Evaporation of binary liquids from a capillary tube

Evaporation of multi-component liquid mixtures in confined geometries, such as capillaries, is crucial in applications such as microfluidics, two-phase cooling devices and inkjet printing. Predicting the behaviour of such systems becomes challenging because evaporation triggers complex spatio-temporal changes in the composition of the mixture. These changes in composition, in turn, affect evaporation. In the present work, we study the evaporation of aqueous glycerol solutions contained as a liquid column in a capillary tube. Experiments and direct numerical simulations show three evaporation regimes characterised by different temporal evolutions of the normalised mass transfer rate (or Sherwood number Sh), namely Sh ((t) over tilde) = 1, Sh similar to 1/root(t) over tilde and Sh similar to exp (-(t) over tilde), where (t) over tilde is a normalised time. We present a simplistic analytical model that shows that the evaporation dynamics can be expressed by the classical relation Sh = exp((t) over tilde), erfc (root(t) over tilde). For small and medium (t) over tilde, this expression results in the first and second of the three observed scaling regimes, respectively. This analytical model is formulated in the limit of pure diffusion and when the penetration depth delta(t) of the diffusion front is much smaller than the length L(t) of the liquid column. When delta approximate to L, finite-length effects lead to Sh similar to exp ((t) over tilde), i.e. the third regime. Finally, we extend our analytical model to incorporate the effect of advection and determine the conditions under which this effect is important. Our results provide fundamental insights into the physics of selective evaporation from a multi-component liquid column.