Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

  • Materials & Fracture · Solids & Structures · Dynamics & Control · Production & Design
  • Published:

Numerical study on a sliding bubble during nucleate boiling

  • 258 Accesses

  • 16 Citations


A numerical method for simulating bubble motion during nucleate boiling is presented. The vapor-liquid interface is captured by a level set method which can easily handle breaking and merging of the interface and can calculate an interfacial curvature more accurately than the VOF method using a step function. The level set method is modified to include the effects of phase change at the interface and contact angle at the wall as well to achieve mass conservation during the whole calculation procedure. Also, a simplified model to predict the heat flux in a thin liquid microlayer is developed. The method is applied for simulation of a sliding bubble on a vertical surface to further understand the physics of partial nucleate boiling. Based on the computed results, the effects of contact angle, wall superheat and phase caange on a sliding bubble are quantified.

This is a preview of subscription content, log in to check access.


C P :

Specific heat at constant pressure

g :


H :

Step function

h :

Grid spacing

h ev :

Evaporative heat transfer coefficient

h fg :

Latent heat of evaporation

k :

Thermal conductivity

L :

Length scale,

N U :

Nusselt number

\(\vec n\) :

Normal unit vector

D :


q :

Heat flux

R :

Effective radius of a bubble

R gas :

Gas constant

R min :

Minimum bubble radius for sliding

T :


ΔT :

T w -T sat

U :

Bubble slide velocity

u, v :

x, y-directional velocities

\(\vec u\) :

Velocity vector, (u, v)

\(\dot V_{micro} \) :

Rate of vapor volume production from the microlayer

ΔV micro :

Control volume surrounding the liquid microlayer

x, y :

Horizontal and vertical coordinates


Liquid film thickness


Interfacial curvature


Dynamic viscosity




Surface tension


Artificial time


Level set function


Contact angle

1, 2:

Points 1 and 2

A, R:

Advancing, receding



l, v:

Liquid, vapor

sat, w:

Saturation, wall


  1. Kays, W. M. and Crawford, M. E., 1980,Convective Heat and Mass Transfer, McGraw-Hill Book Company, New York.

  2. Khrustalev, D. and Faghri, A., 1995, “Heat Transfer During Evaporation on Capillary-Grooved Structeres of Heat Pipes,”J. Heat Transfer, Vol. 117, pp. 740–747.

  3. Lay, J. H., and Dhir, V. K., 1995, “Shape of a Vapor Stem During Nucleate Boiling of Saturated Liquids,”J. Heat Transfer, Vol. 117, pp. 394–401.

  4. Lee, R. C., and Nydahl, J. E., 1989, “Numerical Calculation of Bubble Growth in Nucleate Boiling From Inception Through Departure,”J. Heat Transfer, Vol. 111, pp. 474–479.

  5. Marmur, A., 1998, “Contact-Angle Hysteresis on Heterogeneous Smooth Surfaces: Theoretical Comparison of the Captive Bubble and Drop Methods,”Colloids and Surfaces, Vol. 136, pp. 209–215.

  6. Ryskin, G. and Leal, L. G., 1984, “Numerical Simulation of Free-Boundary Problems in Fluid Mechanics. Part 2,”J. Fluid Mech., Vol. 148, pp. 19–35.

  7. Son, G., Dhir, V. K., and Ramanujapu, N., 1999, “Dynamics and Heat Transfer Associated with a Single Bubble During Nucleate Boiling on a Horizontal Surface,”J. Heat Transfer, Vol. 121, pp. 623–631.

  8. Son, G. and Lee, S. R., 1999, “Numerical Simulation on Rising Bubble Behaviors in Water,” Trans.KSME, Vol. 23, No. 12, pp. 1606–1613. (in Korean)

  9. Sussman, M., Smereka, P., and Osher, S., 1994, “A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow,”J. Comput. Phys., Vol. 114, pp. 146–159.

  10. Takata, Y., Shirakawa, H., Kuroki, T., and Ito, T., 1998, “Numerical Analysis of Single Bubble Departure from a Heated Surface,”Proc. 11th IHTC, Vol. 4, pp. 355–360, Kyongju, Korea.

  11. Thorncroft, G. E., Klausner, J. F., and Mei, R., 1998, “An Experimental Investigation of Bubble Growth and Detachment in Vertical Upflow and Downflow Boiling,”Int. J. Heat Mass Transfer, Vol. 114, pp. 146–159.

  12. Van Helden, W. G. J., Vander Geld, C. W. M., and Boot, P. G. M., 1995, “Forces on Bubbles Growing and Detaching in Flow Along a Vertical Wall,”Int. J. Heat Mass Transfer, Vol. 38, pp. 2075–2088.

  13. Wayner, P. C. Jr., 1992, “Evaporation and Stress in the Contact Line Region,”Proc. of The Engineering Foundation Conference On Pool and External Flow Boiling, pp. 251–256, Santa Barbara, California.

  14. Welch, S. W. J., 1998, “Direct Simulation of Vapor Bubble Growth,”Int. J. Heat Mass Transfer, Vol. 41, pp. 1655–1666.

Download references

Author information

Correspondence to Gihun Son.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Son, G. Numerical study on a sliding bubble during nucleate boiling. KSME International Journal 15, 931–940 (2001). https://doi.org/10.1007/BF03185271

Download citation

Key Words

  • Level Set Method
  • Sliding Bubble
  • Nucleate Boiling
  • Contact Angle