(a) Particle at the fluid/air interface the capillary force acts along the tangent to the fluid surface. (b) A particle on a slide again at a fluid/air interface, due to the incline of this surface and the nonzero value of there will be a net capillary force component acting horizontally (rightward). (c) A negative as depicted would cause a net capillary force away from the surface and so is not stable or expected to occur, eventually the fluid can be expected to part around the particle (d).
Shows the values of (green), (blue), and the horizontal capillary force component (red) over a range of filling angle values for both silica (solid) and copolymer (dotted) particles on a starfrost slide. In the inserts the range shown is that in which and are positive (the former so the particle is in contact with the slide, the later so that it is within the droplet). The values used are for copolymer (contact angle 70°) and silica (contact angle 37°) particles. The contact angle for the glass slide is taken as 35° as measured experimentally. The axis is in meters for and , the values must be divided by 50 to obtain the horizontal capillary force in Newtons.
The profile of the fluid air interface as it contacts with (a) copolymer and (b) silica particles is shown for a range (25°—blue, 40°—red, and 55°—green) of filling angles are shown. When the interface contacts with the second adjacent particle, a small volume of fluid is left between the two particles, this is depicted by the black line on the left hand side. The dotted lines show the contact angle and (outside the circles) the tangent at the contact point of the interface and the particle. The system is axisymmetric, so it is clear that a smaller volume of fluid is trapped between the copolymer particles than the silica ones.
(a) Copolymer on glass, (b) copolymer on silanized glass, and (c) silica on silanized glass all at a concentration of .
A series of images showing individual or small clumps of copolymer particles (red arrow) left behind by the retreating contact line on starfrost slides, the concentration is solids. The interval between images is 0.04 s.
A series of images showing fingers of copolymer particles being developed [(b) and (c)] and then left behind (d) by the retreating contact line on starfrost slides, the concentration is solids. The interval between images is 0.12 s.
A series of images showing line formation (rings when the whole droplet is considered) of copolymer particles being developed as a few particles stick (a), the contact line bows between these particles (b), and then the line is left behind [(c) and (d)] by the retreating contact line on starfrost slides, the concentration is solids. The interval between the first three images is 0.08 s, and between (c) and (d) is 0.04 s.
A series of images showing the formation of long spokes of silica particles by the retreating contact line on starfrost slides, the concentration is solids. The interval between the first three images is 0.08 s, and between (c) and (d) is 0.24 s.
A comparison of the distance the particles are from the contact line, (a) for silica, the concentration is solids, (b) for copolymer prior to line formation, and (c) for copolymer after the initial line is formed, the concentration is solids.
A plot of the width and height (both in pixels) of the droplet as measured from a side view video, an image from which is inserted (upper right) and the calculated contact angle, , plotted in degrees. The ring pattern of left by solids concentration copolymer beads on the starfrost slide is shown in the insert (lower left). Four phases are identified in the process.
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