Evaporation & the coffee-ring effect
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What is a coffee ring?
What is a coffee ring?
A 'coffee-ring' is the ring-like stain that is left behind after a droplet of spilled coffee evaporates from a table. You can see this in action by watching this video made by some of my undergraduate students.
The edge of the droplet - also called the contact line - gets stuck on the table. So, to replace the liquid that evaporates from the contact line, the liquid flows outwards from the centre of the droplet, carrying the coffee particles along. They get deposited in a ring at the contact line.
Why do we care?
Why do we care?
The effect is ubiquitous for a range of liquids and solutes. The effect can be exploited to print micro-circuits in specific patterns or the flow itself may be used to align DNA in DNA mapping. On the other hand, often we want to final deposit to be uniform, like in inkjet printing or in manufacturing OLED screens. In these cases, the coffee ring must be prevented!
I am interested in models that extend the applicability of the classical model in order to make informed decisions on when and how to control the coffee ring formation.
My work
My work
My recent work has looked at the early stages of how the coffee ring forms. In particular, I predict the shape of the ring in terms of the local geometry of the contact line and the local rate of evaporation.
Mathematically, the local deposit can be described in terms of a the probability distribution function of a Gamma distribution, which gives the ring its classic peaked shape.
I have also looked at how gravity can alter the coffee ring profile, in particular finding that it flattens the ring. In some cases, gravity can even lead to multiple rings in the drop!
My current work in the area is threefold.
First, I work alongside Alex Wray (Strathclyde) on solving for the evaporation rate in complicated geometries such as polygons (like pixels on your phone screen!). When the evaporation is driven by diffusion - think heat dispersing in a room - the mathematical problem is highly complex and there are few analytic solutions. Alex and I have derived an asymptotic model that allows us to quick and accurately find the evaporation rate.
Second, I am interested in modelling the growth of the deposit more carefully and, in particular, allowing the coffee particles to get stuck together or jam. This will allow us to get more accurate comparisons to experiments and thus make better predictions. This is work with Jim Oliver (Oxford).
Third, I work with Alex Wray and Alice Thompson (Manchester) on models for optimal control of the coffee ring. We alter the evaporation rate in clever ways to change how the liquid flows in the droplet.
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