Flow animation by unsteady temperature fields

Physics of Fluids

Volumn 16, Issue 11, 2004, Pages

  Yariv, Ehud ^a   Brenner, Howard ^b  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GRAVITATION; THERMAL EXPANSION;

FLOW ANIMATION; MASS CONSERVATION PRINCIPLES; MICROFLUIDIC APPLICATIONS; SMALL-SCALE SYSTEMS;

FLOW OF FLUIDS;

PHYSICS;

EID: 8844224182     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1801091     Document Type: Article

References (11)

1. G. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1967).
2. We exclude here physicochemical effects such as boiling, thermal slip, or temperature-dependent surface tension.
3. Since the density is unaffected by the pressure, the temperature T constitutes a single independent thermodynamic variable.
4. -1. Even for an ideal gas, where β=1/T, realistic values of externally imposed temperature differences are typically small compared with the absolute temperature, whence βΔT≪1 too.
5. 0 /gτL, which is about 10 for micron-size thermal variations occurring in water at moderate frequencies of ∼ 100 Hz (and about 100 in air). Moreover, this ratio increases as the length and time scales shrink, suggesting that in certain microfluidic applications the unsteadily driven flow dominates over buoyancy effects. In this work we focus upon the unsteadiness phenomenon, and therefore neglect gravity effects (which, owing to the linearity of the problem, may always be superimposed).
6. D. D. Joseph, A. Huang, and H. Hu, "Non-solenoidal velocity effects and Korteweg stresses in simple mixtures of incompressible liquids," Physica D 97, 104 (1996).
7. The present solution may therefore be used as a generic Fourier component of a more general time-dependent thermal forcing.
8. This parameter cannot be obtained from the present problem formulation, which avoids the specific details of the far-field behavior.
9. H. A. Stone, A. D. Stroock, and A. Ajdari, "Engineering flows in small devices," Annu. Rev. Fluid Mech. 36, 381 (2004).
10. D. E. Kataoka and S. M. Troian, "Patterning liquid flow on the microscopic scale," Nature (London) 402, 794 (1999).
11. B. S. Gallardo, V. K. Gupta, F. D. Eagerton, L. I. Jong, V. S. Craig, R. R. Shah, and N. L. Abbott, "Electrochemical principles for active control of liquids on submillimeter scales," Science 283, 57 (1999).