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Capillary flow as the cause of ring stains from dried liquid drops

A Publisher Correction to this article was published on 07 April 2021

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When a spilled drop of coffee dries on a solid surface, it leaves a dense, ring-like deposit along the perimeter (Fig. 1a). The coffee—initially dispersed over the entire drop—becomes concentrated into a tiny fraction of it. Such ring deposits are common wherever drops containing dispersed solids evaporate on a surface, and they influence processes such as printing, washing and coating1,2,3,4,5. Ring deposits also provide a potential means to write or deposit a fine pattern onto a surface. Here we ascribe the characteristic pattern of the deposition to a form of capillary flow in which pinning of the contact line of the drying drop ensures that liquid evaporating from the edge is replenished by liquid from the interior. The resulting outward flow can carry virtually all the dispersed material to the edge. This mechanism predicts a distinctive power-law growth of the ring mass with time—a law independent of the particular substrate, carrier fluid or deposited solids. We have verified this law by microscopic observations of colloidal fluids.

a, A 2-cm-diameter drop of coffee containing 1 wt% solids has dried to form a perimeter ring, accentuated in regions of high curvature. b, Spheres in water during evaporation, as described in the text. Multiple exposures are superimposed to indicate the motion of the microspheres.

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Figure 2: A ring stain and a demonstration of the physical processes involved in production of such a stain.
Figure 3: Mechanism of outward flow during evaporation.
Figure 4: Double-logarithmic plot of ring mass M(R, t) against time t for times from 10 to 250 seconds after placement of the drop on the surface, for three different drops whose total drying time was about 800 s.

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We thank H. Li, X. Shi and M. Baildon for their early contributions to this project; J. Crocker, D. Grier and A. Marcus for sharing their expertise, their image analysis code and their facilities; and S. Garoff, L. Mahadevan, S. Esipov, R. Leheny, D. Mueth, E. Ehrichs, J. Knight, S. Blanton, N. Menon, J. Cina and L. Kadanoff for discussions. This work was supported by the NSF-MRSEC, NSF and DOE.

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Correspondence to Robert D. Deegan.

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Deegan, R., Bakajin, O., Dupont, T. et al. Capillary flow as the cause of ring stains from dried liquid drops. Nature 389, 827–829 (1997).

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