Drop Breakup Research Articles

ANALYTICAL STUDY OF THE MECHANISM OF DROPLET DEFORMATION AND BREAKUP IN SHEAR FLOWS

The problem of drop deformation and breakup in shear flow represents academic and practical interest and has attracted close attention over the intervening decades. Drop breakup is important for a wide range of engineering and biomedical applications including production and processing of emulsions, aerosols, etc. Although drop breakup operations are widely used in various industries, however, till quite presently there is no unequivocal treatment of the physical mechanism, which causes the fragmentation of dispersions in shear flows. In this paper the principles of constructing a mathematical model, which predicts the evolution of initially spherical droplet in shear flows of viscous liquid over a wide range of flow regimes as well physical parameters of both liquid phases, are considered. A mathematical model is presented that describes the deformation of a single drop suspended in another immiscible liquid under the combined action of three forces, namely, hydrodynamic force, capillary force and dissipative viscous force. The influence of each of these forces on the process of droplet deformation is discussed in the paper.
 The focus of the study is to more deeply analyze the dynamics of droplet deformation in shear flows and the transitional effects associated with current droplet shapes. Particular attention is paid to the analysis of critical conditions for the onset of irreversible deformation of droplets, which leads to their destruction. The deformed droplet is assumed to be in the form of prolate ellipsoid of revolution. The drop deformation is regarded as motion of the centers mass of the half-drops, symmetrical with respect to the drop center.
 The results of numerical calculations for droplet deformation in shear flows in comparison with experimental data of other authors are presented. A simple criterion for destruction of droplets in shear flows has been obtained. The results of the analysis confirm the reliability of the model and the competency of the assumption made. The model is able to predict the nature of droplet deformation and the conditions for their destruction in shear flows with known operating parameters with a greater degree of accuracy than the existing empirical relationships.

Numerical simulation of coalescence and break-up of drops in shear flow based on the meshless localized radial basis function method

In the present paper, the meshless localized radial basis function (RBF) is proposed for simulating of two-phase incompressible viscous flow. Due to the velocity of the shear flow is very low, the fluid can modeled by Stokes equations. For more convenience the primitive variables, i.e., pressure and velocity components of the Stokes equations are transformed into stream function formulation. The interface of the fluid system is modeled by using Cahn-Hilliard equation. The spatial terms of the governing equations are discretized numerically by using the RBF method. The temporal term is integrated by using fully implicit Euler method. The nonlinear terms of Cahn-Hilliard equation is linearized using the Picard iteration. The proposed method is applied to simulate coalescence and break-up of drops in shear flow. The numerical results show that the deformation of the interface can be modeled without any difficulties.

Transformation of single drop breakup from binary to ternary and multiple in turbulent jet flows

By releasing liquid drops in turbulent jet flows, we investigated the transformation of single drop breakup from binary to ternary and multiple. Silicone oil and deionized water were the dispersed phase and continuous phase, respectively. The probability of binary, ternary, and multiple breakup of oil drops in jet flows is a function of the jet Reynolds number. To address the underlying mechanisms of this transformation of drop breakup, we performed two-dimensional particle image velocimetry (PIV) experiments of single-phase jet flows. With the combination of drop breakup phenomenon and two-dimensional PIV results in a single-phase flow field, these transformation conditions can be estimated: the capillary number ranges from 0.17 to 0.27, and the Weber number ranges from 55 to 111.

Benchmark solutions for flows with rheologically complex interfaces

Complex fluid–fluid interfaces determine for an outsized part the macroscopic material properties of foams and emulsions that appear in applications like food, materials processing and consumer care products. As a step towards predicting these properties, a 2D axisymmetric and a 3D finite element model are developed for simulating the dynamics of one Newtonian drop by a Newtonian matrix fluid with a rheologically complex sharp interface in between. Interfaces with constant interfacial surface tension and with viscous, elastic and viscoelastic extra interfacial stresses are considered. The model has been validated by means of the tactic of manufactured solutions and by comparison with results from other studies using different discretisation methods. Higher-order convergence in space and time is obtained, demonstrating correct implementation of our numerical methods. Benchmark solutions for a drop with a Kelvin–Voigt interface under simple shear flow are provided. Compared to a viscous interface, the drop deformation becomes smaller and therefore the drop becomes less oriented within the direction of flow if interfacial elasticity is added. Fluid–fluid interfaces play a key role within the processing and functioning of multicomponent materials. samples of such materials are emulsions, where fluid drops of 1 phase are dispersed into another fluid phase immiscibly. Dispersion are often useful for designing material structures to e.g. gain synergy of properties. Emulsions are partly for this reason utilized in a spread of applications like in food, paint, cosmetics, materials processing (e.g. polymer blends) and within the industry , but they also appear in nature and biology. The interfacial area to volume ratio in emulsions is comparatively large, since albeit the drops in e.g. polymer blends are small in size (about tens of); they're present in large quantities. Therefore, the interfacial properties determine for an outsized part the general macroscopic material behaviour. When applying flow to an emulsion, the structure is continuously developing through the consecutive and simultaneous deformation, break-up and coalescence of drops interacting with one another and therefore the surrounding fluid during a complex manner. Curvature changes of the interface are opposed or helped by interfacial surface tension between the phases. Surfactants that are often added as stabilisers to the mixture and adsorb at the interface, lower the interfacial surface tension to hamper or hinder coalescence Hence, surfactants are required to get stable emulsions, but they also further complicate the behaviour of the interface. Surfactant concentration gradients within the interface cause spatially varying Marangoni stresses. Surfactant transport within the interface or between the interface and therefore the bulk introduces non-trivial time scales. Besides, interactions within the interface thanks to a big microstructure cause extra and deviatoric interfacial stresses and possibly rheologically complex behaviour of the interface, These complex interfaces can behave intrinsically viscoelastic.

Statistical quantification of drop deformation behaviour and breakup initiation time in high speed air flow

Statistical quantification of drop deformation behaviour and breakup initiation time in high speed air flow

Effects of surface topography on low Reynolds number droplet/bubble flow through a constricted passage

This paper is an attempt to study the effects of surface topography on the flow of a droplet (or a bubble) in a low Reynolds number flow regime. Multiphase flows through a constricted passage find many interesting applications in chemistry and biology. The main parameters that determine the flow properties such as flow rate and pressure drop and govern the complex multiphase phenomena such as drop coalescence and breakup in a straight channel flow are the viscosity ratio, droplet size, and ratio of the viscous forces to the surface tension forces (denoted by the capillary number). However, in flow through a constricted passage, in addition to the above-mentioned parameters, various other geometric parameters such as constriction ratio, length, shape of the constriction, phase angle, and spacing between the constrictions also start playing an important role. Most of the studies done on the problem of drop flow through a constricted passage have aimed to understand the role of physical parameters, with some studies extending their analysis to understand the variation of one or two geometric parameters. However, no study could be found, which explicitly evaluates the role of surface topography. An attempt has been made to unify the current literature as well as analyze the effect of the geometric parameters by understanding the physics and mechanisms involved. The non-dimensional numbers that govern this problem are then identified using the scaling analysis.

Experimental investigation on single drop breakage in two-stream impinging microchannels

Experimental study on drop breakage is carried out in the microchannels utilizing head-on impingement configuration by observing a single drop breakup process. In this study, the breakage of oil drops with a diameter ranging from 30 to 200 μm is investigated in the vicinity of flows impingement region by using high-speed photography at varied flow rate conditions. The most prominent phenomenon of the single drop breakup in the two streams impinging flow field is that the drop tends to break into multiple fragments. The breakage time and the number of daughter drops in the resulting population are statistically analysed and found to be highly dependent on the mother drop size and energy dissipation rate. Two different micro-system geometries, the 600–600 system and the 600–300 system, are compared to evaluate the advantages and disadvantages of swirl flow developed due to the off-axis layout of inlet channels in the 600–300 system. The results show that swirl flow establishes a low-pressure area acting as the dead zone, where a drop can be trapped and then drastically stretched to breakup. Compared with the 600–600 system, the detrimental effect of swirl flow inside the 600–300 system on increasing the breakage time can be offset by a much greater amount of daughter drops generated. In general, the 600–300 system performs more effectively than the 600–600 system because of the less isotropic flow feature. And this superiority is more distinct when the energy dissipation rate is higher.

The Role of Concentration on Drop Formation and Breakup of Collagen, Fibrinogen, and Thrombin Solutions during Inkjet Bioprinting.

The influence of protein concentration on drop formation and breakup of aqueous solutions of fibrous proteins collagen and fibrinogen and globular protein thrombin in different concentration regimes has been investigated during drop-on-demand (DOD) inkjet printing. The capillary-driven thinning and breakup of dilute collagen, fibrinogen, and thrombin solutions, the solutions in which protein molecules are far away from each other, are predominantly resisted by inertial force. Although the capillary-driven thinning and breakup of semidilute unentangled collagen and fibrinogen solutions, the solutions in which protein molecules begin to interpenetrate each other, are predominantly resisted by inertial force on the initial onset of necking, the breakup of droplets is delayed because of the resistance of elastic force. The resistance of viscous force to the necking and breakup of both the dilute and semidilute unentangled protein solutions is negligible. Aggregates or subvisible particles (between 1 and 100 μm) constantly disrupt the formation of droplets for the semidilute unentangled protein solutions, even when their inverse Ohnesorge number (Z) is within the printability range of 4 ≤ Z ≤ 14. Although aggregates are present in the dilute protein solutions, they do not disrupt the formation of droplets.

Numerical study of drop behavior in a pore space

Deformation and breakup of a liquid drop immersed in another immiscible liquid and flowing through a single pore has been studied numerically using a conservative phase-field lattice Boltzmann method. Several benchmarks were conducted to validate the code, including the recovery of Laplace pressure, the layered flow of two immiscible liquids, and the implementation of wetting boundary conditions on a curved surface. Gravity-driven motion of a drop through the pore space was qualitatively compared to the available experimental results. Quantitative assessment of the pressure field across the interface of the moving and deforming drop was performed. Our results show that high Weber number due to low surface tension and low Reynolds number due to low velocity of the continuous liquid promote drop breakage. More viscous drops break easier than less viscous drops. We present the phase charts (Weber vs capillary number) and the critical conditions (Weber as a function of Reynolds number) of drop breakage.

A lattice Boltzmann modeling of viscoelastic drops’ deformation and breakup in simple shear flows

The deformation and breakup of viscoelastic drops in simple shear flows of Newtonian liquids are studied numerically. Our three-dimensional numerical scheme, extended from our previous two-dimensional algorithm, employs a diffusive-interface lattice Boltzmann method together with a lattice advection–diffusion scheme, the former to model the macroscopic hydrodynamic equations for multiphase fluids and the latter to describe the polymer dynamics modeled by the Oldroyd-B constitutive model. A block-structured adaptive mesh refinement technique is implemented to reduce the computational cost. The multiphase model is validated by a simulation of Newtonian drop deformation and breakup under an unconfined steady shear, while the coupled algorithm is validated by simulating viscoelastic drop deformation in the shear flow of a Newtonian matrix. The results agree with the available numerical and experimental results from the literature. We quantify the drop response by changing the polymer relaxation time λ and the concentration of the polymer c. The viscoelasticity in the drop phase suppresses the drop deformation, and the steady-state drop deformation parameter D exhibits a non-monotonic behavior with the increase in Deborah number De (increase in λ) at a fixed capillary number Ca. This is explained by the two distribution modes of the polymeric elastic stresses that depend on the polymer relaxation time. As the concentration of the polymer c increases, the degree of suppression of deformation becomes stronger and the transient result of D displays an overshoot. The critical capillary number for unconfined drop breakup increases due to the inhibitive effects of viscoelasticity. Different distribution modes of elastic stresses are reported for different De.

Asymmetric splash and breakup of drops impacting on cylindrical superhydrophobic surfaces

Drop splash and breakup on cylindrical surfaces play an important role in a wide variety of industrial applications. In this work, water drops with a wide range of impact velocities (1.4 m/s–4.5 m/s) and cylindrical stainless steels with different diameters (1 mm–20 mm) are employed to investigate the asymmetric splash and breakup characteristics of drops impacting on cylindrical superhydrophobic surfaces. We identify two interesting phenomena, asymmetric splash and converging breakup. The splash behavior is found to be asymmetric in different directions, and the drops preferentially splash in the axial direction. Fundamentally, we propose two disparate splash thresholds, referring to the Weber number We and the diameter ratio D* = D/D0, in the azimuthal and axial directions, respectively. The converging breakup is caused by the much more rapid converging of the liquid rim in the axial direction than in the azimuthal direction. The aspect ratio βzmax/βxmax, governing the converging breakup, increases with We and decreases with D*. Fortuitously, the splashing angle θ is demonstrated to only depend on D* rather than We, and the relational expression of θ and D* is provided. Ultimately, we put forward universal relations between the mean diameter and velocity of secondary droplets, resulting from the converging breakup, and the dimensionless parameter We/D*. The results of this work are expected to provide valuable insights into anti-icing and microfluidics fields.

Drop breakup in a symmetric T-junction microchannel under electric field

In the present study, the breakup process of drop in a symmetric T-junction microchannel is numerically investigated. A novel method base on imposing an electric field in the branches of the T-junction is proposed to improve the breakup process of the drop. The results are apprised by the previously published experimental and numerical research in the literature. The comparison depicts that the current results are in good agreement with the previous studies. The effects of the non-dimensional drop length (L*), electric capillary number ( $${\text{Ca}}_{{\text{e}}}$$ ), and permittivity ratio ( $$\varepsilon^{*}$$ ) are studied in detail. The results reveal that using an electric field, the mother drop splits faster in the presence of an electric field when compared with the case without the electric field. It is also concluded that the effect of electrical field is more highlighted when drops are smaller. Furthermore, the breakup time of the drop decreases by increasing the electric capillary number and permittivity ratio.

Experimental Research of Gasdynamic Liquid Drops Breakup in the Supersonic Flow with an Oblique Shock Wave

This paper is devoted to understanding gasdynamic liquid drops breakup in a supersonic flow with presence of an oblique shock wave. An experimental facility, diagnostic tools and an experimental methodology are presented as well as numerical simulations results. Computations and experiments were used to get flow parameters in the duct with supersonic flow at Mach numbers 2.0, 2.5, and 3.0. The droplets were made to interact with a single oblique shock wave generated by a wedge in the test section. Experimental data are obtained for the change in diameter of the droplets and the change in speed of droplets in a supersonic flow at the three Mach numbers. The data are presented for an initial Weber number over the range of 16–115. It is shown that the mass loss rate of droplets are quadratically related to the Weber number, irrespective of the presence of oblique shock.

Influence of the trap potential waveform on surface oscillation and breakup of a levitated charged drop

A charged droplet can be electrodynamically levitated in air using a quadrupole trap by typically applying a sinusoidal electric field. When a charged drop is levitated, it exhibits surface oscillations simultaneously building charge density due to continuous evaporation and subsequently undergoes breakup due to Rayleigh instability. In this work, we examined large-amplitude surface oscillations of a sub-Rayleigh charged drop and its subsequent breakup, levitated by various applied signals such as sine, square, and ramp waveforms at various imposed frequencies, using high-speed imaging (recorded at 100 000–130 000 frames per second). It is observed that the drop surface oscillates in a sphere–prolate–sphere–oblate mode and seldom in a sphere–prolate-sphere mode depending on the intricate interplay of various forces due to charge(q), the intensity of the applied field (Λ), and the shift of the droplet from the geometric center of the trap (zshift). The Fast Fourier Transformation analysis shows that the droplet oscillates with the forced frequency irrespective of the type of the applied waveform. While in the sinusoidal case, the nonlinearities are significant, in the square and ramp potentials, there is an admittance of all the harmonic frequencies of the applied potential. Interestingly, the breakup characteristics of a critically charged droplet are found to be unaffected by the type of the applied waveform. The experimental observations are validated with an analytical theory as well as with the Boundary Integral simulations in the potential flow limit, and the results are found to be in a reasonable agreement.

Interfacial tension and acoustofluidics: some connections, instabilities, experimental results, and theory

It is timely to examine early acoustofluidic studies involving surface tension phenomena. The dynamics of fluid cylinders and the Plateau-Maxwell-Rayleigh interfacial instability have been reviewed [P. L. Marston, Phys. Fluids 29, 029101 (2017)]. Here, some related acoustofluidic experiments on liquid cylinders are noted [S. F. Morse et al., Phys. Fluids 8, 3 (1996); M. J. Marr-Lyon et al., Phys. Rev. Lett. 86, 2293 (2001)]. Those were after modulated radiation pressure investigations of the shape dynamics of levitated drops and bubbles [P. L. Marston, J. Quant. Spectrosc. Radiat. Transfer 254, 107226 (2020)]. Especially noteworthy are the subtleties of acoustically trapping and deforming bubbles in water larger than the size for monopole resonance [T. J. Asaki, P. L. Marston, and E. H. Trinh, J. Acoust. Soc. Am. 93, 706 (1993)]. That ability facilitated a series of measurements of bubble interfacial dynamics and shape [Asaki et al., J. Acoust. Soc. Am. (1994-1997); J. Fluid Mech. (1995); Phys. Rev. Lett. (1995)]. A related discussion of the quadrupole projection of the radiation stress is noteworthy [P. L. Marston, Phys. Rev. E 100, 057001 (2019)] along with early publications reporting the break-up of drops and bubbles in water through the application of modulated acoustic radiation forces.

Experimental study on drop breakup time and breakup rate with drop swarms in a stirred tank

AbstractThe direct experimental data for breakup parameters of drop breakup time, multiple breakage, and breakup rate are urgently required to understand drop breakup phenomena. In this regard, drop breakup experiments were carried out in a stirred tank using a high‐speed online camera. The influences of the rotating speed, interfacial tension, and drop viscosity on the above breakup parameters were then quantitatively investigated. An mechanism correlation for the breakup time is proposed and is further verified by comparing with the results of Solsvik and Jakobsen (Chem Eng Sci, 2015;131:219‐234). The percentage of multiple breakage comparing to binary breakup was statistically counted. The results indicated that the dimensionless drop diameter η = d/dmax can be adopted to characterize the proportion of binary breakup. Finally, the breakup rate was experimentally measured and the breakup probability was calculated using the inverse method.

Experimental Methods for Measuring the Breakup Frequency in Turbulent Emulsification: A Critical Review

The growing interest in using population balance modeling to describe emulsification processes has spurred an interest in experimentally measuring the breakup frequency. This contribution classifies, compares, and critically reviews the different methods that have been suggested for measuring the breakup frequency, applicable to emulsification devices. Two major approaches can be seen in previous studies. The first is ‘single drop breakup experiment’-based studies, which estimate the breakup frequency by observing the fate of individual drops. The second approach involves ‘emulsification experiment’-based studies, which combine measured drop-size distributions with assumptions to allow for estimations of the breakup frequency. This second approach can be further subdivided in three types: Parametric determination, inverse self-similarity-based methods, and direct back-calculation methods. Each of these methods are reviewed in terms of their implementation, reliability, and validity. Suggestions of methodological considerations for future studies are given for each class, together with more general suggestions for further investigations. The overall objective is to provide emulsification researchers with background information when choosing which method to use for measuring the breakup frequency and with support when setting up experiments and data evaluation procedures.

Simulation of drop motion and breakup in narrow pores

We used a boundary-integral algorithm to simulate drops passing through narrow pores, with three possible outcomes: passage without breaking, breakup due to contact with a bifurcation or corner, and breakup due to elongation. Smaller drops with low capillary numbers and high viscosities are more likely to go through the pores without breaking, larger drops are more prone to hit a pore bifurcation and break, and drops with large capillary numbers and same or lower viscosities than the bulk fluid are more likely to experience elongation and breakup. Pore geometry also has a strong effect, with relatively little breakup when there is no bifurcation. Finally, the post-pore size distribution of droplet sizes is relatively broad when the pre-pore size of the parent drops is large, but the post-pore size distribution is narrow for smaller parent drops (due to little or no breakup). These results may help guide emulsification processes.

Approach and breakup of Taylor bubble and Taylor drop in a Hele-Shaw cell

The collision dynamics of a Taylor drop and a Taylor bubble is investigated in an immiscible surrounding liquid. The interaction of both the fluidic entities is studied using experiments and simulation in a vertically aligned Hele-Shaw cell. The steady rise of the bubble and fall of the drop are followed by a deceleration regime where their velocity has decreased due to the pressure imposed by the leading interfaces, indicated by the change in the curvature of their tip. Subsequently, the rapid outward expansion of the bubble has caused the swelling of the tip of the drop. The drop swell has then grown exponentially similar to Rayleigh–Taylor instability and resulted in a split of the bubble into two volumes.

On the validity of different methods to estimate breakup frequency from single drop experiments

Single drop breakup visualizations are the golden standard for experimentally measuring breakup frequency, g, in turbulent flows. There is a growing demand for empirically obtained breakup frequencies, for population balance equation (PBE) based predictive modelling and for comparing to theoretical suggestions. However, five different methods to estimate g from a breakup visualization can be found in previous investigations, many of them contradictory. This study uses analytical and numerical methods to show that only two of the five suggestions result in estimates that are valid (where ‘valid’ means that the breakup frequencies are meaningful in a PBE setting). This case is also used to discuss the difference between the stochastic one drop deformation/breakup view of turbulent fragmentation and the deterministic number density based PBE description, arguing that some aspects of the breakup process will be challenging to describe within the PBE framework, regardless of the choice of breakup frequency model.