Rayleigh stability limit

As a consequence, the droplet breaks up into a stream of smaller droplets, each one continuing to shrink by evaporation until the Rayleigh stability limit is reached again. The process of droplet fission is repeated several times and it is called uneven fission or droplet jet fission [5,6],... 

The decrease of the droplet radius R at constant charge q leads to an increase in the electrostatic repulsion of the charges at the droplet surface until the droplet reaches the Rayleigh stability limit [28] given by ... 

In order to improve the mass spectrum analysis results, the mass spectrometer requires as many detectable gas phase ions as possible. As shown in previous sections, the electrospray produces gas phase ions from its charged droplets when the droplets reach a certain size and either the CRM of IBM model of gas phase ion formation occurs. To produce gas phase ions efficiently, an electrospray must operate in a mode where the droplets produced are relatively small, close to the Rayleigh limit, and also where the droplets are charged sufficiently. Once the droplets reach the Rayleigh stability limit at a fast pace, they can continue on to the CRM an IBM models of gas phase ion formation. 

Previous computations (189) show that the critical value of Rat for non-Boussinesq conditions is approximately the same as that for a Boussinesq fluid in a box heated from below, at least when H2 is the carrier gas. Thus, results from the stability analysis of the classical Rayleigh-Benard problem of a two-dimensional fluid layer heated from below (see reference 190 for a review) may be used to indicate the type of behavior to be expected in a horizontal reactor with insulated side walls. As anticipated from this analysis, an increase in the reactor height from 2 to 4 cm raises the value of Rat to 4768, which is beyond the stability limit, Rat critical = 2056, for a box of aspect ratio 2 (188). The trajectories show the development of buoyancy-driven axial rolls that are symmetric about the midplane and rotating inward. For larger values of Rat (>6000), transitions to three-dimensional or time-de-... 

Fenn and co-workers described electrospray ionization for mass spectrometry analyzing large biomolecules. ESI greatly enhanced MS ability for analysis of proteins or peptides. The mechanism of the ESI source is relatively simple. In an electrospray ionization source, the solution of analytes is nebulized into fine droplets via a capillary tube under a high electric field. The positive charges are accumulated on the surface of the droplets in this field. Later, because of evaporation of droplets, the surface coulombic forces exceed the surface tension and the droplets are dissociated into smaller droplets. This process continues until nanometer-sized droplets are formed. In this way, the ions pass from the source into the mass analyzer, whereas the bulk solvent is pumped away by a vacuum system. The stability limit (Rayleigh limit) of droplets is determined by the Coulomb forces of the accumulated positive... 

Size distribution plays a major role in the microbubble stability, behavior in vivo, and the microbubble acoustic response. The Rayleigh-Plesset equation which describes the microbubble response to pressure waves suggests that ultrasound scattering is proportional to the sixth power of the microbubble diameter [46]. It is not possible, however, to inject large bubbles (e.g., 0.1 or 1 mm in diameter) in the bloodstream, because they would be immediately lodged in the vasculature as emboli, severely limiting the blood flow. Fortunately, microbubbles with the size of several micrometers are still quite echogenic in the ultrasound... 

In a film of infinite lateral extent, k can range from 0 to oo, so a necessary condition for instability is that AH > 2npgh. Since all wave numbers are available in a film of infinite extent, we see that this analysis predicts that the thin film will always be unstable, even with the stabilizing influence of surface tension, to disturbances of sufficiently large wavelength when van der Waals forces are present. Similarly, the Rayleigh Taylor instability that occurs when the film is on the underside of the solid surface will always appear in a film of infinite extent. In reality, of course, the thin film will always be bounded, as by the walls of a container or by the finite extent of the solid substrate. Hence the maximum wavelength of the perturbation of shape is limited to the lateral width, say W, of the film. This corresponds to a minimum possible wave number... 

Most recently (Schneider 2006) an experimental source was used to conduct studies under conditions of total solvent consumption , with pneumatically assisted nebu-lization to stabilize the ESI process, a heated laminar flow chamber to enhance desolvation and ion production, and various atmosphere-to-vacuum aperture diameters to maximize ion transfer. The motivation for these experiments was to investigate the proposal that the reason for the much lower ionization sampling efficiencies at higher flow rates ( o,L.min and above) is that the electrosprayed droplets are much larger in view of the much larger ESI needle tip diameters required to maintain flow rates in this regime, and thus are much less efficiently evaporated down to the Rayleigh and/or ion evaporation limits than the droplets formed from the 1 (tm diameter tips nsed in nano-ESI (Juraschek 1999 Schmidt 2003). 

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