Condensation waves

In biphase systems velocity of the steam is often 10 times the velocity of the liquid. If condensate waves rise and fill a pipe, a seal is formed with the pressure of the steam behind it (Fig. 2). Since the steam cannot flow through the condensate seal, pressure drops on the downstream side. The condensate seal now becomes a piston accelerated downstream by this pressure differential. As it is driven downstream it picks up more liquid, which adds to the existing mass of the slug, and the velocity increases. 

Weak detonations are believed to represent the condensation shocks observed in supersonic wind tunnels [12], [51]. Supercooled water vapor in a supersonic stream has been observed to condense rapidly through a narrow wave. The amount of liquid formed is so small that the equations for purely gaseous waves are expected to apply approximately. Since a normal shock wave would raise the temperature above the saturation point (thus ruling out the ZND structure, for example), and the flow is observed to be supersonic downstream from the condensation wave, it appears reasonable to assume that condensation shocks are weak detonations. This hypothesis may be supported by the fact that unlike chemical reaction rates, the rate of condensation increases as the temperature decreases. Proposals that weak detonations also represent various processes occurring in geological transformations have been presented [52]. 

We now recall that the classical planar rotator model may be used as a model of superfluid He4, 0 being the phase of the condensate wave function, S being related to the superfluid density ps as S = ps(hjm)2, m being the mass of a He4 atom. Thus one can have superfluid-normal fluid transition in d = 2 dimensions, despite the lack of conventional long range order This conclusion seems to be corroborated by experiments on He4 films (Bishop and Reppy, 1978). 

Condensate Waves and Turbulence. As the local condensate film thickness (i.e., the film Reynolds number Rez) increases, the film will become unstable, and waves will begin to grow rapidly. This occurs for Re, > 30. Kapitza [16] has shown that, in this situation, the average film thickness is less than predicted by the Nusselt theory and the heat transfer coefficient increases accordingly. Kutateladze [17] therefore recommends that the following correction be applied to Eq. 14.12 ... 

When a superconductor S is brought into a contact with a non superconducting (normal) metal N the proximity effect mainly defines the properties of this hybrid structure. The concept of the proximity effect is related to the diffusive penetration of the Cooper pairs from S to N metal over some distance [1]. The condensate wave function monotonically decays in the normal metal due to the finite lifetime of superconducting electrons in it. The characteristic distance of the wave function decay is the coherence length gN = hDNl2tikBT)m, where DN is the diffusion coefficient of N metal, and T is the temperature. The %N values are usually order of dozens of nanometers [2]. When the N layer in a S/N proximity effect structure is replaced by a metallic ferromagnet F, the pair wave function from S still penetrates in F and makes the F layer superconducting. 

Since along these characteristics p = const, and u p) = const, we conclude that the characteristics are straight lines on the x, t plane. The equation of vertical (upward) motion of the condensation wave is... 

The second way in which atomic interactions profoundly affect the condensate properties is through their effect on the energy. The effect of atom-atom interactions in the many-body Hamiltonian can be parameterized in the T —> 0 limit in terms of the two-body scattering length. This use of the exact two-body T-matrix in an energy expression is actually a rigorous procedure, and can be fully justified as a valid approximation.One simple theory which has been very successful in characterizing the basic properties of actual condensates is based on a mean-field, or Hartree-Fock, description of the condensate wave function, which is found from the equation ... 

Unlike the fermionic quantum description, the bosonic case is driven by the condensate wave function (the main field) by means of the adapted version of Eq. (1.155), i.e.,... 

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