Droplet Composition Research Articles

Exploring How the Surface-Area-to-Volume Ratio Influences the Partitioning of Surfactants to the Air-Water Interface in Levitated Microdroplets.

Quantitative characterization of the surface of microdroplets is important to understanding and predicting numerous chemical and physical processes, such as cloud droplet formation and accelerated chemistry in microdroplets. However, it is increasingly appreciated that the surface compositions of microdroplets do not necessarily match those of macroscale solution due to their large surface-area-to-volume (SA-V) ratios and confined volumes. In this work, we explore how both droplet size and composition affect the surface composition of microdroplets by measuring the equilibrium surface tensions of levitated microdroplets containing a single surfactant. We measure the critical micelle concentrations (CMCs) for surfactants of various strengths (macroscale CMC values ranging from 0.02 to 10 mM) in microdroplets with radii ranging from 5 to 25 μm. We accurately model the surface tensions of microdroplets using an equilibrium partitioning model that only requires droplet size and adsorption parameters from macroscale measurements as inputs. Our model predicts that surfactants have an "effective CMC" in microdroplets that is always larger in value than the corresponding macroscale CMC. In some instances, the effective CMC of a surfactant in microdroplets is several orders of magnitude larger than both its macroscale CMC and its macroscale solubility limit. We present a simple expression for the effective CMC in microdroplets that depends on both the macroscale CMC of a surfactant and the SA-V ratio of the microdroplet. Ultimately, our experimental results and model can be used broadly to predict microdroplet surface compositions when investigating surface-driven accelerated chemistry in microdroplets or estimating cloud droplet activation.

Molecular-Level Investigation of Binary Fluid Droplets Impacting Surfaces

Droplets impacting with surfaces are commonly encountered processes in the field of protective coatings. The behavior of a colliding binary liquid droplet is sensitive to the impact velocity, surface wetting properties, and the droplet composition. Modeling molecular dynamics and classical density functional theory studies of impacting droplets as well as interfacial-surface free energies was reported on. The presence of two components in the liquid drop makes the surface collision a complicated problem. During the collision the kinetic energy of the drop is converted into heat. Thus, the temperature varies during the collision and throughout the droplet. Two extreme situations were captured by performing both adiabatic and isothermal simulations. Molecular dynamics and classical density functional theory were used to explore the effects of the mixing parameter on the phase diagram of the binary AB mixed droplets. The location of liquid–vapor and liquid–liquid phase separation was determined. In addition, the value of the interfacial tensions of all interfaces was computed. These can be used to predict when an A-rich and B-rich droplet will stay attached and when it will detach.

Evaporation, spreading, and possible uptake of droplets on sorghum (Sorghum bicolor) and cowpea (Vigna unguiculata) leaves using an imaging-based technology.

Sprayed agrochemical droplets have a dynamic evolution on the leaf surface, undergoing changes in shape and volume due to spreading, evaporation, and adsorption. To better understand these processes, an accessible imaging-based experimental methodology is presented to precisely measure droplet spreading, evaporation, and potential uptake by a leaf within a controlled relative humidity environment. Laboratory experiments were conducted to determine the effect of hydrocarbon surfactants, accelerators (light mineral oil), and humectants (high fructose corn syrup) on droplet spread, evaporation, and potential uptake when applied to sorghum (Sorghum bicolor 'Tricker') and cowpea (Vigna unguiculata) leaves. Experiments on cowpea leaves showed uniform spreading and no change in evaporation compared to the predicted rate. In contrast, on sorghum leaves, results suggest that the volume loss rate exceeds the predicted evaporation rate (up to 23%), indicating a potential uptake by the leaves. Some accelerated dynamics on sorghum can be attributed to the lateral spreading observed on hairy leaves along the veins, increasing the contact area by an average of 65%. However, samples containing light mineral oil, typically considered an accelerant to aid in uptake, demonstrated the highest rate but exhibited minimal spreading. The study demonstrates how droplet composition affects droplet dynamics on waxy and hairy leaves by using an imaging-based methodology to measure evaporation rates, volume loss, contact angle, wetted area, and spreading behavior. The findings highlight some of the complex coupling between the crop protection product composition and droplet life cycle on a leaf. © 2024 The Author(s). Pest Management Science published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry.

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

Experimental & numerical investigations of ultra-high-speed dynamics of optically induced droplet cavitation in soft materials

Perfluorocarbon (PFC) droplets represent a novel class of phase-shift contrast agent with a promise in applications in biomedical and bioengineering fields. PFC droplets undergo a fast liquid-gas transition upon exposure to acoustic or optical triggering, offering a potential adaptable and versatile tool as contrast agent in diagnostics imaging and localized drug delivery vehicles in therapeutics systems. In this paper, we utilize advanced imaging techniques to investigate ultra-high-speed inertial dynamics and rectified quasi-static (low-speed) diffusion evolution of optically induced PFC droplet vaporization within three different hydrogels, each of different concentrations, examining effects such as droplet size and PFC core on bubble dynamics and material viscoelastic properties. Gelatin hydrogels reveal concentration-dependent impacts on bubble expansion and material elasticity. Embedding PFC droplets in gelatin increases internal pressure, resulting in higher equilibrium radius and continuous bubble growth during quasi-static evolution. Similar trends are observed in fibrin and polyacrylamide matrices, with differences in bubble behavior attributed to matrix properties and droplet presence. Interestingly, droplet size exhibits minimal impact on bubble expansion during inertial dynamics but influences quasi-static evolution, with larger droplets leading to continuous growth beyond 60 seconds. Furthermore, the core composition of PFC droplets significantly affects bubble behavior, with higher boiling point droplets exhibiting higher maximum expansion and faster quasi-static dissolution rates. Overall, the study sheds light on the intricate interplay between droplet characteristics, matrix properties, and multi-timescale bubble dynamics, offering valuable insights into their behavior within biomimetic hydrogels.

Removal of dichloromethane from gas streams by droplet triggered gas discharge

The removal of dichloromethane (DCM) from gas streams by a novel gas discharge reactor triggered by solution droplets was experimentally investigated. The influences of operation parameters such as input energy, gas flow rate, oxygen concentration, droplet dropping frequency, and the solution composition of droplets on the effectiveness of reactor operation and DCM removal efficiency were examined. Experimental results showed that DCM in the gas stream can be effectively degraded, and the removal of DCM decreased with the increase of the initial DCM concentration in the gas stream. With the increase of droplet dropping frequency, the removal of DCM experiences a process from increase to decrease, and the optimal droplet dropping frequency is around 0.5–1 drop·s−1. It was also found that the oxygen concentration in the range of 5–10 % in the gas stream is better for DCM decomposition, and the use of alkaline solution as droplets can effectively improve the removal of DCM. The final gas phase products of DCM degradation were mainly CO2 and O3 with the presence of O2 in the gas stream, and the liquid phase products were chloride (Cl-) and hypochlorite (ClO-) ions.

Droplet transition behavior and compositional homogenization of TiAl alloys fabricated via dual-wire electron beam-directed energy deposition

The dual-wire electron beam-directed energy deposition (EB-DED) process presents considerable advantages for fabricating titanium aluminide (TiAl) alloys via in situ reactions between Ti and Al. However, variations in the thermophysical properties of pure Ti, pure Al, and TiAl alloys pose challenges in achieving consistent droplet transition behavior and uniform chemical composition. This study explored the effects of wire feeding modes on the forming quality of TiAl alloys and droplet transition behaviors and discussed compositional homogenization and elemental evaporation in TiAl alloy components. Both single-side and double-side feeding modes were utilized, and the electron beam directly melted the Ti wire in the double-side mode, thereby achieving superior surface morphology. Random disturbances and suboptimal wire feeding angles led to the wires deviating from the electron beam center and then being inserted into or passing through the molten pool, thereby degrading the forming quality. By positioning the Al wire tip beneath the Ti wire tip, a common droplet emerged as the Ti droplets melted the Al wire. The droplet transition behavior was regulated by the distance between the wire tips and component surfaces, achieving a liquid bridge transition at distances ranging from 0.75 to 5.82 mm. Although the droplet composition was generally uniform owing to elemental evaporation, the fluctuations among the droplets exceeded those observed in the as-deposited components. The extensive molten pool and keyhole effect enhanced compositional homogenization within the TiAl alloy components. During the deposition process, the evaporation rate of Al surpassed that of Ti due to its higher saturation vapor pressure, consequently yielding a lower actual Al content. The loss rate of Al initially decreased and then increased as the calculated Al content increased, which was influenced by the Al content in the molten pool and temperature variations. This research advances the fundamental understanding of TiAl alloy fabrication via in situ reactions and contributes to the development of the EB-DED process.

AI-powered modular and general-purpose droplet processing system based on single-sided continuous optoelectrowetting chip

Single-sided continuous optoelectrowetting (SCOEW) is a versatile light-controlled digital microfluidic technology. However, the absence of automated algorithms for generating light patterns to manipulate droplets has constrained SCOEW chips to employing only pre-recorded sequences. This limitation hinders SCOEW platforms in effectively addressing common experimental challenges like droplet pinning. To overcome this issue, we have developed a set of algorithms for the automatic generation of droplet-driving light patterns. By integrating these algorithms with machine vision (using YOLOv3) to detect, locate, and classify droplets through video camera input, and employing a path-planning algorithm (A*) to optimize droplet trajectories, our system achieves intelligent functionalities. These include simultaneous manipulation of multiple droplets, automated merging based on color-coded droplet composition, obstacle avoidance, and resolution of potential droplet manipulation failures (such as droplet pinning). In a practical application, we implemented an intelligent loop-mediated isothermal amplification (LAMP) assay on the platform. This modular approach to droplet processing is easily adaptable to other SCOEW hardware, offering potential integration of customizable functionality. The result is a promising suite of portable tools for a variety of biochemical analysis application.

Emulsification characteristics of crude oil with a high content of heavy components and its emulsification mechanism in porous media

There are occurrences of crude oil emulsification following the fracturing shut-in wells in the Jimushar, but the emulsification characteristics and mechanism remain unclear. In this study, the low-field nuclear magnetic resonance technique and visual microdisplacement tests are employed to investigate the emulsification characteristics of crude oil, along with its emulsification mechanism in porous media. Experimental results revealed that the heavy components (asphaltene and resin) enhance crude oil emulsification by increasing the viscous force of water droplets in the oil phase, affecting the size and stability of small water droplets in the oil phase. In the process of flowing through pore throats, emulsions are formed primarily by stretching and snap-off action, with stretching preferring to form smaller droplet-size emulsions, while snap-off results in the division of larger oil droplets into two smaller ones. The primary factors causing a large oil droplet to be stretched into smaller droplets include changes in the composition of the oil droplet, external tension, and the duration of these forces acting on the droplet. Capillary forces can emulsify crude oil and water at the pore scale, resulting in a reduction of the absorption rate. However, this rate can be restored when the capillary forces are strong enough for the water phase to penetrate and break through the emulsified layer. This study offers valuable insights into understanding the adaptability of the emulsification flooding mechanism.

Lipid Regulatory Element Interact with CD44 on Mitochondrial Bioenergetics in Bovine Adipocyte Differentiation and Lipometabolism.

The CD44 gene is a critical factor in animal physiological processes and has been shown to affect insulin resistance and fat accumulation in mammals. Nevertheless, little research has been conducted on its precise functions in lipid metabolism and adipogenic differentiation in beef cattle. This study analyzed the expression of CD44 and miR-199a-3p during bovine preadipocyte differentiation. The luciferase reporter assay demonstrated that CD44 was a direct target of miR-199a-3p. Increased accumulation of lipid droplets and triglyceride levels, altered fatty acid metabolism, and accelerated preadipocyte differentiation were all caused by the upregulation of miR-199a-3p or a reduction in CD44 expression. CD44 knockdown upregulated the expression of adipocyte-specific genes (LPL and FABP4) and altered the levels of lipid metabolites (SOPC, l-arginine, and heptadecanoic acid). Multiomics highlights enriched pathways involved in energy metabolism (MAPK, cAMP, and calcium signaling) and shifts in mitochondrial respiration and glycolysis, indicating that CD44 plays a regulatory role in lipid metabolism. The findings show that intracellular lipolysis, glycolysis, mitochondrial respiration, fat deposition, and lipid droplet composition are all impacted by miR-199a-3p, which modulates CD44 in bovine adipocytes.

Buildup and Consumption of Species in Emulsion Droplets during Aqueous Suzuki Coupling Correlate with Yield.

Fluorescence lifetime imaging microscopy (FLIM) provides spatiotemporal resolution of the changing composition of emulsion droplets during aqueous-surfactant Suzuki coupling. In contrast to previous investigations, the present experiments characterize the full course of a catalytic chemical reaction, addressing key questions about reaction species buildup and correlating these microscale behaviors with bench-scale product yields. At low concentrations of (active) catalyst, droplet environments are stable; however, at higher concentrations, emulsion droplet environments change markedly. These changes are consistent with the buildup and consumption of reaction species inside the droplets. A combination of FLIM and bright-field imaging pinpoints limitations in catalyst solubility as controlling rate and degree of buildup of species in droplets. These solubility limitations are also identified as the cause of a reaction induction period and an origin of the rate-and-reproducibility advantage obtained by adding THF cosolvent. The subsequent mechanistic model from these data led to a bench-scale reaction optimization, wherein premixing the catalyst components bypasses the catalyst induction period, resulting in a faster reaction. The understanding generated by FLIM thus provides an early example of how visualizing changes in droplet compositions on the microscale during ongoing aqueous-organic reactions can be leveraged for enhancing efficiencies in bench-scale reactions.

High Frequency and Addressable Impedance Measurement System for On-Site Droplet Analysis in Digital Microfluidics

Digital microfluidics is a novel technique for manipulating discrete droplets with the advantages of programmability, small device size, low cost, and easy integration. The development of droplet sensing methods advances the automation control of digital microfluidics. Impedance measurement emerges as a promising technique for droplet localization and characterization due to its non-invasive nature, high sensitivity, simplicity, and cost-effectiveness. However, traditional impedance measurement approaches in digital microfluidics based on the high-voltage actuating signal are limited in sensing accuracy in practical applications. In this paper, we propose a novel droplet impedance sensing system for digital microfluidics by introducing a low-voltage and addressable measurement circuit, which enables impedance measurement over a wide frequency range. The proposed measurement system has also been used for detecting the droplet composition, size, and position in a digital microfluidic chip. The improved impedance sensing method can also promote the applications of the digital microfluidic, which requires high accuracy, real-time, and contactless sensing with automatic sample pretreatment.

Roles of plastoglobules and lipid droplets in leaf neutral lipid accumulation during senescence and nitrogen deprivation.

Upon abiotic stress or senescence, the size and/or abundance of plastid-localized plastoglobules and cytosolic lipid droplets, both compartments devoted to neutral lipid storage, increase in leaves. Meanwhile, plant lipid metabolism is also perturbed, notably with the degradation of thylakoidal monogalactosyldiacylglycerol (MGDG) and the accumulation of neutral lipids. Although these mechanisms are probably linked, they have never been jointly studied, and the respective roles of plastoglobules and lipid droplets in the plant response to stress are totally unknown. To address this question, we determined and compared the glycerolipid composition of both lipid droplets and plastoglobules, followed their formation in response to nitrogen starvation, and studied the kinetics of lipid metabolism in Arabidopsis leaves. Our results demonstrated that plastoglobules preferentially store phytyl-esters, while triacylglycerols (TAGs) and steryl-esters accumulated within lipid droplets. Thanks to a pulse-chase labeling approach and lipid analyses of the fatty acid desaturase 2 (fad2) mutant, we showed that MGDG-derived C18:3 fatty acids were exported to lipid droplets, while MGDG-derived C16:3 fatty acids were stored within plastoglobules. The export of lipids from plastids to lipid droplets was probably facilitated by the physical contact occurring between both organelles, as demonstrated by our electron tomography study. The accumulation of lipid droplets and neutral lipids was transient, suggesting that stress-induced TAGs were remobilized during the plant recovery phase by a mechanism that remains to be explored.

Fluorescence Lifetime Measurement For Studying Evaporation Of Bi-Component Droplet

Sprays are essential in engineering applications like evaporators and combustion chambers. Predicting the evaporation of multi-component liquid droplets is complex due to changing composition and properties. Measuring droplet composition is challenging, with limited non-intrusive methods available. Raman spectroscopy faces hurdles like weak signals and interference. Intensity based Laser-Induced Fluorescence (LIF) requires optical models to interpret data due to varying droplet size and position. Fluorescent dyes in liquid mixtures are sensitive to temperature, complicating measurements. Fluorescence lifetime measurements offer a promising alternative, being an absolute quantity less affected by reabsorption. This study develops a novel method using fluorescence lifetime to analyze droplet composition, leveraging Time-Correlated Single Photon Counting (TCSPC) for precise measurements. Factors such as dye concentration, solvent polarity, and temperature sensitivity are investigated. Calibration curves for ethanol-water mixtures correlate fluorescence lifetime with volume fraction. Experimental setups use TCSPC and femtosecond lasers for dye excitation. Results show that fluorescence lifetime decreases linearly with solvent polarity and is influenced by temperature and dye concentration. High dye concentrations cause self-quenching, altering temperature sensitivity. The method was applied to study the evaporation of ethanol-water droplets under acoustic levitation. Findings indicate that evaporation rates slow as the water fraction increases, with initial measurements showing higher water content due to partial evaporation. This research introduces a novel technique for droplet compositional analysis using fluorescence lifetime, providing insights into optimizing measurement accuracy and advancing understanding in engineering and related fields.

Manipulating the duration of picoinjection controls the injected volume of individual droplets.

The ability to add reagents into droplets is required in many microfluidic workflows. Picoinjection can address this need; however, it is unable to control the injection volume for each individual droplet. Here, we present an improved picoinjection method that can inject controlled volumes into individual droplets. We achieve this by adjusting the injection duration for each picoinjection event. This improved picoinjection method can be used to create complex microfluidic workflows that are able to control the biochemical composition of individual droplets.

Child droplet compositions produced by puffing and micro-explosion of two-liquid parent droplets

The paper presents the experimental research findings on the compositions of child droplets produced by puffing and micro-explosion of parent two-liquid droplets. The droplets under study consisted of water and rapeseed oil. The research was carried out with varying concentrations of liquids in droplets, ambient temperatures, heating arrangements and initial sizes of two-liquid droplets. Parent droplets were heated in a flame, in a muffle furnace, and on a heated substrate. Child droplet compositions were identified using Laser Induced Fluorescence. Compositions were separated based on the difference in the fluorescence of liquids in child droplets exposed to laser radiation. Typical distributions of child droplets by size were obtained for water and rapeseed oil during parent droplet fragmentation when there was a group of contributing factors. The child droplet sizes were measured for water and rapeseed oil. Laser Induced Fluorescence was successfully used to identify different liquids in child droplets following the micro-explosive fragmentation of two-liquid droplets. The experimental data were processed to establish functional relationships between the main factors, parameters and integral characteristics of the investigated processes. Dimensionless criterion relationships and mathematical expressions were proposed for transferring the experimental results to different scales and conditions for heating two-liquid droplets. The applicability of this approach was described. Guidelines were provided on developing the proposed approach for heterogeneous compositions of parent droplets.

Electrokinetic Desalting and Salting of Water-in-Oil Droplets.

Droplet-based microfluidic platforms demand modifications to the droplet composition to facilitate reactions and analyses. However, limited techniques exist to modify the droplet contents post their generation. Here, ion transport across two ion-exchange membranes possessing distinct selectivity is employed to introduce ions into (salt) or extract ions from (desalt) water-in-oil droplets. The ion concentration distribution and transport mechanisms are visualized using a precipitation reaction and a charged fluorescent tracer. Furthermore, current measurements reveal characteristic regimes in desalting and salting modes and demonstrate that the rates of ion transport linearly correlate with applied voltage and the ionic strength of the droplets. Importantly, up to 98% desalting efficiency is achieved. This technique advances droplet-based sample preparation through the straightforward manipulation of droplet contents.

Measurement report: Cloud and environmental properties associated with aggregated shallow marine cumulus and cumulus congestus

Abstract. Mesoscale organization of marine convective clouds into linear or clustered states is prevalent across the tropical and subtropical oceans, and its investigation served as a guiding focus for a series of process study flights conducted as part of the Aerosol Cloud meTeorology Interactions oVer the western ATlantic Experiment (ACTIVATE) during summer 2020, 2021, and 2022. These select ACTIVATE flights involved a novel strategy for coordinating two aircraft, with respective remote sensing and in situ sampling payloads, to probe regions of organized shallow convection for several hours. The main purpose of this measurement report is to summarize the aircraft sampling approach, describe the characteristics and evolution of the cases, and provide an overview of the datasets that can serve as a starting point for more detailed modeling and analysis studies. Six flights are described, involving a total of 80 dropsonde profiles that capture the environment surrounding clustered shallow convection. The flights include detailed observations of the vertical structure of cloud systems, comprising up to 20 in situ sampling levels. Four cases involved deepening convection rooted in the marine boundary layer that developed vertically to 2–5 km with varying precipitation amounts, while two cases captured more complex and developed cumulus congestus systems extending above 5 km. In addition to the thermodynamic and dynamic characterization afforded by dropsonde and in situ measurements, the datasets include cloud and aerosol microphysics, trace gas concentrations, aerosol and droplet composition, and cloud and aerosol remote sensing from high-spectral-resolution lidar and polarimetry.

Discovery of a hyperalkaline liquid condensed phase: significance toward applications in carbon dioxide sequestration.

Bicarbonate ion-containing solutions such as seawater, natural brines, bovine serum and other mineralizing fluids have been found to contain hyperalkaline droplets of a separate, liquid condensed phase (LCP), that have higher concentrations of bicarbonate ion (HCO3 -) relative to the bulk solution in which they reside. The existence and unique composition of the LCP droplets have been characterized by nanoparticle tracking analysis, nuclear magnetic resonance spectroscopy, fourier transform infrared spectroscopy, dissolved inorganic carbon analysis and refractive index measurements. Carbon dioxide can be brought into solution through an aqueous reaction to form LCP droplets that can then be separated by established industrial membrane processes as a means of concentrating HCO3 -. Reaction of calcium with the LCP droplets results in calcium carbonate precipitation and mineral formation. The LCP phenomenon may bear on native mineralization reactions and has the potential to change fundamental approaches to carbon capture, sequestration and utilization.

A bicarbonate-rich liquid condensed phase in non-saturated solutions in the absence of divalent cations.

Bicarbonate (HCO3 -) and sodium (Na+)-containing solutions contain droplets of a separate, bicarbonate-rich liquid condensed phase (LCP) that have higher concentrations of HCO3 - relative to the bulk solution in which they reside. The existence and composition of the LCP droplets has been investigated by nanoparticle tracking analysis, nuclear magnetic resonance spectroscopy, refractive index measurements and X-ray pair distribution function analysis. The bicarbonate-rich LCP species is a previously unaccounted-for, ionic phenomenon which occurs even in solutions with solely monovalent cations. Its existence requires re-evaluation of models used to describe and model aqueous solution physicochemistry, especially those used to describe and model carbonate mineral formation.