Plesset Zwick

At a later stage of bubble growth, heat diffusion effects are controlling (as point c in Fig. 2.9), and the solution to the coupled momentum and heat transfer equations leads to the asymptotic solutions and is closely approximated by the leading term of the Plesset-Zwick (1954) solution,... 

For contact angle <(> = 0 and 8 << R, Eq. (2-58) should be reduced to Plesset-Zwick s equation based on the thin boundary layer assumption thus, 4>e = tt/2. 

This reduces to the leading term of the Plesset-Zwick asymptotic solution, Eq. (43), for large time, or for i (0) = 0. The displacement between the two bubble radius expressions when the bubble radius has increased tenfold is... 

For the exact solution, Eq. (20), for a uniform initial superheat, (p -while the plane approximation, treating the liquid surrounding the bubble as a semi-infinite slab, gives < )<. = 1. It is incorrectly stated then that, for (jj = 0 and 5 J , the Plesset-Zwick thin thermal boundary layer solution leads to... 

In this expression for h2st the Nusselt number Nu is the greater of a sphere forced convection Nusselt ntimber or one derived from the Plesset-Zwick bubble growth formula ... 

Analytical analyses for the growth of a single bubble have been performed for simple geometrical shapes, using a simplified heat transfer model. Plesset and Zwick (1954) solved the problem by considering the heat transfer through the bubble interface in a uniformly superheated fluid. The bubble growth equation was obtained... 

Plesset MS, Zwick SA (1954) The growth of vapor bubbles in superheated. J Appl Phys 25 474-478... 

As one limiting case, let us assume no heat transfer limitations so that the pressure inside the bubble is invariant at Pvp(To). Then, using Eqs. (8) and (9), as shown by Plesset and Zwick (1954),... 

As indicated in Sec. IIB, ordinary nucleate boiling is a two-step process. First, nuclei must appear. Second, the nuclei must grow into bubbles large enough to move away from the nucleation sites. The rate of heat absorption by the liquid may be controlled by either one or both of these two processes. The growth of a nucleus (tiny bubble) into ordinary bubbles has received attention recently. The theoretical attack of Forster and Zuber was discussed in Sec. IIB2. Inasmuch as the theory of Zwick and Plesset (P3, P4, Zl, Z2) represents another attempt to obtain exact expressions for bubble growth, and since the theory fits well with the few data for steam bubbles in superheated water, their theoretical method is summarized below. 

It is not necessary to assume the liquid film to be completely stagnant. Radial motion can be allowed for, but with some difficulty. It was noted in Sec. IIB2 that Forster and Zuber state that conduction is the chief mode of heat transfer (compared with convection due to radial motion). Eddies or motions of the liquid tangent to the bubble are neglected. The Zwick-Plesset theory likewise excludes eddies. The derivation is lengthy therefore the final typical equations are presented here without proof. 

FIGURE 15.19 Bubble growth with the formation of an evaporation wave resulting in entrainment of small droplets into the bubble. 1, experimental data 2, Plesset and Zwick heat-transfer-controlled solution (Eq. 15.37) 3, Rayleigh solution with r(f) = 0 at t = 0.16 s 4, liquid pressure (from Barthau and Hahne [45], with permission). 

Plesset M.S., Zwick S.A. A nonsteady Heat Diffusion Problem with spherical Symmetry // J. Appl. Phys. 1952. V.23. N 1. P. 95-99. Fridrichsberg D.A. A handbook on colloid chemistry. Leningrad Chemistry, 1974. (in Russian). Goncharov V.K., Wementeva N.Yu. 

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