Tia Maria is a coffee liqueur made originally in Jamaica using Jamaican coffee beans.
It is beautiful to watch patterns form on the layer of cream on a Tia Maria, and how different patterns form in layers of cream of different thickness.
This is all caused by convection. Convection is the bulk movement of fluid, often associated with temperature differences, called thermal convection. In Tia Maria and cream the convection is driven by a difference in concentration, and is called solutal convection.
The important component is the alcohol in the Tia Maria.
After the cream is poured on top of the liqueur, the alcohol begins to diffuse through the cream layer.
When it reaches the surface it alters the surface tension: the more alcohol at the surface, the lower the surface tension. Regions of higher surface tension then pull liquid towards them from the regions of low surface tension.
As the surface liquid is pulled away, the liquid beneath these regions of low surface tension takes its place.
But this liquid contains yet more alcohol, because it has come from the part of the cream nearer to the Tia Maria below. It has an even lower surface tension and in turn gets dragged away.
This positive feedback mechanism creates convection, which continues as long as there is a concentration difference to sustain it.
This type of convection, driven by surface tension, is called B’enard-Marangoni convection and it is particularly relevant to thin layers of fluid. It is important in situations like drying paint, and the same capillary or surface-tension forces also cause other types of patterns in alcoholic drinks, like the tears in glasses of wine.
The other important mechanism that can cause convection is buoyancy.
But buoyancy-driven, or Rayleigh-B’enard convection, cannot be causing the patterns in Tia Maria because cream is lighter than Tia Maria, so Tia Maria with cream on top is buoyantly stable.
The patterns that form when a fluid starts to convect by either of these mechanisms have been well studied in situations such as rolls of clouds in the sky, or hexagons formed in a frying pan when a layer of oil is heated. Tia Maria is an oddity because the patterns are not normal rolls or hexagons.
Similar patterns have also been reported in the scientific literature, in particular in papers written in the early decades of the twentieth century.
The worm-like patterns in thin layers of cream were called vermiculated rolls, and the toroidal cells in thicker layers, isolated cells. Both appear when there is a surface film on top of the convecting substance that hinders movement between the surface and the bulk of the liquid.
In this case, the fatty cream is partially blocking the surface, so these patterns appear.
More recent convection research has tended to ignore these types of patterns, and the old experiments have often been considered as inaccurate because the fluids were impure; the different patterns were thought to be the result of impurity.
We have tried to redress this. After seeing the patterns in Tia Maria, we carried out solutal convection experiments with simpler pure fluids that still show the same patterns.
You can find a thorough account, both with Tia Maria and more conventional lab chemicals, in Physica A as detailed above.