XX. <i>On the equilibrium of liquid conducting masses charged with electricity</i>

Rayleigh, Lord

doi:10.1080/14786448208628425

Cited by 1,656 publications

(708 citation statements)

References 0 publications

Supporting

Mentioning

689

Contrasting

Unclassified

Order By: Relevance

“…Because the liquid is conductive, charge migration can occur up to the scission point (d sp ) at which the connection ruptures. For deriving eq 1, Rayleigh [32] assumed that fragmentation is triggered by shape oscillations. Droplet deformations were described in terms of spherical harmonics, and he concluded that the fragmentation channel having the lowest ⌬E ts is associated with quadrupole (prolate-oblate [9]) oscillations, whereas higher order deformations are less effective at mediating disintegration [42].…”

Section: Introductionmentioning

confidence: 99%

“…In addition, proposals for scenarios involving elements of both models have been put forward [30,31]. A solvent droplet is said to be at the Rayleigh limit when its net charge reaches a value Q R that is given by [1,32] where 0 is the permittivity of the vacuum, and ␥ is the surface tension. In the ESI-MS literature the relationship between Q R and droplet stability is often treated somewhat casually, using statements such as [33] "[it was] found that as the solvent evaporated the density of charges on the droplet surface would increase to a critical value, now known as the 'Rayleigh limit', at which Coulomb repulsion would overcome surface tension.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

“…(1) How exactly can the interplay of Coulomb forces and surface tension be interpreted, considering that the two factors do not even share the same physical units? (2) What is the reason for the generally observed asymmetry in product size, considering that Rayleigh's mechanism [32] should favor the formation of two equally sized fragments [9,18,34,35]? (3) What are the consequences of offspring droplets being ejected from the tip of extended protrusions, instead of being emitted from the surface of a more or less spherical parent droplet?…”

mentioning

confidence: 99%

“…A solvent droplet is said to be at the Rayleigh limit when its net charge reaches a value Q R that is given by [1,32] …”

mentioning

confidence: 99%

See 4 more Smart Citations

A simple model for the disintegration of highly charged solvent droplets during electrospray ionization

Konermann

2009

J. Am. Soc. Mass Spectrom.

View full text Add to dashboard Cite

This work uses a minimalist model for deciphering the opposing effects of Coulomb repulsion and surface tension on the stability of electrosprayed droplets. Guided by previous observations, it is assumed that progeny droplets are ejected from the tip of liquid filaments that are formed as protrusions of an initially spherical parent. Nonspherical shapes are approximated as assemblies of multiple closely spaced beads. This strategy greatly facilitates the calculation of electrostatic and surface energies. For a droplet at the Rayleigh limit the model predicts that growth of a very thin filament is a spontaneous process with a negligible activation barrier. In contrast, significant barriers are encountered for the formation of larger diameter filaments. These different barrier heights favor highly asymmetric droplet fission because the dimensions of the filament determine those of the ejected droplet(s). Substantial charge accumulation occurs at the filament termini. This allows each progeny droplet to carry a significant fraction of charge, despite its very small volume. In the absence of a long connecting filament, relieving electrostatic stress through progeny droplet emission would be ineffective. The model predicts the prevalence of fission events leading to the formation of several progeny droplets, instead of just a single one. Ejection bursts are followed by collapse back to a spherical shape. The resulting charge depleted system is incapable of producing additional progeny droplets until solvent evaporation returns it to the Rayleigh limit. Despite the very simple nature of the model used here, all of these predictions agree with experimental data. E lectrospray ionization (ESI) mass spectrometry (MS) has evolved into one of the most versatile and widely used analytical techniques. The ESI process itself has been subject of numerous studies (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12] and references therein). Analyte solution is passed through a metal capillary to which high voltage has been applied, and solvent droplets emanate from the tip of a Taylor cone at the capillary outlet [11]. Each droplet carries a net charge due to protons or other cationic species that reside at the air/liquid interface. Solvent evaporation and droplet fission are fundamental elements of the ESI process. Evaporation increases the surface charge density to a point where fission occurs. The disintegration process triggered in this way is highly asymmetric, leading to the formation of several small progeny droplets that carry away only a small fraction of mass, but a disproportionately high amount of charge [13,14]. High-speed imaging is an important tool for gaining insights into the breakup mechanism [15,16]. More recently, the rapid solidification of charged nanodroplets using sol-gel techniques has provided a means to capture transient droplet shapes and study them by microscopy [17]. Also, molecular dynamics simulations represent an interesting approach in this area [9,10]. All those studies reveal that disintegrati...

show abstract

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

“…A solvent droplet is said to be at the Rayleigh limit when its net charge reaches a value Q R that is given by [1,32] …”

mentioning

confidence: 99%

See 3 more Smart Citations

A simple model for the disintegration of highly charged solvent droplets during electrospray ionization

Konermann

2009

J. Am. Soc. Mass Spectrom.

View full text Add to dashboard Cite

show abstract

A coupled boundary/finite element method for the computation of magnetically and electrostatically levitated droplet shapes

Song

1999

Int. J. Numer. Meth. Engng.

View full text Add to dashboard Cite

Fabrication and Application of Nanofibrous Scaffolds in Tissue Engineering

Tuan

2009

CP Cell Biology

View full text Add to dashboard Cite

Nanofibers fabricated by electrospinning are morphological mimics of fibrous components of the native extracellular matrix, making nanofibrous scaffolds ideal for three‐dimensional cell culture and tissue engineering applications. Although electrospinning is not a conventional technique in cell biology, the experimental setup may be constructed in a relatively straightforward manner, and the procedure can be carried out by individuals with limited engineering experience. Here, we detail a protocol for electrospinning of nanofibers and provide relevant specific details concerning the optimization of fiber formation (Basic Protocol 1). The protocol also includes conditions required for preparing biodegradable polymer solutions for the fabrication of nonwoven and aligned nanofibrous scaffolds suitable for various cell/tissue applications. In addition, information on effective cell loading into nanofibrous scaffolds and cellular constructs grown in a bioreactor is provided (Basic Protocol 2). Instructions for building the electrospinning apparatus are also included (see the Support Protocol). Curr. Protoc. Cell Biol. 42:25.2.1‐25.2.12. © 2009 by John Wiley & Sons, Inc.

show abstract

XX. On the equilibrium of liquid conducting masses charged with electricity

Cited by 1,656 publications

References 0 publications

A simple model for the disintegration of highly charged solvent droplets during electrospray ionization

A simple model for the disintegration of highly charged solvent droplets during electrospray ionization

A coupled boundary/finite element method for the computation of magnetically and electrostatically levitated droplet shapes

Fabrication and Application of Nanofibrous Scaffolds in Tissue Engineering

Contact Info

Product

Resources

About