Monodisperse Droplets Research Articles

Investigation and insights on the on-demand generation of monodispersed emulsion droplets from a floating capillary-based open microfluidic device.

Simple and stable generation of monodispersed droplets with volume from picolitre to nanoliter is one of the key factors in high-throughput quantitative microreactors for chemical and biomedical applications. In this work, an efficient method that could realize simple manipulating microflow with a broad operation window for preparing monodispersed droplets with controllable diameter is developed. The microfluidic device is constructed by inserting a capillary with an oblique angle (α) into the continuous phase, named a floating capillary-based open microfluidic device (FCOMD). The transition of droplet-generating mode between dripping and jetting can be achieved by changing capillary number and α. A computational model based on the volume-of-fluid/continuum-surface-force method to explain the controllability of α on the droplet formation regime and droplet breakage, verifying the synergistic effect of ΔP and Fb, facilitates the droplet pinching. A descending order of Pn of capillary with different α is that 45° > 30° > 15° > 60° > 75°, leading to the same order of generated droplet's D. When compared with the traditional capillary co-flow device, the generating throughput of the integrated FCOMD obtained by integrating different numbers of capillaries is at least ten times. Moreover, water in oil, oil in water double-emulsion, colloidal dispersed droplets, and liquid crystal droplets with diameters ranging from 25 to 800μm are prepared on-demand by the FCOMD, indicating the universality of the microfluidic device. Thus, the FCOMD shows the features of simplicity, practicability, and flexibility, offering valuable guidance for generating controllable droplets with wide size change and showing a great potential application in material science, foods, pharmaceuticals, and cosmetics.

Experimental and model‐based investigation of the droplet size distribution during the mixing process in a batch‐settling cell

AbstractThe design of a liquid–liquid gravity settler relies on the experimental investigation and model‐based description of the phase separation process in a batch‐settling cell. However, according to the current state of the art, the modelling assumes a monodisperse droplet size distribution (DSD), which can lead to an inaccurate settler design. This study considers the polydispersity of the initial DSD resulting from the mixing process in the settling cell to enhance the model accuracy. DSDs of o/w and w/o dispersions during the mixing process in a settling cell are investigated in this work for 2‐methyltetrahydrofuran/water and decane/water material systems at hold‐ups of 25–50 vol.% and stirrer speeds of 400–850 min−1. Sauter mean diameters (SMD) and DSD shapes are analyzed to identify the influence of the investigated parameters on the SMD and DSD and to model the SMD and DSD. The experimental investigation shows that stirrer speed, hold‐up, and interfacial tension significantly affect the DSD, while the viscosity of the continuous phase plays a minor role. The SMD is correlated to the Weber number, viscosity group, and hold‐up by a model with a mean absolute percentage error (MAPE) of 3.6%. The DSD is described by a log‐normal distribution function with a MAPE of 5%. The SMD and DSD models presented in this work can be used to describe the initial DSD of the phase separation process in a batch‐settling cell, considering polydispersity and thus increasing the modelling accuracy of the phase separation process.

Step emulsification for monodisperse droplet creation using a connection-free PDMS microchip

Microfluidic technology for generating monodisperse droplets has significantly advanced various scientific and industrial applications. However, reliance on complex infrastructure, such as external pumps and intricate connections, limits its widespread adoption. In this study, we focused on passive droplet formation through step emulsification (SE) using a connection-free polydimethylsiloxane (PDMS) microchip. Our microchip design enabled droplet formation without the need for external pumps for active flow control, instead utilizing the pressure differential created between inlet reservoirs and a shared sealed-outlet space when degassed PDMS was exposed to atmospheric pressure. We began with a simple design and through progressive refinement of the microchip geometry, we achieved a more advanced design that facilitated detailed analysis of droplet formation dynamics. This design allowed for real-time observation of the droplet formation process, including time-dependent variations in droplet formation rate and the associated gentle changes in droplet size, which were intrinsic characteristics of connection-free PDMS microchips. Experiments demonstrated that a triangular nozzle design significantly improved droplet size uniformity, with a coefficient of variation in droplet diameter below 2 % under optimal conditions. These results highlighted the potential of connection-free SE microchips for generating highly uniform droplets in a simplified and efficient manner.

Microscale Templating of Functional Particles Using Self-Limiting Electrospray Deposition.

Electrospray deposition (ESD) uses strong electric fields applied to solutions and dispersions exiting a capillary to produce charged monodisperse droplets driven toward grounded targets. Self-limiting electrospray deposition (SLED) is a phenomenon in which highly directed, uniform, and even 3D coatings can be achieved by trapping charge in the deposited film, redirecting the field lines to uncoated regions of the target. However, when inorganic particles are added to SLED sprays, the buildup of charge required to repel incoming material is disrupted as particle loading increases. Due to its fibril gelling behavior, methylcellulose (MC) SLED can form nanowire morphologies. These wires, when used as a binder, can separate particles and prevent percolation. In this work, a variety of conductive and insulating particles are explored using patterned and un-patterned substrates. This exploration allows us to maximally load particles for high-concentration and highly controlled self-limiting functional sprays. This is demonstrated using Ti3C2Tx MXene to functionalize an interdigitated electrode for use as a supercapacitor.

Active Fréedericksz Transition in Active Nematic Droplets

Active nematic liquid crystals have the remarkable ability to spontaneously deform and flow in the absence of any external driving force. While living materials with orientational order, such as the mitotic spindle, can self-assemble in quiescent active phases, reconstituted active systems often display chaotic, periodic, or circulating flows under confinement. Quiescent active nematics are, therefore, quite rare, despite the prediction from active hydrodynamic theory that confinement between two parallel plates can suppress flows. This spontaneous flow transition—named the active Fréedericksz transition by analogy with the conventional Fréedericksz transition in passive nematic liquid crystals under a magnetic field—has been a cornerstone of the field of active matter. Here, we report experimental evidence that confinement in spherical droplets can stabilize the otherwise chaotic dynamics of a 3D extensile active nematics, giving rise to a quiescent—yet still out-of-equilibrium—nematic liquid crystal. The active nematics spontaneously flow when confined in larger droplets. The composite nature of our model system composed of extensile bundles of microtubules and molecular motors dispersed in a passive colloidal liquid crystal allows us to demonstrate how the interplay of activity, nematic elasticity, and confinement impacts the spontaneous flow transition. The critical diameter increases when motor concentration decreases or nematic elasticity increases. Experiments and simulations also demonstrate that the critical confinement depends on the confining geometry, with the critical diameter in droplets being larger than the critical width in channels. Biochemical assays reveal that neither confinement nor nematic elasticity impacts the energy-consumption rate, confirming that the quiescent active phase is the stable out-of-equilibrium phase predicted theoretically. Further experiments in dense arrays of monodisperse droplets show that fluctuations in the droplet composition can smooth the flow transition close to the critical diameter. In conclusion, our work provides experimental validation of the active Fréedericksz transition in 3D active nematics, with potential applications in human health, ecology, and soft robotics. Published by the American Physical Society 2024

Generating nano/microliter droplets with on-demand repetition rates by femtosecond filament-fabricated superhydrophobic bevel needle nozzles

Nano- and micro-droplets provide a platform for microanalysis of a variety of biochemical reactions with less consumption of reagents and large-extent elimination of cross-contamination, but stable generation of such monodisperse droplets with an on-demand size and repetition rate should be first established. Here, we present a simple and robust approach to generate nano/microliter (nL/μL) droplets with predetermined size and repetition rate by using femtosecond laser filament-fabricated stainless bevel needle nozzles (BNNs). We demonstrate that hierarchically heterogeneous micro/nanostructures can be directly formed on both the inner and outer surfaces of BNNs by femtosecond laser filament processing, and that after a heat treatment the fabricated BNNs show an excellent superhydrophobic property with the water contact angle of ∼160° and the rolling-off angle of ∼0.4°. With the superhydrophobic BNNs (19–27 gauge), we produce monodisperse water droplets (2.5 μL–87 nL) with nearly the same sizes as the needle diameters, and dispense them repeatedly with on-demand repetition rates from sub-1 Hz to more than 100 Hz over several orders of the flow rate. The results provide a new way for generating microdroplets on demand for various droplet-based applications.

Fabrication of Conical Microstructure Array for Stable Droplet Generation Over Wide Flow Rate Range.

Droplet generators with the ability to resist flow fluctuations are of importance for microfluidic chip analysis systems. However, obtaining stably desired-size droplets is still a bugbear since even slight fluctuations can cause polydisperse droplets. In this study, a high-performance droplet generator is achieved with a functional conical array housed in the junction of the channels. The conical microstructures are fabricated through the selective etching of the scratched silicon nitride/silicon (Si3N4/Si) substrate in potassium hydroxide (KOH) etchant, where the combination of lateral and normal material removal contributes to the structure formation. It is found that the key role of the conical microstructures is to regulate the flow rate of the continuous phase, which allows droplet generation to turn to the necking phase and enables droplets to shed more easily. It is also noted that the droplet generator with such a conical array can produce monodisperse droplets in wide-range flow, providing new insights for high-quality device design.

Elimination of satellite droplets in droplet streams by superposing harmonic perturbations

In tin-droplet laser-produced plasma sources, uniform droplet streams with large droplet spacing are desired to minimize the interference of explosion on neighboring droplets. Such droplet streams can be generated in low wavenumber regimes. However, satellite droplets easily appear among main droplets in those regimes, resulting in plenty of undesirable debris. Herein, a novel odd harmonic superposition perturbation method is proposed to eliminate satellite droplets and enhance droplet spacing of uniform droplet streams. The superposition number (N) and the phase difference (θ) of odd harmonic perturbations are adjusted to facilitate the coalescence of satellite droplets with main droplets. First, the superposed odd-order harmonic components could induce additional disturbance growth in jet surfaces, and finally lead to the asymmetric necking on filaments formed between two adjacent main droplets, featured as various carrot-shaped configurations. This asymmetric necking will cause unbalanced surface tension forces at the two sides of filaments, resulting in a velocity difference between satellite and main droplets. Based on this principle, by setting N and k to 3 and 0.2, respectively, satellite droplets positioned above main droplets accelerate, while those below decelerate, achieving complete coalescence between main and satellite droplets. Furthermore, the phase difference is found to determine the jet breakup location and satellite droplet merging characteristics. As θ varies from 0° to 90°, the droplet size significantly decreases while the droplet spacing remains constant since the perturbation energy increases. The merge direction of satellite droplets reverses from upward to downward due to enhanced unbalanced surface tension forces and velocity differences. As θ continuously increases to 270°, the droplet size further decreases along with a slight decrease in droplet spacing. Finally, by setting N = 3 and θ = 0°, mono-disperse tin droplet streams with a mean diameter of 31.5 μm and a maximum droplet spacing-to-diameter ratio of 17.7 are successfully formed. This work presents a novel approach for eliminating satellite droplets to achieve uniform tin droplet streams with large droplet spacing without increasing the droplet diameter.

Morphology and heat transfer of a train of microdroplets impinging on the heated surface for spray cooling

Owing to the superior cooling performance of the droplet impingement process, the spray cooling is widely used in various industries including aerospace, e-motors, data centres and so on. In the present study, the morphological evolution and heat transfer characteristics of vertical and oblique impacts on the heated surface were investigated experimentally and numerically. A droplet generation system and a substrate heating system were designed to observe continuous vertical and oblique droplets impinging on the hot surface by a high-speed camera. The coupled Level Set and VOF (CLS-VOF) model and adaptive mesh refinement technique were used to establish a mathematical model for a train of micro-sized droplets impinging on the heated surface, which was validated by experimental data. The film that spreads on the surface exhibits asymmetry due to the horizontal velocity of the droplets. When continuous droplets impinge vertically on the heated wall, the evolution of the crown and the wall temperature appear periodic. The effects of impingement angles on morphological patterns and heat transfer of a train of micro-sized monodispersed droplets with the same Weber numbers were analyzed further. The results indicated that with a smaller angle of impingement, the crown is more likely to splash, and the crown asymmetry is less obvious.

Droplet Microfluidics for High-Throughput Screening and Directed Evolution of Biomolecules.

Directed evolution is a powerful technique for creating biomolecules such as proteins and nucleic acids with tailor-made properties for therapeutic and industrial applications by mimicking the natural evolution processes in the laboratory. Droplet microfluidics improved classical directed evolution by enabling time-consuming and laborious steps in this iterative process to be performed within monodispersed droplets in a highly controlled and automated manner. Droplet microfluidic chips can generate, manipulate, and sort individual droplets at kilohertz rates in a user-defined microchannel geometry, allowing new strategies for high-throughput screening and evolution of biomolecules. In this review, we discuss directed evolution studies in which droplet-based microfluidic systems were used to screen and improve the functional properties of biomolecules. We provide a systematic overview of basic on-chip fluidic operations, including reagent mixing by merging continuous fluid streams and droplet pairs, reagent addition by picoinjection, droplet generation, droplet incubation in delay lines, chambers and hydrodynamic traps, and droplet sorting techniques. Various microfluidic strategies for directed evolution using single and multiple emulsions and biomimetic materials (giant lipid vesicles, microgels, and microcapsules) are highlighted. Completely cell-free microfluidic-assisted in vitro compartmentalization methods that eliminate the need to clone DNA into cells after each round of mutagenesis are also presented.

Investigation of piezoelectric printing devices for oil-free and on-demand picolitre monodisperse droplet generation

Picolitre monodisperse droplet printing technology has important applications in biochemistry, such as accounting for quantitative analysis and single-cell analysis, and can be used for parallel high-throughput analysis of biomarkers and chemicals. However, commonly used droplet generation devices require complex control systems or customised microfluidic chips, making them costly and difficult for researchers to operate. Additionally, generating picolitre monodisperse droplets with microfluidic devices necessitates the introduction of an oil phase to block and separate the liquid. This requirement can reduce the throughput of the target droplets and cause cell contamination, hindering the adoption of this technology. By employing a common 1-mm-diameter capillary in the laboratory in combination with a piezoelectric transducer, we have achieved on-demand picolitre droplet printing of less than 100 pL in an oil-free environment. The device was found to be biocompatible with K562 cells. This approach is less costly, offers greater operational freedom, and is easier to integrate with other downstream assay modules or even handheld cell-printing devices. This study holds great potential for application in areas such as single-cell analysis, cell sampling, and pharmaceutical analysis.

A novel high-DPI and monodisperse droplet inkjet printhead with the piezoelectric cutter

High dots per inch (DPI) is the core index of inkjet printer, which is hindered by satellite ink droplet. Herein, we propose a novel high-DPI and monodisperse droplet inkjet printhead with the piezoelectric cutter. The as-established model has optimized the inkjet printhead structural parameters, actuating and cutting signal waveforms. The cutter element achieves moving the break-up point to the middle of the ink column, reducing the length of tail and generating a monodisperse droplet. Additionally, the cutter consistently reduces the droplet length with different ink properties including viscosity, density, surface tension, and contact angle, exhibiting high applicability. The research results provide an in-depth study on the design of high-DPI and monodisperse inkjet printheads, offering an efficient approach to improve inkjet printhead performance.

Application Of Two Dye Two-Color Laser-Induced Fluorescence Spectroscopy On Droplets Of Green Solvent Mixtures Containing Water And Ethanol

In order to reach a higher sustainability, the utilization of green solvents is decisive in many technical applications. Water and ethanol substitute more complex solvents, showing advantages like ecological manufacturing, reusability or biodegradation. Both liquids are found in various industrial areas, ranging from a use as additives in biofuels, coolants or solvents for extraction in pharmaceutical, medical or food industries. Regarding these industrial processes, important variables are the liquid phase temperature and the composition in binary fluids. The focus of this work is two dye two-color laser induced fluorescence (2c-LIF) measurements in ethanol, water and their mixtures. Liquid phase thermometry via 2c LIF requires a selection of suitable fluorescence dyes regarding solubility, temperature sensitivity and the interaction among the dyes themselves. A mixture of a temperature sensitive and a temperature insensitive dye is used in order to reach a large change in signal ratio for thermometry. In this work, two dyes – fluorescein disodium (FL) and sulforhodamine 101 (SRh), as proposed by Chaze et al. (Chaze et al. 2016) – are analyzed regarding their absorption and emission behavior in various ethanol/water mixtures, which are examples of "green solvents". The absorption spectra of the dissolved dye mixture are measured with a spectrophotometer at temperatures from 293 K to 343 K. Information on the temperature dependent absorption of the single dyes and reabsorption effects in ethanol/water mixtures is obtained. Additionally, the fluorescence of the mixtures is analyzed spectrally and by an imaging system. Therefore, a fiber coupled spectrometer and a system with two sCMOS cameras equipped with a long distance (LD) microscope are applied for simultaneous detection of the signal of tempered solutions a monodisperse droplet chain. A study of small droplets with sizes below 50 μm are evaluated and the limit of the spectral detection system is determined and discussed. The application of the measurement technique to several solvent mixtures is investigated. Additionally, an application for composition investigations of binary water/ethanol droplets via 3c-LIF is proposed.

Three-dimensional rainbow refractometry.

We propose a new, to the best of our knowledge, rainbow technique called three-dimensional rainbow refractometry (TDRR), with a cylindrical lens in the signal collecting system. With a TDRR model based on the ray transfer matrix developed, it is proved that the tilt angle of the rainbow signal is related to the axial position of the droplet, which helps to obtain the 3D position. By converting rainbow scattering angle calibration into the system parameter calibration, a new rainbow data processing program is written in combination with the model to obtain the refractive index and the particle size. With TDRR, we measured a monodisperse droplet stream of deionized water at room temperature for experimental validation and obtained the refractive index with an absolute error of less than 0.0015, the droplet size with an error within ±5%, and the axial position with an error within ±3%, which demonstrated a high accuracy of TDRR.

Sensing area-variable electrode for wide-range droplet size detection

Microfluidic droplets of various sizes are applied in a broad spectrum of biological and chemical processes and require high uniformity for reliable outcomes. Although various droplet detection methods have been employed to achieve monodisperse droplets, the capacitive method stands out for its ease of use and rapid response, enabling real-time feedback control. However, this method has limitations in terms of significantly altering the droplet size, resulting in increased continuous phase consumption and the need for microchannel and sensing component replacements. In response, we present the Sensing Area-Variable Electrode (SAVE), which is designed to produce monodisperse droplets across a broad size range without excessive continuous phase consumption and without requiring the frequent replacement of sensing components. The experimental results demonstrate that using the SAVE electrode enables the generation of monodisperse 0.2, 0.4, and 1.0 nL droplets by simply replacing the disposable microchannel while reusing the sensing components. Moreover, the adaptable number of droplets achieved by microchannel replacement allows the SAVE electrode to be effectively utilized in droplet digital polymerase chain reaction (ddPCR) assays, providing a balance between sensitivity and throughput. Consequently, the SAVE electrode addresses the limitations of the capacitive detection method and offers a versatile solution for various droplet-based biological and chemical processes, including ddPCR assays.

Flow behavior and characteristic parameters of droplets in counter-current mini-channel extractor

Achieving the counter-current flow in mini-channel extractor is a challenge. The formation and characteristic parameters of droplets in mini-channel counter-current extractor were systematically investigated to provide a guide for the realization and operation of counter-current extraction. A mixture of P507 diluted with sulfonated kerosene was served as dispersed phase, while 0.2 mol/L LaCl3 solution was used as continuous phase. Droplets rapidly deformed from the nearly-spherical shape to ellipsoidal shape after detaching from nozzles, eventually floated upwards as monodisperse droplets with same spacing. Sauter mean diameter of droplets decreased with the increase of superficial velocity of organic phase, yet increased with the increase of superficial velocity of aqueous phase. The specific interfacial area of droplets increased with the increasing superficial velocity of organic phase, and slightly decreased with the increasing superficial velocity of aqueous phase. The correlations of droplet characteristic parameters were established using dimensional analysis for further prediction and analysis.

Scalable Jet‐Based Fabrication of PEI‐Hydrogel Particles for CO2 Capture

The capture, regeneration, and conversion of CO2 from ambient air and flue gas streams are critical aspects of mitigating global warming. Solid sorbents for CO2 absorption are very promising as they have high mass transfer areas without energy input and reduce emissions and minimize corrosion as compared to liquid sorbents. However, precisely tunable solid CO2 sorbents are difficult to produce. Here, we demonstrate the high‐throughput production of hydrogel‐based CO2‐absorbing particles via liquid jetting. By wrapping a liquid jet consisting of an aqueous solution of cross‐linkable branched polyethylenimine (PEI) with a layer of suspension containing hydrophobic silica nanoparticles, monodisperse droplets with a silica nanoparticle coating layer was formed in the air. A stable Pickering emulsion containing PEI droplets was obtained after these ejected droplets were collected in a heated oil bath. The droplets turn into mm‐sized particles after thermal curing in the bath. The diameter, PEI content, and silica content of the particles were systematically varied, and their CO2 absorption was measured as a function of time. Steam regeneration of the particles enabled cyclic testing, revealing a CO2 absorption capacity of 6.5 ± 0.5 mol kg−1 solid PEI in pure CO2 environments and 0.7 ± 0.3 mol kg−1 solid PEI for direct air capture. Several thousands of particles were produced per second at a rate of around 0.5 kg per hour, with a single nozzle. This process can be further scaled by parallelization. The complete toolbox for the design, fabrication, testing, and regeneration of functional hydrogel particles provides a powerful route toward novel solid sorbents for regenerative CO2 capture.

Effect of Acoustics on Droplet Grouping Behaviour in a Single Stream of Droplets

Droplet and particle grouping can be influenced by applying an acoustic field and have practical applications such as particle scavenging and aerosol filters of engine exhaust and air purifiers. The present work experimentally investigates the influence of a standing acoustic wave on a single stream of droplets. The experimental setup consists of an acoustic transducer and a reflector plate through which the droplet stream passes in the presence or absence of an external pressure field generated by a standing acoustic wave. A droplet stream is generated with the help of a nozzle connected to a pressurized working fluid supply and piezoelectric transducer to control the spacing between droplets. The effect of the acoustic pressure field on the droplet stream generated by the nozzle operated at different piezoelectric excitation frequencies and fluid pressures is investigated. Droplet stream characteristics at every nozzle excitation frequency are observed with a high-speed camera when the acoustic field is switched OFF and ON. The competing effect of nozzle excitation frequency and acoustic field is observed. At lower nozzle frequencies, the nozzle generates an unstable stream of droplets having different sizes and spacings between them. When the acoustic field is applied at these lower frequencies, the stream of droplets becomes organized, and in some cases, it becomes equispaced and of the same size. However, an opposite behavior is observed at higher frequencies. In these cases, as the acoustic field is applied, an equispaced mono-disperse droplet stream becomes unstable due to the coalescence of droplets within the stream.

Engineering Interconnected Open-Porous Particles via Microfluidics Using Bijel Droplets as Structural Templates.

Designing porous structures is key in materials science, particularly for separation, catalysis, and cell culture systems. Bicontinuous interfacially jammed emulsion gels represent a unique class of soft matter formed by kinetically arresting the separation of the spinodal decomposition phase, which is stabilized by colloidal particles with neutral wetting. This study introduces a microfluidic technique to create highly interconnected open-porous particles using bijel droplets stabilized with hexadecyltrimethylammonium bromide (CTAB)-modified silica particles. Monodisperse droplets comprising a hydrophobic monomer, water, ethanol, silica particles, and CTAB were initially formed in the microfluidic device. The diffusion of ethanol from these droplets into the continuous cyclohexane phase triggered spinodal decomposition within the droplets. The phase-separated structure within the droplets was stabilized by the CTAB-modified silica particles, and subsequent photopolymerization yielded microparticles with highly interconnected, open pores. Moreover, the influence of the ratio of the CTAB and silica particles, fluid composition, and microchannel direction on the final structure of the microparticles was explored. Our findings indicated that the phase-separated structure of the particles transitioned from oil-in-water to water-in-oil as the CTAB/silica ratio was increased. At intermediate CTAB/silica ratios, microparticles with bicontinuous structures were formed. Regardless of the fluid composition, the pore size of the particles increased with time after phase separation. However, this coarsening was arrested 15 s after droplet formation in the CTAB-modified silica particles, accompanied by a change in the particle shape from spherical to ellipsoidal. In situ observations of the bijel droplet formation revealed that the particle shape deformation is caused by the rolling of elastic bijel droplets at the bottom of the microchannel. As such, the channel setup was altered from horizontal to vertical to prevent the deformation of bijel droplets, resulting in spherical particles with open pores.

Connecting finite-time Lyapunov exponents with supersaturation and droplet dynamics in a turbulent bulk flow.

The impact of turbulent mixing on an ensemble of initially monodisperse water droplets is studied in a turbulent bulk that serves as a simplified setup for the interior of a turbulent ice-free cloud. A mixing model was implemented that summarizes the balance equationsof water vapor mixing ratio and temperature to an effective advection-diffusion equationfor the supersaturation field s(x,t). Our three-dimensional direct numerical simulations connect the velocity and scalar supersaturation fields in the Eulerian frame of reference to an ensemble of cloud droplets in the Lagrangian frame of reference. The droplets are modeled as point particles with and without effects due to inertia. The droplet radius is subject to growth by vapor diffusion. We report the dependence of the droplet size distribution on the box size, initial droplet radius, and the strength of the updraft, with and without gravitational settling. In addition, the three finite-time Lyapunov exponents λ_{1}≥λ_{2}≥λ_{3} are monitored which probe the local stretching properties along the particle tracks. In this way, we can relate regions of higher compressive strain to those of high local supersaturation amplitudes. For the present parameter range, the mixing process in terms of the droplet evaporation is always homogeneous, while it is inhomogeneous with respect to the relaxation of the supersaturation field. The probability density function of the third finite-time Lyapunov exponent, λ_{3}<0, is related to the one of the supersaturation s by a simple one-dimensional aggregation model. The probability density function (PDF) of λ_{3} and the droplet radius r are found to be Gaussian, while the PDF of the supersaturation field shows sub-Gaussian tails.