Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session F27: Focus Sessions: The Physics of Electrospray and Electrospinning: Current Knowledge and State of the Art IElectro
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Chair: Alfonso Ganan Calvo, Universidad de Sevilla Room: 709 |
Monday, November 20, 2017 8:00AM - 8:13AM |
F27.00001: The Taylor--Melcher leaky dielectric model as a macroscale electrokinetic description Ehud Yariv, Ory Schnitzer As the Taylor-Melcher electrohydrodynamic model hinges upon the presence of nonzero interfacial-charge density, it appears to be in contradiction with the aggregate electro-neutrality implied by ionic screening. Following a brief synopsis by Baygents {\&} Saville (1989) we derive the macroscale description appropriate for leaky dielectric liquids, starting from the electrokinetic equations and addressing the double limit of thin space-charge layers and strong fields. Electrokinetic transport within the electrical `triple layer' comprising the genuine interface and the adjacent space-charge layers is embodied in effective boundary conditions; these, together with the simplified transport within the bulk domains, constitute the requisite macroscale description, which essentially coincides with the familiar equations of Taylor {\&} Melcher. A key quantity in our macroscale description is the `apparent' surface-charge density, provided by the transversely-integrated triple-layer microscale charge. At leading order, this density vanishes due to the expected Debye-layer screening; its asymptotic correction provides the `interfacial' surface-charge density appearing in the Taylor-Melcher model. Our unified electrohydrodynamic treatment provides a reinterpretation of both the Taylor-Melcher conductivity-ratio parameter and the electrical Reynolds number. Our procedure explains the oversight which has prevented Baygents {\&} Saville from matching the triple layer with the bulk. [Preview Abstract] |
Monday, November 20, 2017 8:13AM - 8:26AM |
F27.00002: Static structure of a pointed charged drop Juan Fernandez de la Mora The static equilibrium structure of an equipotential drop with two symmetric Taylor cones is computed by assigning a charge distribution along the $z$ axis $q’(z)=\sum B_n(L^2-z^2)^{n+1/2}$. Taylor’s local equilibrium at the poles $z=L,-L$ fixes two of the $B_n$ coefficients as a function of the other, determined by minimizing stress imbalance. Just two optimally chosen terms in the $B_n$ expansion yield imperceptible errors. Prior work has argued that an exploding drop initially carrying Rayleigh’s charge qR is quasi static. Paradoxically, quasi-static predictions on the size of the progeny drops emitted during a Coulombic explosion disagree with observations. The static drop structure found here also models poorly a Coulomb explosion having an equatorial over polar length ratio (0.42) and the a drop charge exceeding those observed (0.28-0.36 and $q_R/2$). Our explanation for this paradox is that, while the duration $t_c$ of a Coulomb explosion is much larger than the charge relaxation time, the dynamic time scale for drop elongation is typically far longer than $t_c$. Therefore, the pressure distribution within the exploding drop is not uniform. A similar analysis for a drop in an external field fits well the experimental shape. [Preview Abstract] |
Monday, November 20, 2017 8:26AM - 8:39AM |
F27.00003: The incept of ejection from a fresh Taylor cone and subsequent evolution Jose M. Lopez-Herrera, Alfonso Ganan-Calvo Within a certain range of applied voltages, a pendant drop suddenly subject to an intense electric field develops a cusp from which a fast liquid ligament issues. The incept of this process has common roots with other related phenomena like the Worthington jets, the jet issued after surface bubble bursting or the impact of a drop on a liquid pool. This is experimentally and numerically demonstrated. However, given the electrohydrodynamic nature of the driver in the formation of a Taylor cone, a number of electrokinetic processes take place in the rapid tapering flow, whose characteristic times should be carefully compared to the ones of the flow. As a result, universal scaling laws for the size and charge of the top drop have been obtained. Subsequently, sustaining the applied electric field, the ejection continues and the issuing liquid ligament releases a train of droplets of varying size and charge. Under appropriate conditions and if the liquid suctioned by the electric field is replenished, the system reaches a (quasi)steady state asymptotically. The degree of compliance of the size and charge of those subsequent droplets with previously proposed scaling laws of steady Taylor cone-jets has been studied. Computational code Gerris and an extended electrokinetic module is used. [Preview Abstract] |
Monday, November 20, 2017 8:39AM - 8:52AM |
F27.00004: Scaling laws for first and second generation electrospray droplets Osman Basaran, Krishnaraj Sambath, Christopher Anthony, Robert Collins, Brayden Wagoner, Michael Harris When uncharged liquid interfaces of pendant and free drops (hereafter referred to as parent drops) or liquid films are subject to a sufficiently strong electric field, they can emit thin fluid jets from conical tip structures that form at their surfaces. The disintegration of such jets into a spray consisting of charged droplets (hereafter referred to as daughter droplets) is common to electrospray ionization mass spectrometry, printing and coating processes, and raindrops in thunderclouds. We use simulation to determine the sizes and charges of these first-generation daughter droplets which are shown to be Coulombically stable and charged below the Rayleigh limit of stability. Once these daughter droplets shrink in size due to evaporation, they in turn reach their respective Rayleigh limits and explode by emitting yet even smaller second-generation daughter droplets from their conical tips. Once again, we use simulation and theory to deduce scaling laws for the sizes and charges of these second-generation droplets. A comparison is also provided for scaling laws pertaining to different generations of daughter droplets. [Preview Abstract] |
Monday, November 20, 2017 8:52AM - 9:05AM |
F27.00005: The importance of energy dissipation in cone-jets operating in the nanometric regime Manuel Gamero-Castaño Cone-jets of highly conductivity liquids (electrical conductivity near or larger than 1 S/m) are able to produce sprays of nanodroplets with narrow diameter distributions. This unique ability is of great interest in manufacturing, spacecraft propulsion and hypervelocity impact research. Most of the experimental work in cone-jets has been done under conditions leading to micrometric and larger droplets. Theoretical results have been validated with these data, and are used to guide research in the nanometric regime with the expectation of a valid extrapolation. However, the nanometric regime departs from the micrometric regime due to the increased importance of energy dissipation, which raises the temperature in the fluid and alters properties like viscosity, electrical conductivity, and surface tension (M. Gamero-Casta\~{n}o, J. Fluid Mech. 662, 493-513 (2010)). These thermal effects have not been considered either in the modelling or in the analysis of experiments, and must be accounted for in order to develop a fundamental understanding of electrospraying in the nanometric regime. This presentation will describe the experimental demonstration of energy dissipation, as well as ongoing modeling work that takes into account this phenomenon. [Preview Abstract] |
Monday, November 20, 2017 9:05AM - 9:18AM |
F27.00006: The “Saturn-rings” instability: streaming from the equator of a drop in a uniform electric field Petia Vlahovska, Quentin Brosseau Drops in electric fields or flow can develop pointy ends emitting thin threads (tip-streaming). The instability results from destabilization of the interface near a stagnation point of a convergent flow. I will present experimental realization of a streaming due to stagnation line instability. A drop placed in a uniform electric field flattens and develops a sharp edge around the equator, which is the stagnation line of the electrohydrodynamic flow. The flow draws from the rim a thin sheet which destabilizes and sheds fluid threads encircling the drop. Subsequently the fluid rings breakup, due to capillary instability, into droplets. The rim streaming creates visually striking “Saturn-rings” around the equator of a drop. [Preview Abstract] |
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