Resulting Drop Size Research Articles

Statistics of drops generated from ensembles of randomly corrugated ligaments

The size of drops generated by the capillary-driven disintegration of liquid ligaments plays a fundamental role in several important natural phenomena, ranging from heat and mass transfer at the ocean-atmosphere interface to pathogen transmission. The inherent nonlinearity of the equations governing the ligament destabilization leads to significant differences in the resulting drop sizes, owing to small fluctuations in the myriad initial conditions. Previous experiments and simulations reveal a variety of drop size distributions, corresponding to competing underlying physical interpretations. Here, we perform numerical simulations of individual ligaments, the deterministic breakup of which is triggered by random initial surface corrugations. The simulations are grouped in a large ensemble, each corresponding to a random initial configuration. The resulting probability distributions reveal three stable drop sizes, generated via a sequence of two distinct stages of breakup. Four different distributions are tested, volume-based Poisson, Gaussian, Gamma, and Log-Normal. Depending on the time, range of droplet sizes and criteria for success, each distribution has successes and failures. However, the Log-Normal distribution roughly describes the data when fitting both the primary peak and the tail of the distribution while the number of droplets generated is the highest, while the Gamma and Log-Normal distributions perform equally well when fitting the tail. The study demonstrates a precisely controllable and reproducible framework, which can be employed to investigate the mechanisms responsible for the polydispersity of drop sizes found in complex fluid fragmentation scenarios.

Dynamics of jet breakup and the resultant drop size distribution-effect of nozzle size and impingement velocity

Dynamics of jet breakup and the resultant drop size distribution-effect of nozzle size and impingement velocity

Subgrid scale modeling of droplet bag breakup in VOF simulations

The mesh-dependency of the breakup of liquid films, including their breakup length scales and resulting drop size distributions, has long been an obstacle inhibiting the computational modeling of large-scale spray systems. With the aim of overcoming this barrier, this work presents a framework for the prediction and modeling of subgrid-thickness liquid film formation and breakup within two-phase simulations using the volume of fluid method. A two-plane interface reconstruction is used to capture the development of liquid films as their thickness decreases below the mesh size. The breakup of the film is predicted with a semi-analytical model that incorporates the film geometry captured through the two-plane reconstruction. The framework is validated against experiments of the bag breakup of a liquid drop at We=13.8 through the comparison of the resulting drop size and velocity distributions. The generated distributions show good agreement with experimental results for drop resolutions as low as 25.6 cells across the initial diameter. The presented framework enables these drop breakup simulations to be performed at a computational cost three orders of magnitude lower than the cost of simulations utilizing adaptive mesh refinement.

PH-dependent electrostatic interactions between enzymes and nanoparticles in Pickering emulsions – Influence on activity and droplet size

Pickering emulsions (PE) are liquid-liquid systems that are stabilized by solid (nano)particles at the fluid interface. They offer higher stability, easier separation and lower toxicity compared to classical emulsions stabilized by surfactants. Common applications range from food science to drug delivery. In the last decade they have become of more interest in the field of multiphasic biocatalysis. First, this study aims to present the influence of pH, salt strength and particle charge on enzyme activity. The different behavior of two lipases (CaLA and CRL) is shown. While the activity optimum of CaLA changed from pH 6.5 to pH 5 by applying particles with negative instead of positive surface charge, the CRL activity optimum stayed at pH 5–5.5. This enables particle charge as an additional parameter to optimize biocatalytic reactions in PEs. Second, the resulting drop sizes were measured to elucidate further interactions between the enzymes and particles in PEs. Drop sizes in PEs prepared with CaLA were not influenced by pH, but increased for positively and decreased for negatively charged particles upon the addition of CaLA. Electrostatic attraction between particles and CRL increased the droplet diameter from 10 μm up to 30 μm and therefore destabilized the PE for both particle types.

High-pressure homogenizer valve design modifications allowing intensified drop breakup without increasing power consumption. I. Optimization of current design-principle

This study uses a model-based design approach (CFD coupled to well-established emulsification correlations) to investigate how to choose the valve dimensions of a high-pressure homogenizer so as to achieve intensified drop breakup without increasing the power consumption. Results show how design modifications influence the thermodynamic efficiency of the homogenizer via two effects, a friction factor and a factor related to how high a dissipation rate of turbulent kinetic energy that the design delivers in the centre of the jet. By simple design modifications, thermodynamic efficiency can be increased by 4 % (compared to a representative contemporary valve design) by decreasing the inlet chamber angle, and an additional 5 % by carefully adjusting the outlet chamber angles so as to ensure that the jet exits the gap free of the wall, but then bends and re-attaches to the wall further downstream. The modifications are predicted to allow for achieving the same resulting drop size but with a 17 % lower power draw, compared to a standard contemporary valve, or alternatively a smaller resulting drop diameter at constant power draw.

Open-source pneumatic pressure pump for drop-based microfluidic flow controls

An open-source pneumatic pressure pump is engineered for driving fluid flow in a microfluidic device. It is designed to be a cost-effective and customizable alternative to commercial systems. The pneumatic pressure pump utilizes a single open-source microcontroller to control four dual-valve pressure regulators. The control scheme is written in the Arduino development environment and the user interface is written in Python. The pump was used to pressurize water and a fluorinated oil that have similar viscosities. The pump can accurately control pressures to a resolution of less than 0.02 psig with rapid response times of less than one second, overshoot of desired pressures by less than 30%, and setting response times of less than two seconds. The pump was also validated in its ability to produce water-in-oil drops using a drop-making microfluidic device. The resultant drop size scaled as expected with the pressures applied to the emulsion phases. The pump is the first custom-made dual-valve regulator that is used to precisely control fluid flow in a microfluidic device. The presented design is an advancement towards making more fully open-source pneumatic pressure pumps for controlling flow in microfluidic devices.

Effect of surfactants and interfacial rheology on equilibrium drop size in turbulent liquid-liquid dispersions

Surfactants are often required to stabilize liquid-liquid dispersions produced by high shear mixers. Due to the high power input, drops are deformed rapidly in the dispersion zone so the dynamic interfacial properties governed by the surfactant adsorption rate can have a significant impact on the resulting drop size. The objective of this work is to develop a fundamental link between surfactant adsorption dynamics, interfacial properties, and turbulent emulsification processes. To ensure constant bulk surfactant concentration during dispersion, equilibrium drop size for dilute dispersions produced by a batch rotor-stator mixer were studied. Silicone oils of various viscosity were dispersed in aqueous nonionic surfactant solutions. Drop size distributions (DSD) were measured via a video microscopy/automated image analysis technique. Equilibrium interfacial tension was measured via a pendant drop technique, as a function of surfactant concentration. The dynamic surface tension was similarly measured. The data were fit to the Langmuir adsorption isotherm and the long-times approximation to the Ward – Tordai equation and the adsorption parameters and surfactant diffusivities so obtained were employed, with an estimate of the drop deformation timescale, to estimate the surface dilational modulus (Esd) or Marangoni stress acting on the drop’ surface due to interfacial tension gradients. Trends observed in the measured equilibrium mean drop size and DSD are explained in terms of the interfacial and rheological properties. Below the CMC, Esd peaks and the drop size increases with bulk surfactant concentration, despite a decrease in equilibrium interfacial tension. Above the CMC, Marangoni stresses are small but the presence of the surfactant still modifies the rheology of the interface, increasing the effective viscosity of the drops. A comprehensive set of mechanistic models for drop size in turbulent flows, based on Kolmogorov-Hinze theory, was developed and modified to partially account for the effect of surfactants via an appropriately defined effective viscosity. The approach allows integration of surfactant phenomena into widely accepted correlations for drop size in surfactant free systems.

Cavitation-induced microjets tuned by channels with alternating wettability patterns

A laser pulse focused near the closed end of a glass capillary partially filled with water creates a vapor bubble and an associated pressure wave. The pressure wave travels through the liquid toward the meniscus where it is reflected, creating a fast, focused microjet. In this study, we selectively coat the hydrophilic glass capillaries with hydrophobic strips along the capillary. The result after filling the capillary is a static meniscus which has a curvature markedly different than an unmodified capillary. This tilting asymmetry in the static meniscus alters the trajectory of the ensuing jets. The hydrophobic strips also influence the advancing contact line and receding contact line as the vapor bubble expands and collapses. We present thirteen different permutations of this system which includes three geometries and four coating schemes. The combination of geometry and coatings influences the jet breakup, the resulting drop size distribution, the trajectory of the jet tip, and the consistency of jet characteristics across trials. The inclusion of hydrophobic strips promotes jetting in line with the channel axis, with the most effective arrangement dependent on channel size.

Towards a Standard Method for Estimating Fragmentation Rates in Emulsification Experiments

The fragmentation rate function connects the fundamental drop breakup process with the resulting drop size distribution and is central to understanding or modeling emulsification processes. There is a large interest in being able to reliably measure it from an emulsification experiment, both for generating data for validating theoretical fragmentation rate function suggestions and as a tool for studying emulsification processes. Consequently, several methods have been suggested for measuring fragmentation rates based on emulsion experiments. Typically, each study suggests a new method that is rarely used again. The lack of an agreement on a standard method has become a substantial challenge. This contribution critically and systematically analyses four influential suggestions of how to measure fragmentation rate in terms of validity, reliability, and sensitivity to method assumptions. The back-calculation method is identified as the most promising—high reliability and low sensitivity to assumption—whereas performing a non-linear regression on a parameterized model (as commonly suggested) is unsuitable due to its high sensitivity. The simplistic zero-order method is identified as an interesting supplemental tool that could be used for qualitative comparisons but not for quantification.

Active control of jet breakup and droplet formation using temperature modulation

Different regimes of temperature modulated breakup were studied using a slender jet model. The instability is induced through capillary and Marangoni stresses and can be used to control droplet formation in terms of intact length and resultant drop size distribution, which is otherwise irregular due to the inevitable presence of background noise. When thermal modulation is weak, the surface tension gradient forces act only as a trigger and curvature-gradient forces soon take over and grow exponentially downstream of the jet due to inertio-capillary growth. When thermal modulation is strong, the surface tension gradient forces not only act as a trigger, but remain significant till breakup.

Experimental investigation on the influence of system pressure on resulting spray quality and jet breakup applying pressure adapted twin-fluid nozzles

The present work aims for the isolated investigation of the influence of system pressure on spray quality of twin-fluid atomizers. An approach of pressure adapted nozzles was applied, allowing for constant mass flows, gas-to-liquid ratio as well as fluid velocities at the nozzle orifice independent of system pressure. Two Newtonian liquids featuring viscosities of 1 and 100 mPa · s were used, varying the system pressure from 1 to 16 bar for gas velocities of 60, 80 and 100 m·s−1. A phase doppler analyzer was applied for measurement of resulting drop size and velocity. Primary breakup morphology was detected by a high-speed camera. Two regions with different dependencies of spray quality on system pressure were identified. Applying pressure adapted nozzles while increasing system pressure, first results in a decrease of droplet size followed by an increase. A maximum of the dynamic pressure of the gas phase was determined at minimum droplet size, which is explained based on the theory of a free jet. The observations are underlined by images of the high-speed camera. Here, a change in breakup morphology from fiber type to a mixture of fiber type and non-axisymmetric Rayleigh type breakup at high system pressure was observed.

Secondary Breakup of Drops

Secondary atomization of droplets generated from primary atomization is observed in high-speed flows. In natural scenarios, falling raindrops undergo aerodynamic breakup that modifies the resulting drop size distribution on the ground. In this article, we review some aspects of the drop breakup mechanisms, initial deformation, drag characteristics, and time scales of breakup. We also review some of the secondary atomization models, such as TAB and DDB, proposed in the literature. We discuss the role of new numerical algorithms for two-phase flow simulations in providing insights into the exact physical mechanisms involved during drop breakup.

Low-pressure twin-fluid atomization: Effect of mixing process on spray formation

The present work comparably examines four different twin-fluid atomizers operated under the same operating conditions. Spray formation was examined by several approaches. The internal flow pattern was estimated using a simplified analytical approach, and the results were supported by the observation of the liquid discharge in the near-nozzle region. A high-speed back illumination was used for visualisation of the primary breakup. In the region of fully developed spray, the dynamics of droplets was studied using a phase-Doppler analyser (PDA). The information obtained from all methods was then correlated. Results show that the spray formation process depends mainly on the internal design of twin-fluid atomizer at low gas to liquid ratios (GLR). The amount of gas influences the character of the internal two-phase flow, a mechanism of the liquid breakup, droplet dynamics and a resulting drop size distribution. Differences among the atomizers are reduced with the increase in GLR. Moreover, it was shown that a certain mixing process can inherently create the annular internal flow which generates a stable spray characterized by relatively low mean droplet size.

An investigation into the relationship between catastrophic inversion and emulsion phase behaviors

The catastrophic inversion process from an oil-continuous to a polar phase-continuous emulsion was investigated with a system consisting of silicone oil, water and a nonionic surfactant. The polar phase involved an aqueous micellar solution, an inverse micellar solution, a hexagonal liquid crystal and a lamellar liquid crystal. Results indicated that a suitable polar phase structure with a positive spontaneous curvature was required for the formation of multiple emulsions leading to inversion at a relatively low dispersed phase fraction. Differences observed in the inversion pattern and the resultant drop size were explained in terms of the rheology of the polar phase and interfacial tension. The inverted emulsions were gel emulsions exhibiting similar viscoelastic behavior regardless of the specific polar phase structure. The same viscoelastic behavior was also exhibited in a lamellar liquid crystal (but not in a hexagonal liquid crystal) suggesting a common response mechanism to shear.

The breakup of levitating water drops observed with a high speed camera

Abstract. Collision-induced water drop breakup in a vertical wind tunnel was observed using a high speed camera for interactions between larger drop sizes (up to 7 mm diameter) than have previously been experimentally observed. Three distinct collisional breakup types were observed and the drop size distributions from each were analysed for comparison with predictions of fragment distributions from larger drops by two sets of established breakup parameterisations. The observations showed some similarities with both parameterisations but also some marked differences for the breakup types that could be compared, particularly for fragments 1 mm and smaller. Modifications to the parameterisations are suggested and examined. Presented is also currently the largest dataset of bag breakup distributions observed. Differences between this and other experimental research studies and modelling parameterisations, and the associated implications for interpreting results are discussed. Additionally, the stochastic coalescence and breakup equation was solved computationally using a breakup parameterisation, and the evolving drop-size distribution for a range of initial conditions was examined. Initial cloud liquid water content was found to have the greatest influence on the resulting distribution, whereas initial drop number was found to have relatively little influence. This may have implications when considering the effect of aerosol on cloud evolution, raindrop formation and resulting drop size distributions. Calculations presented show that, using an ideal initial cloud drop-size distribution, ~1–3% of the total fragments are contributed from collisional breakup between drops of 4 and 6 mm.

Characterization of gelatinized corn starch suspensions and resulting drop size distributions after effervescent atomization

Effervescent atomization is a promising method for economical atomization of high viscous liquids like gelatinized corn starch suspensions. The gelatinization of starch has strong influence on the viscosity of starch suspensions. It was characterized adapting a method for determination of the gelatinization degree. Rheological properties of gelatinized corn starch suspensions with concentrations ranging from 5 to 7 wt.-% were investigated. Effervescent atomization proved to be largely invariant to variations of liquid viscosity in this range. Relative gas injection pressure proved to be of highest influence on the resulting drop size distribution when varying only atomizer geometry. Applying Abel inversion to drop size measurement results depicted the opposite trend of drop sizes depending on radial position in the spray than observed by other researchers working with aqueous glass bead suspensions. Compared to conventional external mixing pneumatic atomization a reduction of atomization gas quantity of up to four times could be achieved.

The Impact of Density Ratio on the Liquid Core Dynamics of a Turbulent Liquid Jet Injected Into a Crossflow

Atomizing liquids by injecting them into crossflows is a common approach in gas turbines and augmentors. Much of our current understanding of the processes resulting in atomization of the jets, the resulting jet penetration and spray drop size distribution have been obtained by performing laboratory experiments at ambient conditions. Yet, operating conditions under which jets in crossflows atomize can be far different from ambient. Hence, several dimensionless groups have been identified that are believed to determine jet penetration and resulting drop size distribution. These are usually the jet and crossflow Weber and Reynolds numbers and the momentum flux ratio. In this paper, we aim to answer the question of whether an additional dimensionless group, the liquid to gas density ratio must be matched. We perform detailed simulations of the primary atomization region using the refined level set grid (RLSG) method to track the motion of the liquid/gas phase interface. We employ a balanced force, interface projected curvature method to ensure high accuracy of the surface tension forces, use a multiscale approach to transfer broken off, small scale nearly spherical drops into a Lagrangian point particle description allowing for full two-way coupling and continued secondary atomization, and employ a dynamic Smagorinsky large eddy simulation (LES) approach in the single phase regions of the flow to describe turbulence. We present simulation results for a turbulent liquid jet (q=6.6, We=330, and Re=14,000) injected into a gaseous crossflow (Re=740,000) analyzed under ambient conditions (density ratio 816) experimentally by Brown and McDonnell [2006, “Near Field Behavior of a Liquid Jet in a Crossflow,” Proceedings of the ILASS Americas, 19th Annual Conference on Liquid Atomization and Spray Systems]. We compare simulation results obtained using a liquid to gas density ratio of 10 and 100. The results show that the increase in density ratio causes a noticeable increase in liquid core penetration with reduced bending and spreading in the transverse directions. The post-primary atomization spray penetrates further in both the jet and transverse direction. Results further show that the penetration correlations for the windward side trajectory commonly reported in the literature strongly depend on the value of threshold probability used to identify the leading edge. Correlations based on penetration of the jet’s liquid core center of mass, on the other hand, can provide a less ambiguous measure of jet penetration. Finally, the increase in density ratio results in a decrease in wavelength of the most dominant feature associated with a traveling wave along the jet as determined by proper orthogonal decomposition.

Prediction of drop sizes for liquid–liquid systems in stirred slim reactors—Part II: Multi stage impellers

Based on the successful predictions of transient drop sizes in the first part of this research (Maaß et al., Prediction of drop sizes for liquid–liquid systems in stirred slim reactors—part I: single stage impellers. Chem. Eng. J., 162 (2010) 792–801), this part is a straight continuation and extension of the earlier work. The predictive capabilities of the used population balance equation model are increased for single stage impellers and transferred to scale-up procedures of such applications. Therefore different scale-up rules for liquid–liquid systems are tested experimentally and by simulations in two different sized, geometrically similar vessels. The multi stage impellers are tested against comparable single stage impellers in terms of power consumption, mixing time and minimum impeller speed. Especially for high aspect ratios (larger than three), multi stage impellers successfully compete with the single stage ones. The measured drop size distributions in slim reactors with multi stage impellers showed no dependency on the local position, although the dispersion process is tedious due to the compartmentalization. The simulations are not able to reflect this initial phase of the dispersion process, but are in close agreement with the experiments after complete dispersion is fulfilled. Based on these experiences the aspect ratio is increased up to five and the resulting drop size can be predicted with reasonable deviations (lower than 10%). The results of the scale-up of this multi stage impeller liquid–liquid system do not lead to a clear conclusion. Although the simulations recommend the use of constant power input, the experiments could not support this. None of the other traditional scale-up rule are supported by the experiments. Overall, the results of power consumption, mixing time and dispersion behavior show the great potential of multi stage impellers for process optimization and intensification in slim reactors.

A non-linear model for impinging jets atomization

The problem considered is predicting the characteristics of the spray produced by atomization of an attenuating liquid sheet formed by the impingement of two liquid jets of equal diameters and momenta. A second-order non-linear perturbation analysis is employed to model the evolution of harmonic instability waves that lead to sheet distortion and fragmentation. The onset of atomization occurs when the uneven surface modulations of the thinning sheet bring its upper and lower interfaces in contact. It is found that the sheet is torn into ligaments at each half wavelength. The instability of the ligaments causes their eventual disintegration into drops. The results indicate that sheet breakup length, time, and resultant drop size decrease as Weber number is increased. A higher Weber number induces a greater sheet breakup thickness. The breakup length, thickness, time, and drop size are diminished at larger impingement angles. The theoretical predictions of the present non-linear model are in good agreement with available experimental data and empirical correlations for sheet breakup length and drop size.

Interfacial aspects of water drop formation at micro-engineered orifices

The formation of emulsions with micro-engineered silicon based arrays of micro-orifices is a relatively new technique. Until now, only the preparation of oil-in-water emulsions was studied due to the hydrophilic nature of silicon. This work evaluates the emulsification of water into n-hexadecane with hydrophobized arrays of micro-orifices. We have studied the drop formation rate, the number of active pores and the drop size. In contrast to conventional macroporous membranes used for membrane emulsification, we observed high dispersed phase fluxes up to 4600 L h −1 m −2 bar −1 while all pores being active at applied pressures below 2 times the critical pressure. The drop diameter was independent from the applied pressure difference. We observed a pressure dependent lag time between drop formations at low emulsification pressures. The lag time is related to the rate of surfactant diffusion to the water–oil interface causing a reduction of the interfacial tension. A significant influence of the used hydrophobization agents, perfluorinated octyltrichlorosilane (FOTS) and octyltrichlorosilane (OTS), was found for the resulting drop sizes and the number of active pores.