# Difference between revisions of "Influence of Substrate Conductivity on Circulation Reversal in Evaporating Drops"

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In this paper, Ristenpart ''et. al.'' study the flow patterns inside liquid drops on flat surfaces. Evaporation from the drops' surfaces leads to a thermal gradient and, thus, a gradient in surface tension. Displaying the [[Marangoni Effect| Marangoni effect]], fluid flows from regions with low surface tension to regions with high surface tension. The authors ask, within the drop, what direction is this Marangoni flow? Using both theoretical and experimental approaches the authors determine conditions which result in two different flow patterns. | In this paper, Ristenpart ''et. al.'' study the flow patterns inside liquid drops on flat surfaces. Evaporation from the drops' surfaces leads to a thermal gradient and, thus, a gradient in surface tension. Displaying the [[Marangoni Effect| Marangoni effect]], fluid flows from regions with low surface tension to regions with high surface tension. The authors ask, within the drop, what direction is this Marangoni flow? Using both theoretical and experimental approaches the authors determine conditions which result in two different flow patterns. | ||

+ | [[Image:Coordinates.png|300px|thumb|right|Figure 1 from [1].]] | ||

Figure 1 is a diagram of a drop with important parameters labeled. The magnitude of the arrows directed away from the drop shows the relative rates of evaporation at different places on the drop's surface. <math>\kappa_L</math> and <math>\kappa_s</math> are the thermal conductivities of the liquid and the substrate respectively. <math>\theta_c</math> labels the contact angle. | Figure 1 is a diagram of a drop with important parameters labeled. The magnitude of the arrows directed away from the drop shows the relative rates of evaporation at different places on the drop's surface. <math>\kappa_L</math> and <math>\kappa_s</math> are the thermal conductivities of the liquid and the substrate respectively. <math>\theta_c</math> labels the contact angle. | ||

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Critical K | Critical K |

## Revision as of 15:31, 15 November 2009

## Overview

- [1] Ristenpart, W., Kim, P., Domingues, C., Wan, J, & Stone, H. Physical Review Letters. 99, 234502-1 - 234502-4 (2007).

- Keywords: Evaporation, Marangoni Effect, Contact Angle, Thermal Conduction, Surface Tension

## Summary

In this paper, Ristenpart *et. al.* study the flow patterns inside liquid drops on flat surfaces. Evaporation from the drops' surfaces leads to a thermal gradient and, thus, a gradient in surface tension. Displaying the Marangoni effect, fluid flows from regions with low surface tension to regions with high surface tension. The authors ask, within the drop, what direction is this Marangoni flow? Using both theoretical and experimental approaches the authors determine conditions which result in two different flow patterns.

Figure 1 is a diagram of a drop with important parameters labeled. The magnitude of the arrows directed away from the drop shows the relative rates of evaporation at different places on the drop's surface. <math>\kappa_L</math> and <math>\kappa_s</math> are the thermal conductivities of the liquid and the substrate respectively. <math>\theta_c</math> labels the contact angle.

Critical K
<math>k_{R}^{crit}=tan(\theta_{c})cot\left(\frac{\theta_c}{2}+\frac{\theta_c^2}{\pi}\right)</math>