Review on the physics of electrospray: From electrokinetics to the operating conditions of single and coaxial Taylor cone-jets, and AC electrospray

Dripping, jetting and tip streaming have been studied up to a certain point separately by both fluid mechanics and microfluidics communities, the former focusing on fundamental aspects while the latter on applications. Here, we intend to review this field from a global perspective by considering and linking the two sides of the problem. First, we present the theoretical model used to study interfacial flows arising in droplet-based microfluidics, paying attention to three elements commonly present in applications: viscoelasticity, electric fields and surfactants. We review both classical and current results of the stability of jets affected by these elements. Mechanisms leading to the breakup of jets to produce drops are reviewed as well, including some recent advances in this field. We also consider the relatively scarce theoretical studies on the emergence and stability of tip streaming in open systems. Second, we focus on axisymmetric microfluidic configurations which can operate on the dripping and jetting modes either in a direct (standard) way or via tip streaming. We present the dimensionless parameters characterizing these configurations, the scaling laws which allow predicting the size of the resulting droplets and bubbles, as well as those delimiting the parameter windows where tip streaming can be found. Special attention is paid to electrospray and flow focusing, two of the techniques more frequently used in continuous drop production microfluidics. We aim to connect experimental observations described in this section of topics with fundamental and general aspects described in the first part of the review. This work closes with some prospects at both fundamental and practical levels.

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Dripping, jetting and tip streaming

Dripping, jetting and tip streaming have been studied up to a certain point separately by both fluid mechanics and microfluidics communities, the former focusing on fundamental aspects while the latter on applications. Here, we intend to review this field from a global perspective by considering and linking the two sides of the problem. In the first part, we present the theoretical model used to study interfacial flows arising in droplet-based microfluidics, paying attention to three elements commonly present in applications: viscoelasticity, electric fields and surfactants. We review both classical and current results about the stability of jets affected by these elements. Mechanisms leading to the breakup of jets to produce drops are reviewed as well, including some recent advances in this field. We also consider the relatively scarce theoretical studies on the emergence and stability of tip streaming flows. In the second part of this review, we focus on axisymmetric microfluidic configurations which can operate on the dripping and jetting modes either in a direct (standard) way or via tip streaming. We present the dimensionless parameters characterizing these configurations, the scaling laws which allow predicting the size of the resulting droplets and bubbles, as well as those delimiting the parameter windows where tip streaming can be found. Special attention is paid to electrospray and flow focusing, two of the techniques more frequently used in continuous drop production microfluidics. We aim to connect experimental observations described in this section of topics with fundamental and general aspects described in the first part of the review. This work closes with some prospects at both fundamental and practical levels.

The convective and absolute instability of a viscoelastic liquid jet falling under gravity is examined for axisymmetrical disturbances. We use the upper-convected Maxwell model to provide a mathematical description of the dynamics of a viscoelastic liquid jet. An asymptotic approach, based on the slenderness of the jet, is used to obtain the steady state solutions. By considering traveling wave modes, we derive a dispersion relation relating the frequency to the wavenumber of disturbances which is then solved numerically using the Newton-Raphson method. We show the effect of changing a number of dimensionless parameters, including the Froude number, on convective and absolute instability. In this work, we use a mapping technique developed by Kupfer, Bers, and Ram [“The cusp map in the complex-frequency plane for absolute instabilities,” Phys. Fluids 30, 3075–3082 (1987)] to find the cusp point in the complex frequency plane and its corresponding saddle point (the pinch point) in the complex wavenumber plane for absolute instability. The convective/absolute instability boundary is identified for various parameter regimes.

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Convective and absolute instability of viscoelastic liquid jets in the presence of gravity

Linear stability of confined coaxial jets in the presence of gas velocity oscillations with heat and mass transfer

A three-dimensional temporal linear instability analysis is performed for charged viscoelastic liquid jets moving in an inviscid gas under an axial electric field; the analytical dimensionless dispersion relation is derived in this paper. The viscoelastic fluid described by the Oldroyd-B model is intended to be a Taylor–Melcher leaky dielectric, while the ambient gas is treated as perfectly dielectric. Results show that two local growth rate maxima exist in the axisymmetric mode, and the instability domain can be simply connected or can consist of two separate regions separated by a stable area, depending mainly upon the axial electric field intensity and two viscoelastic parameters considered here, i.e. the time constant ratio and residual stress tension. It is found that the radial electric field has dual effects on the axisymmetric instability and it enhances the asymmetric instability, while the axial electric field affects the asymmetric mode non-monotonically versus different surface charge, and inhibits the axisymmetric mode. The competition between the axisymmetric and asymmetric instabilities reveals that the axial electric field will promote the predominance of asymmetric instability over the axisymmetric mode, which causes the bending motion in most experimental observations. An energy budget is also applied to explain the variation trend in the temporal growth rate versus different radial and axial electric fields.

Temporal instability of charged viscoelastic liquid jets under an axial electric field

Linear stability of confined swirling annular liquid layers in the presence of gas velocity oscillations with heat and mass transfer

The linear temporal instability of a viscoelastic liquid sheet has been studied here, in the presence of gas velocity oscillations. The Floquet theory was applied to solve this problem. More than one unstable region appeared and these regions were divided into the Kelvin–Helmholtz (K–H) and the parametric unstable regions. In the K–H unstable region, the disturbance grew in the form of travelling waves; but in the parametric unstable regions, the disturbance was in the form of standing waves. An increase in oscillation amplitude contributed to the growth of instability in both regions, due to the stronger hydrodynamic force and parametric resonance, respectively; and the parametric unstable regions were more sensitive to the increased amplitude. The main effect of the oscillation frequency was to change the location of the parametric unstable regions. A viscoelastic liquid sheet can behave with greater stability than its Newtonian counterpart in all unstable regions; however, zero shear viscosity, stress relaxation time, and deformation retardation time all affect the parametric regions more dramatically than the K–H unstable regions. The parametric unstable region is more sensitive to viscous dissipation than the K–H unstable regions, resulting in a shift in the leading role between the different unstable regions. The competition between the K–H and parametric unstable regions is discussed in detail here.

Linear instability of viscoelastic planar liquid sheets in the presence of gas velocity oscillations

The invention provides a device for measuring the charge-to-mass ratio of a separate charged-particle, which can measure the charge-to-mass ratio of a separate charge-particle The device is simple in structure and easy to operate Unlike the currently available device whose measuring objects are all charged clusters rather than a separate charged particle, the device of the invention is able to obtain more accurate measuring results The device of the invention comprises a uniform electric field generation device and a grating range measurement system The uniform electric field generation device is used to enable the charge particle to make uniformly accelerated motion in the uniform electric field generated by the uniform electric field generation device; and the grating range measurement system is used to obtain the motion trajectory of the charged particle in the uniform electric field Based on the corresponding relationship between the trajectory of uniformly accelerated motion and the imposed external force, the charge-to-mass ratio of the charged-particle is determined

Luo Xie

Papers

Temporal instability of charged viscoelastic liquid jets under an axial electric field

Linear stability of confined swirling annular liquid layers in the presence of gas velocity oscillations with heat and mass transfer

Linear instability of viscoelastic planar liquid sheets in the presence of gas velocity oscillations

Device for measuring the charge-to-mass ratio of separate charged-particle

Linear analysis and energy budget of viscous liquid jets in both axial and radial electric fields