill.

Quasistatic drop sliding downhill. Gravity is very weak for a small drop, and the motion is very slow, so the drop maintains nearly a hemisphere.

Datafile: Fig_4_9.fe

Fig. 4-10 Drop climbing step.

The yellow facets have a lower contact angle than the pink facets, so the drop migrates to the top level. The datafile has a script named "transfer" that takes care of moving contact line vertices from the lower level to the step; it is run frequently during evolution.

Datafile: Fig_4_10.fe

Fig. 4-16 Defect pinning a drop.

The hydrophobic side is pushing the drop to the hydrophilic side, but a hydrophobic defect is blocking the motion of the contact line. The defect is implemented here as just some "fixed" vertices and edges.

Datafile: Fig_4_16.fe

Fig. 4-17 Drop sliding around a defect.

The same set-up as figure 4-16, but starting the drop more to the side, so it can squeeze around the defect.

Datafile: Fig_4_17.fe

Fig. 4-21 Drop on hydrophilic strip.

Drop confined to a hydrophobic strip. The sides of the strip are implemented as one-sided constraints.

Datafile: Fig_4_21.fe

Fig. 4-22 Cases for drop on hydrophilic strip.

		Drop on hydrophobic strip, at various volumes. For the largest voluem, the contact line is permitted to move out on the hydrophobic region. Datafiles: Fig_4_22_a.fe Fig_4_22_b.fe Fig_4_22_c.fe Fig_4_22_d.fe

Fig. 4-23 End views of the four cases.

		End views of the same shapes as Fig. 2.22. Datafiles: Fig_4_23_a.fe Fig_4_23_b.fe Fig_4_23_c.fe Fig_4_23_d.fe

Fig. 4-28 Bulging between square rods.

The three films each have level-set constraint contact lines on the faces of the rods with contact angle 120, and level-set constraints with zero contact angle on their ends. A one-sided constraint prevents the contact lines from moving beyond the corners. Three bodies are defined, one for each film, and given different pressures in "gogo". Even though the bodies look like just one connected body, remember that Evolver defines a body as a set of facets, and doesn't know or care if the body interiors are separate or not. To get the correct body volumes, constraint content integrands are needed, and because the tops of the contact lines move, some named quantities with vertex_scalar_integrand are used.

Datafile: Fig_4_28.fe

Fig. 4-29 Drop on ridge.

Both sides of the ridge have the same contact angle, 100 degrees, but gravity makes the ridge top an unstable equilibrium. A slight shove to the right was given before evolving the second image.

Datafile: Fig_4_29.fe

Fig. 4-30 Drop in valley.

Stable equilibrium in a valley. Starting position on the left, after evolution on the right.

Datafile: Fig_4_30.fe

Fig. 4-37 Drop on top of pillars.

Droplet wetting the tops of a 6x6 grid of square pillars. The contact angle on the sides of the pillars is 165 degrees. This datafile actually defines just one pillar, and has a script that can generate and arbitrary size grid, with droplet.

Datafile: Fig_4_37.fe

Fig. 4-40 Drop on pillars, sagging.

Drop on more widely spaced pillars, with contact angle on sides of 80 degrees. The yellow substrate is completely nonwetting, implemented as a one-sided constraint. The datafile here defines the 4 x 4 grid of pillars by brute force, not to be recommended. Use the datafile of fig. 4-37 if you want to do pillars.

Datafile: Fig_4_40.fe

Fig. 4-41 Drop over hole.

There are two separate surfaces here, the top of the droplet and the surface over the hole. Because the pressure is the same throughout, both are sections of spheres of the same radius.

Datafile: Fig_4_41.fe

Fig. 4-42 Drop on sparse pillars.

The pillars here are too thin and too far apart to have much affect on the basically spherical shaped of the droplet.

Datafile: Fig_4_42.fe

Fig. 4-43 Drop on close-set pillars.

With pillars this large and close together, it is easy for the droplet to sit on top.

Datafile: Fig_4_43.fe

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