Effect of substrate cooling and droplet shape

Vahid Bazargan, Ph.D. Thesis: Department of Mechanical Engineering, The University of British Columbia, March 2014, © Vahid Bazargan, 2014

Substrate cooling and droplet shape


Sessile droplets are liquid droplets resting on a flat substrate. During the evaporation of small sessile droplets, the contact line of the droplet undergoes two different stages: pinned stage with fixed contact area and de-pinned stage with fixed contact angle. An evaporation with a pinned contact line produces a flow inside the droplet toward the contact line. This flow carries particles and deposits them near the contact line. This causes the commonly observed “coffee-ring” phenomenon. This thesis provides a study of the evaporation process and the evaporation-induced flow of sessile droplet and brings insights into the deposition of particles from colloidal suspensions.

Here we first study the evaporation of small sessile droplets and discuss the importance of the thermal conductivity of the substrate on the evaporation process. We show how current evaporation models produce a significant error for droplet sizes below 500 µm. Our model includes thermal effects, in particular, it includes the thermal conductivity of the substrate that provides heat to the droplet to balance the latent heat of evaporation. It considers the whole time of evaporation with the pinned and the de-pinned stages by defining a virtual movement of the contact line that is related to the evolution of the contact angle and is based on experimental results. Our model is in agreement with experimental results for droplets smaller than 500 µm with an error below 2%.

Furthermore, we study the evaporation of line droplets with finite sizes and discuss the complex behavior of the contact lines during evaporation. We apply an energy formulation and show that the contact line starts receding from the two ends of line droplets with a contact angle above the receding contact angle of spherical
droplets. And then we show the evaporation-induced flow inside the line droplets.

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