Rayleigh wavelength, critical

The Rayleigh instability (Section 14.1.2) of the pore channel is neglected. Pores attached to grain boundaries have increased critical Rayleigh instability wavelengths [7],... 

When one fluid overlays a less dense fluid, perturbations at the interface tend to grow by Rayleigh-Taylor instability (LI, T4). Surface tension tends to stabilize the interface while viscous forces slow the rate of growth of unstable surface waves (B2). The leading surface of a drop or bubble may therefore become unstable if the wavelength of a disturbance at the surface exceeds a critical value... 

While the Rayleigh instability of a cylindrical surface is driven by the surface energy, the flat surface of a thin film can become unstable under the influence of van der Waals forces (see Chapter 5). In this case, the surface tension provides a restoring force which stabilizes short-wavelength undulations. Again, the critical wavelength is determined by a balance of the free energies (see the problems at the end of this chapter). 

Assume that the peak is characterized by the critical condition for Kelvin-Helmholtz instability and for this critical wavelength the fastest growing wavelength from Rayleigh-Taylor instability can be used. Show that it can be used to obtain a correlation for the peak heat flux. Also assume where needed that... 

The Kelvin-Helmholtz instability is similar to the Rayleigh-Taylor instability, except that the former allows a relative velocity between the fluids, u. Using the same concept of Grace et al. (1978), Kitscha and Kocamustafaogullari (1989) applied the Kelvin-Helmholtz instability theory to model the breakup of large bubbles in liquids. Wilkinson and van Dierendonck (1990) applied the critical wavelength to explain the maximum stable bubble size in high-pressure bubble columns ... 

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