Rayleigh instability limit

How the droplets produced upon ESI are transformed to the ions observed in the mass spectrum is not yet well xmderstood. As the solvent in the droplets evaporates, the droplets shrink and the ions contained in them accumulate at the surface to minimize coulombic repulsion between the charges. This process can continue until the Rayleigh instability limit is reached, at which the droplets disintegrate ("explode") into smaller droplets (Figure 1.15) that also shrink by solvent loss. Sequential subdivision through coulombic explosion at the Rayleigh limit may be repeated until the... 

There is a limit to the charge that the surface of a droplet can sustain, for the electrical stress generated by the surface charges can balance the surface tension forces. At that point the droplet becomes unstable and breaks up. Lord Rayleigh (1882) analyzed the criterion of instability for a conducting droplet using spherical harmonics to describe the modes of oscillation. The natural frequency of the nth mode of oscillation of a droplet was found to be given by... 

The basic features of the two models can be summarized as follows. In the CRM, the droplets shrink until the resulting instability breaks up the parent droplet into a hatch of offspring droplets, each of which continues to evaporate until it too reaches the Rayleigh limit. This sequence continues until the offspring droplets ultimately become so small that they contain only one analyte... 

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... 

The Rayleigh limit is defined as the amount of charge on a drop at which the repulsive electric force overcomes the surface tension, leading to drop instability. " This limit is expressed as... 

For the Brownian-particle approximation, it is assumed that the aerosol system is stable over some experimental time. Particles are stable and their motions are uncorrelated. A special case in which the particles are treated as rigid bodies is frequently termed the Rayleigh gas. Of course, a characteristic feature of an aerosol is its inherent instability due to coagulation and deposition. Therefore, this approximation is limited to experimental times collision... 

Reference Solvent Droplet diameter range (pm) Onset of Instability (% of Rayleigh limit) % of mass lost in breakup" % of charge lost in breakup... 

The macroscopic desaiption has been impressively successful in a number of areas, such as fluid mechanics, for studying complex flows and fluid instabilities, including the Rayleigh-Taylor, Kelvin-Helmholz, and Richtmyer-Meshkov instabilities. But it becomes inaccurate for problems in which the detailed atomistic processes affect the macroscopic behavior of the medium, or when the scale of the medium is small enough that the continuum approximation becomes questionable. Such situations are often found in studies of properties and defects of micro- or nanosystems where the continuum methods can describe only qualitative tendencies, the quality of quantitative results may be difficult to ascertain. Also, the approach has limited applicability since it does not incorporate molecular-scale enthalpic interactions between different species present in the system and requires input (viscosities. 

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