# Microscale schlieren visualization of near-bubble mass transport during boiling of 2-propanol/water mixtures in a square capillary

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## Abstract

In this study, we successfully utilize the microscale schlieren method to visualize the microscale mass transport near the vapor–liquid interface during boiling of 2-propanol/water mixtures in a square capillary. Because the variation in the refractive index with composition is much greater than that with temperature, the microscale schlieren method proves to be a powerful tool for investigating the solutocapillary convection without the interference of thermocapillarity. When the difference between the equilibrium vapor and liquid mole fractions is large, we observe high concentration gradients near the vapor–liquid interface due to both mass diffusion and the solutocapillary effects. Although the solutocapillary convection is decidedly affected by the eruptive nature of the boiling process, the near-bubble mass transport still plays a vital role in boiling heat transfer. In a square capillary of *d* = 900 μm, mass diffusion dominates and the depletion of 2-propanol near the vapor–liquid interface increases. This leads to an increase in the local bubble point causing the deterioration of heat transfer for 2-propanol/water mixtures. However, in the smaller square capillary of *d* = 500 μm, the solutocapillary effect becomes more important. The induced convection near the contact line helps to augment the boiling heat transfer at *x* = 0.015, despite the fact that mass diffusion tends to cause a higher concentration gradient normal to the bubble front during the boiling process. Herein, we prove that the microscale schlieren method is able to provide valuable insight into the leverage between different mechanisms in heat transfer during the vaporization process of 2-propanol/water mixtures in a square capillary.

## Keywords

Heat Transfer Coefficient Boiling Heat Transfer Marangoni Number Bubble Point Boiling Process## List of symbols

*d*Inner dimension of the square capillary

*D*Mass diffusion coefficient

*h*Heat transfer coefficient

*I*Intensity

*k*Thermal conductivity

*l*Radial distance between the interface and the center of the Marangoni vortex

*M*Molar mass

*Ma*Marangoni number

*n*Refractive index

*q*″Input heat flux

*R*_{i}Radius of curvature of the vapor–liquid interface

*T*Temperature

- Δ
*T*_{h} Superheat

*t*Thickness

*V*Molar volume

*v*Velocity

*X*Cartesian coordinate along the capillary tube

*x*Liquid mole fraction of 2-propanol in water

*Y*Cartesian coordinate perpendicular to the heating wall

*y*Vapor mole fraction of 2-propanol in water

*Z*Cartesian coordinate opposite to the gravity direction

## Greek

*θ*Azimuthal angle in the spherical coordinate

*μ*Viscosity

*ρ*Density

*σ*Surface tension

## Subscript

- az
Azeotrope

- bp
Bubble point

- d
Dew point

- g
Borosilicate glass

- i
Vapor–liquid interface

- ideal
Ideal

- l
Liquid

- s
Heated wall of the capillary

- ss
Stainless steel ANSI 304

- v
Vapor

- 0
Reference

- 1
More volatile component of the binary mixture, 2-propanol

- 2
Less volatile component of the binary mixture, water

- ||
Direction parallel to the vapor–liquid interface

- ⊥
Direction normal to the vapor–liquid interface

## Notes

### Acknowledgments

This work is supported by the Ministry of Science and Technology of Taiwan under Grant Number NSC 101-2221-E-002-064-MY3. The authors also wish to acknowledge and thank Tzu-hsun Hsiao for his assistance with the microscale schlieren setup.

## Supplementary material

Supplementary material 1 (MP4 228 kb)

Supplementary material 2 (MP4 735 kb)

Supplementary material 3 (MP4 301 kb)

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