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 aim of this paper is to characterize large-scale instabilities during the primary breakup process in liquid centered coaxial air-water jets. The interest here is to investigate the role of annular air swirl on such instabilities. A coaxial airblast atomizer that incorporates an axial swirler is considered for this purpose. The atomizer was operated in a wide range of the Weber number, Weg(80–958), momentum flux ratio, M(1–26), and air swirl strength, S(0–1.6). High-speed shadowgraphic images of the primary jet breakup process were recorded. Proper orthogonal decomposition (POD) analysis of the time-resolved images was performed for each operating condition. The 2nd and 3rd POD modes depicted some universal spatial features which refer to large scale instabilities. Three different dominant large scale instabilities were identified, viz., jet flapping, wavy breakup, and explosive breakup, for the entire range of the injector operating condition either in the presence or absence of air swirl. It was found that jet flapping (referred to as the lateral oscillation of the tail end of the jet) is the dominant mode of jet instability for a lower range of M, while explosive jet breakup (referred to as the radial expansion of the jet) governs jet breakup unsteadiness for a higher range of M. The wavy or sinuous mode of breakup is a secondary mechanism relevant under low M conditions. The mechanisms of large scale instabilities and the role of air swirl in that context are explained based on the Fourier analysis of the temporal coefficients of the corresponding POD modes.

Large scale instabilities in coaxial air-water jets with annular air swirl

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

Theoretical breakup model in the planar liquid sheets exposed to high-speed gas and droplet size prediction

This paper investigates the axisymmetric instability of a viscoelastic compound jet, for which the constitutive relation is described by the Oldroyd B model. It is found that a viscoelastic compound jet is more unstable than a Newtonian compound jet, regardless of whether the viscoelastic compound jet is inner-Newtonian-outer-viscoelastic, inner-viscoelastic-outer-Newtonian, or fully viscoelastic. It is also found that an increase in the stress relaxation time of the inner or outer fluid renders the jet more unstable, while an increase in the time constant ratio makes the jet less unstable. An analysis of the energy budget of the destabilization process is performed, in which a formulation using the relative rate of change of energy is adopted. The formulation is observed to provide a quantitative analysis of the contribution of each physical factor (e.g., release of surface energy and viscous dissipation) to the temporal growth rate. The energy analysis reveals the mechanisms of various trends in the temporal growth rate, including not only how the growth rate changes with the parameters, but also how the growth rate changes with the wavenumber. The phenomenon of the dispersion relation presenting two local maxima, which occurred in previous research, is explained by the present energy analysis.

Instability of viscoelastic compound jets

The instability of gas-surrounded Rayleigh viscous jets is investigated analytically and numerically in this paper. Theoretical analysis is based on a second-order perturbation expansion for capillary jets with surface disturbances, while the axisymmetric two-dimensional, two-phase simulation is conducted by applying the Gerris code for jets subjected to velocity disturbances. The relation between the initial surface and velocity disturbance amplitude was obtained according to the derivation of Moallemi et al. [“Breakup of capillary jets with different disturbances,” Phys. Fluids 28, 012101 (2016)], and the breakup lengths resulting from these two disturbances agree well. Analytical and numerical breakup profiles also coincide satisfactorily, except in the vicinity of the breakup point, which shrinks forcefully. The effects of various parameters (i.e., oscillation frequency, Reynolds number, Weber number, and gas-to-liquid density ratio) have also been examined by comparing spatial growth rate, second-ord...

Instability of gas-surrounded Rayleigh viscous jets: Weakly nonlinear analysis and numerical simulation

This paper investigates the spatial instability of a double-layer viscous liquid sheet moving in a stationary gas medium. A linear stability analysis is conducted and two situations are considered, an inviscid-gas situation and a viscous-gas situation. In the inviscid-gas situation, the basic state of the entire gas phase is stationary and the analytical dispersion relation is derived. Similar to single-layer sheets, the instability of double-layer sheets presents two unstable modes, the sinuous and the varicose modes. However, the result of the base-case double-layer sheet indicates that the cutoff wavenumber of the dispersion curve is larger than that of a single-layer sheet. A decomposition of the growth rate is performed and the result shows that for small wavenumbers, the surface tension of all three interfaces and the aerodynamic forces of both the lower and upper gases contribute significantly to the unstable growth rate. In contrast, for large wavenumbers the major contribution to the unstable growth rate is only the surface tension of the upper interface and the aerodynamic force of the upper gas. In the viscous-gas situation, although the majority of the gas phase is stationary, gas boundary layers exist at the vicinity of the moving liquid sheet, and the stability problem is solved by a spectral collocation method. Compared with the inviscid-gas solution, the growth rate at large wavenumber is significantly suppressed. The decomposition of growth rate indicates that all the aerodynamic and surface tension terms behave consistently throughout the entire unstable wavenumber range. The effects of various parameters are discussed. In addition, the effect of gas viscosity and the gas velocity profile is investigated separately, and the results indicate that both factors affect the maximum growth rate and the dominant wavenumber, although the effect of the gas velocity profile is stronger than that of the gas viscosity.

Spatial instability of viscous double-layer liquid sheets

Linear instability of compound liquid threads in the presence of surfactant is investigated. The limitation of one-dimensional approximation in previous work is removed so both unstable modes can be captured. The squeezing mode is much more sensitive to surfactant effects than the stretching mode.

Linear instability of compound liquid threads in the presence of surfactant

This paper investigates the temporal instability of an eccentric compound liquid thread. Results of linear stability are obtained for a typical case in the context of compound threads in microencapsulation. It is found that the disturbance growth rate of an eccentric compound liquid thread is close to that of the corresponding concentric one, in terms of both the maximum growth rate and the dominant wavenumber. Furthermore, linear stability results over a wide parameter range are obtained and the conclusion is basically unchanged. Energy balance of the destabilization process is analyzed to explain the mechanism of instability, and it is found that although the disturbance growth rate of an eccentric compound thread is close to that of the corresponding concentric thread, their energy balances are distinctively different. The disturbance interface shape and disturbance velocity distributions are plotted. It is found that the behavior of the disturbance velocity in the cross section plane is different from...

Han-yu Ye

Papers

Instability of viscoelastic compound jets

Instability of gas-surrounded Rayleigh viscous jets: Weakly nonlinear analysis and numerical simulation

Spatial instability of viscous double-layer liquid sheets

Linear instability of compound liquid threads in the presence of surfactant

Instability of eccentric compound threads