Collapse rate

Intensity of collapse, rate of the reaction, threshold/ nucleation, almost all physical properties Gas content, nucleation, collapse phase... 

If a gravitationally bound clump forms, the relative velocities of the particles within the clump must be damped before the clump can collapse to form a solid planetesimal. Gas drag and particle-particle collisions will do this, with damping being more effective for small particles. The collapse rate is limited by the pressure of gas within the clump - as particles move inwards, the gas becomes compressed, opposing further collapse (Cuzzi Weidenschilling 2006). The rate of collapse is set by the time required for particles to settle to the center, which may be hundreds of orbital periods for millimeter-sized particles (Cuzzi Weidenschilling 2006). 

More recent studies by Pandit et al. using a horn (20 kHz) to study the effect of the ratio of horn to column diameter on the foam drainage and collapse rate have revealed that high-intensity US can destabilize the static foam structure [168]. The efficiency of the US horn has been related to the position of its tip also, the use of periodic ultrasound vibrations has proved more efficient (viz. to save energy and operating expenses) than continuous application [167]. 

The off diagonal elements of the symmetric rate constant The rate constant matrix in the orthogonal system The collapsed rate constant matrix... 

Bulk liquid temperature Intensity of collapse, rate Optimum value exits, gener-... 

Ideally, there should be two identical columns, one fitted with a high pressure drop distributor for use at low velocities (up to 1 cm/s) when measuring uMF and um, and a second one fitted with a lower pressure drop distributor which will allow measurement of deaeration rates and collapse rates at velocities up to 30 cm/ s. Alternatively, if only one column is available, two different distributors must be used (and replaced as required). 

Cohesive powders in group C display a different collapse rate as shown in Fig. 39. The bed does not bubble even at a gas velocity... 

The relative significance of the effects of the liquid inertia and the heat transfer on the collapse rate was recently reported (Fla). 

The foam collapse rate Wp as a function of surfactant concentration can be called foam formation isotherm (Fig. 6.2). As it is seen from Fig. 6.2, that Wp sharply increases in a narrow concentration range below adsorption layer saturation. The Wp° value can thus be a characteristic of the aggregation stability of foams during the formation process. 

Fig, 6,3 Concentration relationships of the collapse rate of bubble foam (O) and high-expansion foam ( ) surface tension of the aqueous solution of C]o-Cn sodium alkyl sulphates ( ) and the relative residual concentration in die dispersion medium of a high-expansion foam in wt% ( ) foaming rate 0.83 cm /s (O), 13.5cmVs( ) ... 

A poorly piped variation of this system (Fig. 17.5e) caused pressure fluctuations and inability to keep column pressure constant in one case (194). The author is familiar with two more troublesome cases with a similar piping arrangement, while a fourth similar case was reported by Hollander (164). With the Fig. 17.5e scheme, subcooled liquid mixes with dew point vapor. Collapse of vapor takes place at the point of mixing. The rate of vapor collapse varies with changes in subcooling, overhead temperature, and condensation rate. Variation of this collapse rate induces pressure fluctuations. The above problem (194) was completely eliminated by separating the liquid line from the vapor line, and extending the liquid line well below the liquid surface. The vapor line entered at the previous inlet. 

Here was adopted for simplicity that a = 1/2 and a 1 (the latter inequality is satisfied for bubbles with Ro > >1 mkm). Phase plot of diis equation is presented in Figure 7.2.2. It is seen that for k = -1 (collapsing cavity) z —>Zi as t —> if Zq > Zj. The stationary point z = Zj is unstable. The rate of die cavity collapse z = Zj in the asymptotic regime satisfies inequality Zp < Z < (f where Zp = -RCp is equal to the collapse rate of the cavity in a pure viscous fluid with viscosity of polymeric solution ii. It means diat the cavity closure in viscoelastic solution of polymer at asymptotic stage is slower dian in a viscous liquid with the same equilibrium viscosity. On the contrary, die expansion under the same conditions is faster at k = 1 Zp cavity expansion in a pure solvent widi die viscosity (1- P)q. Tliis result is explained by different behavior of the stress tensor component controlling the fluid rheology effect on the cav-... 

In fact, it is apparent that the collapse rate is controlled by a slower component (A in our case), which increases the nanoshells lifetime. 

Figure 7.27 Collapse rate influenced by (a) ratio of frequencies and (b) volume fractions of components.

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