A general interfacial energy balance equation taking into account surface energy variation is derived for viscous two-layer flows. Application of this interfacial energy equation to a thin liquid layer heated from one side using a one-layer model shows that thermocapillary induced surface energy variation has a tendency to stabilize the system, resulting in an increase in the critical Marangoni number for the onset of thermocapillary instability. Thermocapillary induced surface energy variation tends to decrease the temperature of hot surface spots and increase the temperature of cold surface spots through an absorb-release mechanism. This absorb-release mechanism increases the free surface’s capability to convect thermal energy from hot spots to cold spots and thus redistributes the disturbance energy evenly across the free surface. This new stabilizing effect becomes stronger at high surface temperature and at high surface dilatation rate.
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Surface Energy Variation Effect on the Onset of Thermocapillary Instability of a Thin Liquid Layer Heated from the Side
Lin Wu,
Lin Wu
Department of Electrical Engineering, Princeton University, Princeton, NJ 08540
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Kang Ping Chen
e-mail: k.p.chen@asu.edu
Kang Ping Chen
Department of Mechanical & Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106
Search for other works by this author on:
Lin Wu
Department of Electrical Engineering, Princeton University, Princeton, NJ 08540
Kang Ping Chen
Department of Mechanical & Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106
e-mail: k.p.chen@asu.edu
Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division March 5, 2002; revision received September 17, 2002. Associate Editor: G. P. Peterson.
J. Heat Transfer. Feb 2003, 125(1): 63-69 (7 pages)
Published Online: January 29, 2003
Article history
Received:
March 5, 2002
Revised:
September 17, 2002
Online:
January 29, 2003
Citation
Wu, L., and Chen, K. P. (January 29, 2003). "Surface Energy Variation Effect on the Onset of Thermocapillary Instability of a Thin Liquid Layer Heated from the Side ." ASME. J. Heat Transfer. February 2003; 125(1): 63–69. https://doi.org/10.1115/1.1527909
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