In physics, a "coffee ring" is a pattern left by a puddle of particle-laden liquid after it evaporates. The phenomenon is named for the characteristic ring-like deposit along the perimeter of a spill of coffee. It is also commonly seen after spilling red wine. The mechanism behind the formation of these and similar rings is known as the coffee ring effect or in some instances, the coffee stain effect, or simply ring stain.

Flow mechanism

Writing in Nature, Robert D. Deegan of The University of Chicago and coworkers show that the pattern is due to capillary flow induced by the differential evaporation rates across the drop: liquid evaporating from the edge is replenished by liquid from the interior.[1] The resulting edgeward flow can carry nearly all the dispersed material to the edge.

Follow-up work by Hu and Larson suggests the evaporation induces a Marangoni flow inside a droplet. The flow, if strong, actually redistributes particles back to the center of the droplet. Thus, for particles to accumulate at the edges, the liquid must have a weak Marangoni flow, or something must occur to disrupt the flow.[2] For example, surfactants can be added to reduce the liquid's surface tension gradient, disrupting the induced flow. Hu and Larson do mention that water has a weak Marangoni flow to begin with, which is then reduced significantly by natural surfactants. Later H. Burak Eral and colleagues in Physics of Complex Fluids group in University of Twente evoked alternating voltage electrowetting to suppress coffee stains noninvasively (i.e. no need to add surface active materials).[3] This method shakes the contact line by alternatively increasing and decreasing contact angle effectively depinning the contact line as the droplet evaporates. Furthermore, with appropriate choice of excitation frequency internal flow fields can be generated counteracting the capillary flow increasing the efficiency of the suppression. In 2013, researchers from the Karlsruhe Institute of Technology, Germany revealed that in an inkjet printing process the coffee ring effect can also be suppressed by a rapid viscosity increase during drying.[4]

Recently, Byung Mook Weon of Sungkyunkwan University and Jung Ho Je of Pohang University of Science and Technology showed an observation of reverse particle motion that repels the coffee-ring effect because of the capillary force near the contact line.[5] The reversal takes place when the capillary force prevails over the outward coffee-ring flow by the geometric constraints.
Determinants of size and pattern

Recent work of Bhardwaj et al. showed the pH of the solution of the drop also influences the final deposit pattern.[6] The transition between these patterns is explained by considering how DLVO interactions such as the electrostatic and Van der Waals forces modify the particle deposition process.

At the microscopic level, Shen, Ho, and Wong of University of California, Los Angeles suggest that the lower limiting size of a coffee ring is dependent on the time scale competition between the liquid evaporation and the movement of suspended particles.[7] When the liquid evaporates much faster than the particle movement near a three-phase contact line, coffee ring cannot be formed successfully. Instead, these particles will disperse uniformly on a surface upon complete liquid evaporation. For suspended particles of size 100 nm, the minimum diameter of the coffee ring structure is found to be 10 μm, or about 10 times smaller than the width of human hair. In a study published in Nature in August 2011, a team of University of Pennsylvania physicists has shown that the shape of particles in the liquid is responsible for coffee ring effect.[8][9] On porous substrates, the competition among infiltration, particle motion and evaporation of the solvent governs the final deposition morphology.[10]

The self-pinning of the contact line by particle confinement was studied by Byung Mook Weon of Sungkyunkwan University and Jung Ho Je of Pohang University of Science and Technology. They suggested that a critical linear packing fraction is required for the self-pinning by a balance between the spreading and the net capillary forces at the contact line.[11]

The coffee ring effect is utilized in convective deposition by researchers wanting to order particles on a substrate using capillary-driven assembly. Utilized by various groups including Velev[12] at North Carolina State University and Gilchrist[13] at Lehigh University using principles developed by Dimitrov and Nagayama,[14] replacing a stationary droplet with an advancing meniscus drawn across the substrate. This process differs from dip-coating in that evaporation drives flow along the substrate as opposed to gravity.

Dongmao Zhang et al. have utilized coffee-ring drying pattern to pre-concentrate the protein solutions prior to Raman analysis in so called Drop Coating Deposition Raman (DCDR) technique.[15][16][17]

R. D. Deegan, O. Bakajin, T. F. Dupont, G. Huber, S. R. Nagel, T. A. Witten (1997). "Capillary flow as the cause of ring stains from dried liquid drops". Nature 389 (6653): 827–829. Bibcode:1997Natur.389..827D. doi:10.1038/39827.
Hua Hu, Ronald Larson (2006). "Marangoni Effect Reverses Coffee-Ring Depositions". Journal of Physical Chemistry B 110 (14): 7090–7094. doi:10.1021/jp0609232. PMID 16599468.
Eral H.B., Mampallil-Agustine D., Duits M.H.G., Mugele F. (2011). "Suppressing the coffee stain effect: how to control colloidal self-assembly in evaporating drops using electrowetting". Soft Matter 7 (7): 7090–7094. Bibcode:2011SMat....7.4954E. doi:10.1039/C1SM05183K.
A. Friederich, J. R. Binder, W. Bauer (2013). "Rheological Control of the Coffee Stain Effect for Inkjet Printing of Ceramics". Journal of the American Ceramic Society 96: 2093–2099. doi:10.1111/jace.12385.
B. M. Weon and J. H. Je (2010). "Capillary force repels coffee-ring effect". Physical Review E 82: 015305(R). Bibcode:2010PhRvE..82a5305W. doi:10.1103/PhysRevE.82.015305.
Bhardwaj; et al. (2010). "Self-Assembly of Colloidal Particles from Evaporating Droplets: Role of DLVO Interactions and Proposition of a Phase Diagram". Langmuir 26 (11): 7833–42. doi:10.1021/la9047227. PMID 20337481.
Xiaoying Shen, Chih-Ming Ho, Tak-Sing Wong (2010). "Minimal Size of Coffee Ring Structure". Journal of Physical Chemistry B 114 (16): 5269–5274. doi:10.1021/jp912190v. PMC 2902562. PMID 20353247.
P. J. Yunker, T. Still, M. A. Lohr, A. G. Yodh (2011). "Suppression of the coffee-ring effect by shape-dependent capillary interactions". Nature 476 (7360): 308–311. Bibcode:2011Natur.476..308Y. doi:10.1038/nature10344.
"Coffee-ring effect explained". Retrieved 21 August 2011.
Min Pack, Han Hu, Dong-Ook Kim, Ying Sun (2015). "Colloidal drop deposition on porous substrates: competition among particle motion, evaporation and infiltration". Langmuir. doi:10.1021/acs.langmuir.5b01846.
B. M. Weon and J. H. Je (2013). "Self-pinning by colloids confined at a contact line". Physical Review Letters 110: 028303. Bibcode:2013PhRvL.110b8303W. doi:10.1103/PhysRevLett.110.028303.
B. G. Prevo, O. D. Velev (2004). "Controlled rapid deposition of structured coatings from micro-and nanoparticle suspensions". Langmuir 20 (6): 2099–2107. doi:10.1021/la035295j.
P. Kumnorkaew, Y. K. Ee, N. Tansu, J. F. Gilchrist (2008). "Investigation of the Deposition of Microsphere Monolayers for Fabrication of Microlens Arrays". Langmuir 24 (21): 12150–12157. doi:10.1021/la801100g.
A. S. Dimitrov, K. Nagayama (1995). "Steady-state unidirectional convective assembling of fine particles into two-dimensional arrays". Chemical Physics Letters 243 (5–6): 462–468. Bibcode:1995CPL...243..462D. doi:10.1016/0009-2614(95)00837-T.
Dongmao Zhang, Yong Xie, Melissa F. Mrozek, Corasi Ortiz, V. Jo Davisson, Dor Ben-Amotz (2003). "Raman Detection of Proteomic Analytes". Analytical Chemistry 75 (21): 5703–5709. doi:10.1021/ac0345087.
Dongmao Zhang, Melissa F. Mrozek, Yong Xie, Dor Ben-Amotz (2004). "Chemical Segregation and Reduction of Raman Background Interference Using Drop Coating Deposition". Applied Spectroscopy 58 (8): 929–933. Bibcode:2004ApSpe..58..929Z. doi:10.1366/0003702041655430.
Dongmao Zhang, Karthikeshwar Vangala, DongPing Jiang, Sige Zou, Tibor Pechan (2010). "Drop Coating Deposition Raman Spectroscopy of Fluorescein Isothiocyanate Labeled Protein". Applied Spectroscopy 64 (10): 1078–1085. Bibcode:2010ApSpe..64.1078Z. doi:10.1366/000370210792973497.

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