Expanding/collapsing time

Effects of Water Hammer. Water hammer has a tremendous and dangerous force that can collapse floats and thermostatic elements, overstress gauges, bend mechanisms, crack trap bodies, rupture fittings and heat exchange equipment, and even expand piping. Over a period of time, this repeated stress on the pipe will weaken it to the point of rupture. 

Transient cavitation bubbles are voids, or vapour filled bubbles, believed to be produced using sound intensities in excess of 10 W cm. They exist for one, or at most a few acoustic cycles, expanding to a radius of at least twice their initial size, (Figs. 2.16 and 2.20), before collapsing violently on compression often disintegrating into smaller bubbles. (These smaller bubbles may act as nuclei for further bubbles, or if of sufficiently small radius (R) they can simply dissolve into the bulk of the solution under the action of the very large forces due to surface tension, 2a/R. During the lifetime of the transient bubble it is assumed that there is no time for any mass flow, by diffusion of gas, into or out of the bubble, whereas evaporation and condensation of liquid is assumed to take place freely. If there is no gas to cushion the implosion... 

The transition from the expanded state to the collapsed one and vice versa is controlled by diffusion of the solvent in the gel [56, 57], It was found [56] that the kinetics of swelling and deswelling of the gel is determined by local motions controlled by the diffusion equation in which the diffusion coefficient is given by the ratio of the bulk modulus to the frictional factor (between network and liquid). Whereas in our samples with a volume 1 cm3, the transition from one to another equilibrium state takes several days, for submicron spheres this time... 

The Baade method (Baade 1926 Branch and Patchett 1973 Kirshner and Kwan 1974), as generalized to objects of arbitrary redshift emitting an arbitrary continuum spectrum (Wagoner 1980, 1987) provides a powerful, relatively reliable way to directly determine the distance to any expanding (or collapsing) spherically symmetric source with a well defined photosphere. As indicated in the last section, if we restrict our attention to times t well after the time t when any particular shell of matter was last accelerated, the radius of the photosphere is given by... 

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