Surface Morphology of Drying Latex Films: Multiple Ring Formation

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Reference

Surface morphology of drying latex films: multiple ring formation

Shmuylovich L, Shen AQ, Stone HA

Langmuir 18: 3441-3445 (2002)

Summary

Rings formed by the evaporation of a solution containing 0.88 um particles. The drop volume is written below each image, while the outer ring diameter is written above. The colors in the images were inverted.
The "pinning" and "un-pinning" of the contact line of the solution with 0.88 um particles. Insets show two histograms: one of the distances traversed between "sticking events", and one of the time between pinning events.

The experiment was simple: a small drop of a monodisperse solution of particles (either 0.008% (w/w) solution of 0.88 um diameter particles, or 0.01% solution of 3.15 um particles) was placed on a glass microscope slide. The drying process was then captured on camera. As the solution evaporated it formed concentric rings of particle arrays.


It was observed that a larger drops size produced more rings that covered a wider area. Using solutions of larger particles decreased the number of rings, but did not have a significant effect on the diameter of the outer rings. Studying the dynamics of the contact line during liquid evaporation revealed that the motion is not continuous. Rather, the contact line became "pinned" and unable to move for periods of time, with different parts of the same ring being able to be pinned and unpinned at the same time.

Soft Matter Aspects

This paper presented data that explored the effects on contact line behavior of varying sizes of drops or particles. It also presents a qualitative, stochastic model to explain the observed contact line pinning. In brief, the contact line (the edge of the evaporating drop) moves until it runs into a particle (in fact, the higher rate of evaporation at the contact creates a convective flow that results in an outward flux of particles). A particle at the contact line "pins" the contact line, leading to an even greater evaporation rate and an even greater flux of particles towards the edge. The result of this is a concentrated array of particles that is left behind after the contact line continues to recede. These arrays take on the form of a 2D hexagonal crystalline structure.

The experimental data also supported a simple scaling law. If the particles in solution have a radius a and a volume fraction <math>\phi</math>, then the average distance between two particles is <math>\frac{a}{\phi^3}</math>. If we ignore the convective flow created by the higher evaporation rate at the edge of the drop, then the contact line will on average move a distance proportional to <math>\frac{a}{\phi^3}</math> before encountering another particle and getting pinned. This relationship explains why increasing the size of the particles decreased the number of rings observed after full evaporation.

Schematic of the model proposed to explain the stick-slip motion of the receding contact line

The formation of ordered arrays by evaporating solutions of particles has many applications in material science. Of particular interest is the ability of dying particle suspension to form controlled 2D structures. This capability is of great interest for arraying biopolymers such as proteins. Though most biotechnological applications do not currently require spacial control at the resolution of single molecules, accurate 2D patterning will gain importance as diagnostic and analytical assays continue to drive up throughput by increasing the density of deposited molecules.

Two-dimensional hexagonal crystaline formed by 3.15 um particles.