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

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+ | -flow in the corners, contact angle receding | ||

+ | -clear pdms, can see through to observe particles | ||

+ | -critical values, how abruptly does the flow change? | ||

+ | -open questions presented by the authors, coffee ring |

## Revision as of 15:52, 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>k_L</math> and <math>k_S</math> are the thermal conductivities of the liquid and the substrate respectively. <math>\theta_c</math> labels the contact angle.

The authors determine that there are two qualitatively different flow patterns. Both patterns have the same streamlines shown in figure 4. However, the direction of the flow depends on the contact angle and the relative thermal conductivities <math>k_L</math> and <math>k_S</math>.

The researchers determined theoretically that the critical ratio of thermal conductivities <math>k_R=\frac{k_S}{k_L}</math> above which fluid flows radially inward across the surface of the drop and radially outward over the surface of the substrate. Below <math>k_R</math> the fluid flows in the opposite direction.

Ristenpart *et. al.* determined that <math>k_R</math> depends on the critical angle as follows:
<math>k_{R}^{crit}=tan(\theta_{c})cot\left(\frac{\theta_c}{2}+\frac{\theta_c^2}{\pi}\right)</math>

The researchers check this equation by observing the flow in evaporating drops of four different fluids: methanol, ethanol, isopropanol, and chloroform. The qualitative observations of flow direction by observing suspended particle flow follow the predictions of the critical thermal conductivity ratio.

## Soft Matter Details

-flow in the corners, contact angle receding -clear pdms, can see through to observe particles -critical values, how abruptly does the flow change? -open questions presented by the authors, coffee ring