Monitoring Aqueous Sucrose Solutions Using Droplet Microfluidics: Ice Nucleation, Growth, Glass Transition, and Melting.

Freezing and freeze-drying processes are commonly used to extend the shelf life of drug products and to ensure their safety and efficacy upon use. When designing a freezing process, it is beneficial to characterize multiple physicochemical properties of the formulation, such as nucleation rate, crystal growth rate, temperature and concentration of the maximally freeze-concentrated solution, and melting point. Differential scanning calorimetry has predominantly been used in this context but does have practical limitations and is unable to quantify the kinetics of crystal growth and nucleation. In this work, we introduce a microfluidic technique capable of quantifying the properties of interest and use it to investigate aqueous sucrose solutions of varying concentration. Three freeze-thaw cycles were performed on droplets with 75-µm diameters at cooling and warming rates of 1 °C/min. During each cycle, the visual appearance of the droplets was optically monitored as they experienced nucleation, crystal growth, formation of the maximally freeze-concentrated solution, and melting. Nucleation and crystal growth manifested as increases in droplet brightness during the cooling phase. Heating was associated with a further increase as the temperature associated with the maximally freeze-concentrated solution was approached. Heating beyond the melting point corresponded to a decrease in brightness. Comparison with the literature confirmed the accuracy of the new technique while offering new visual data on the maximally freeze-concentrated solution. Thus, the microfluidic technique presented here may serve as a complement to differential scanning calorimetry in the context of freezing and freeze-drying. In the future, it could be applied to a plethora of mixtures that undergo such processing, whether in pharmaceutics, food production, or beyond.

A unified surface tension model for multi-component salt, organic, and surfactant solutions.

Despite the fact that the surface tension of liquid mixtures is of great importance in numerous fields and applications, there are no accurate models for calculating the surface tension of solutions containing water, salts, organic, and amphiphilic substances in a mixture. This study presents such a model and demonstrates its capabilities by modelling surface tension data from the literature. The presented equations not only allow to model solutions with ideal mixing behaviour but also non-idealities and synergistic effects can be identified and largely reproduced. In total, 22 ternary systems comprising 1842 data points could be modelled with an overall root mean squared error (RMSE) of 3.09 mN m-1. In addition, based on the modelling of ternary systems, the surface tension of two quaternary systems could be well predicted with RMSEs of 1.66 mN m-1 and 3.44 mN m-1. Besides its ability to accurately fit and predict multi-component surface tension data, the model also allows to analyze the nature and magnitude of bulk and surface non-idealities, helping to improve our understanding of the physicochemical mechanisms that influence surface tension.

Surface tension models for binary aqueous solutions: a review and intercomparison.

The liquid-air surface tension of aqueous solutions is a fundamental quantity in multi-phase thermodynamics and fluid dynamics and thus relevant in many scientific and engineering fields. Various models have been proposed for its quantitative description. This Perspective gives an overview of the most popular models and their ability to reproduce experimental data of ten binary aqueous solutions of electrolytes and organic molecules chosen to be representative of different solute types. In addition, we propose a new model which reproduces sigmoidal curve shapes (Sigmoid model) to empirically fit experimental surface tension data. The surface tension of weakly surface-active substances is well reproduced by all models. In contrast, only few models successfully model the surface tension of aqueous solutions with strongly surface-active substances. For substances with a solubility limit, usually no experimental data is available for the surface tension of supersaturated solutions and the pure liquid solute. We discuss ways in which these can be estimated and emphasize the need for further research. The newly developed Sigmoid model best reproduces the surface tension of all tested solutions and can be recommended as a model for a broad range of binary mixtures and over the entire concentration range.

Homogeneous freezing of water droplets for different volumes and cooling rates.

To understand the crystallization of aqueous solutions in the atmosphere, biological specimens, or pharmaceutical formulations, the rate at which ice nucleates from pure liquid water must be quantified. There is still an orders-of-magnitude spread in the homogeneous nucleation rate of water measured using different instruments, with the most important source of uncertainty being that of the measured temperature. Microfluidic platforms can generate hundreds to thousands of monodisperse water-in-oil droplets, unachievable by most other techniques. However, most microfluidic devices previously used to quantify homogeneous ice nucleation rates have reported high temperature uncertainties, between ±0.3 and ±0.7 K. We use the recently developed Microfluidic Ice Nuclei Counter Zurich (MINCZ) to observe the freezing of spherical water droplets with two diameters (75 and 100 µm) at two cooling rates (1 and 0.1 K min-1). By varying both droplet volume and cooling rate, we were able to probe a temperature range of 236.5-239.3 K with an accuracy of ±0.2 K, providing reliable data where previously determined nucleation rates suffered from large uncertainties and inconsistencies, especially at temperatures above 238 K. From these data and from Monte Carlo simulations, we demonstrate the importance of obtaining a sufficiently large dataset so that underlying nucleation rates are not overestimated at higher temperatures. Finally, we obtain new parameters for a previous parameterisation by fitting to our newly measured nucleation rates, enabling its use in applications where ice formation needs to be predicted.

Gibbsian Thermodynamics of Wenzel Wetting (Was Wenzel Wrong? Revisited).

When a drop is in contact with a rough surface, it can rest on top of the rough features (the Cassie-Baxter state) or it can completely fill the rough structure (the Wenzel state). The contact angle (θ) of a drop in these states is commonly predicted by the Cassie-Baxter or Wenzel equations, respectively, but the accuracy of these equations has been debated. Previously, we used fundamental Gibbsian composite-system thermodynamics to rigorously derive the Cassie-Baxter equation, and we found that the contact line determined the macroscopic contact angle, not the contact area that was originally proposed. Herein, to address the various perspectives on the Wenzel equation, we apply Gibbsian composite-system thermodynamics to derive the complete set of equilibrium conditions (thermal, chemical, and mechanical) for a liquid drop resting on a homogeneous rough solid substrate in the Wenzel mode of wetting. Through this derivation, we show that the roughness must be evaluated at the contact line, not over the whole interfacial area, and we propose a new Wenzel equation for a surface with pillars of equal height. We define a new dimensionless number H = h(1 - λsolid)/R to quantify when the drop's radius of curvature (R) is large enough compared to the size of the pillars for the new Wenzel equation to be simplified (h is the pillar height; λsolid is the line fraction of the spherical cap's circumference that is on the pillars). Our new line-roughness Wenzel equation can be simplified to cos θW = ρ cos θY when H ≪ 1, where ρ is the line roughness. We also perform a thermodynamic free-energy analysis to determine the stability of the equilibrium states that are predicted by our new Wenzel equation.

Comparison of three multi-cryoprotectant loading protocols for vitrification of porcine articular cartilage.

Vitrification is a cryopreservation technique for the long-term storage of viable tissue, but the success of this technique relies on multiple factors. In 2012, our group published a working vitrification protocol for intact human articular cartilage and reported promising chondrocyte recovery after using a four-step multi-cryoprotectant (CPA) loading method that required 570 min. However, this protocol requires further optimization for clinical practice. Herein, we compared three multi-step CPA loading protocols to investigate their impact on chondrocyte recovery after vitrification of porcine articular cartilage on a bone base, including our previous four-step protocol (original: 570 min), and two shorter three-step protocols (optimized: 420 min, and minimally vitrifiable: 310 min). Four different CPAs were used including glycerol, dimethyl sulfoxide, ethylene glycol and propylene glycol. As vitrification containers, two conical tubes (50 ml and 15 ml) were evaluated for their heat transfer impact on chondrocyte recovery after vitrification. Osteochondral dowels were cored into two diameters of 10.0 mm and 6.9 mm with an approximately 10-mm thick bone base, and then allocated into the twelve experimental groups based on CPA loading protocol, osteochondral dowel size, and vitrification container size. After vitrification at -196 °C and tissue warming and CPA removal, samples in all groups were assessed for both chondrocyte viability and metabolic activity. The optimized protocol proposed based on mathematical modelling resulted in similar chondrocyte recovery to our original protocol and it was 150 min shorter. Furthermore, this study illustrated the role of CPA permeation (dowel size) and heat transfer (container size) on vitrification protocol outcome.

Using engineering models to shorten cryoprotectant loading time for the vitrification of articular cartilage.

Osteochondral allograft transplantation can treat full thickness cartilage and bone lesions in the knee and other joints, but the lack of widespread articular cartilage banking limits the quantity of cartilage available for size and contour matching. To address the limited availability of cartilage, vitrification can be used to store harvested joint tissues indefinitely. Our group's reported vitrification protocol [Biomaterials 33 (2012) 6061-6068] takes 9.5 h to load cryoprotectants into intact articular cartilage on bone and achieves high cell viability, but further optimization is needed to shorten this protocol for clinical use. Herein, we use engineering models to calculate the spatial and temporal distributions of cryoprotectant concentration, solution vitrifiability, and freezing point for each step of the 9.5-h protocol. We then incorporate the following major design choices for developing a new shorter protocol: (i) all cryoprotectant loading solution concentrations are reduced, (ii) glycerol is removed as a cryoprotectant, and (iii) an equilibration step is introduced to flatten the final cryoprotectant concentration profiles. We also use a new criterion-the spatially and temporally resolved prediction of solution vitrifiability-to assess whether a protocol will be successful instead of requiring that each cryoprotectant individually reaches a certain concentration. A total cryoprotectant loading time of 7 h is targeted, and our new 7-h protocol is predicted to achieve a level of vitrifiability comparable to the proven 9.5-h protocol throughout the cartilage thickness.

Gibbsian Thermodynamics of Cassie-Baxter Wetting (Were Cassie and Baxter Wrong? Revisited).

Over the past decade, there has been a debate over the correct form of the Cassie-Baxter equation, which describes the expected contact angle of a liquid drop on a heterogeneous surface. The original Cassie-Baxter equation uses an area fraction of each solid phase calculated over the entirety of the surface, and its derivation is based on an assumption not all surfaces necessarily satisfy. Herein, we introduce fundamental Gibbsian composite-system thermodynamics as a new approach for deriving the complete set of equilibrium conditions for a liquid drop resting on a heterogeneous multiphase solid substrate. One of the equilibrium conditions is a form of the Cassie-Baxter equation that uses a line fraction determined at the contact line outlining the perimeter of the solid-liquid contact area. We elucidate the practical implications of using the line fraction for common patterns of heterogeneities.

Model for the Surface Tension of Dilute and Concentrated Binary Aqueous Mixtures as a Function of Composition and Temperature.

Surface tension dictates fluid behavior, and predicting its magnitude is vital in many applications. Equations have previously been derived to describe how the surface tension of pure liquids changes with temperature, and other models have been derived to describe how the surface tension of mixtures changes with liquid-phase composition. However, the simultaneous dependence of surface tension on temperature and composition for liquid mixtures has been less studied. Past approaches have required extensive experimental data to which models have been fit, yielding a distinct set of fitting parameters at each temperature or composition. Herein, we propose a model that requires only three fitting procedures to predict surface tension as a function of temperature and composition. We achieve this by analyzing and extending the Shereshefsky (J. Colloid Interface Sci. 1967, 24 (3), 317-322), Li et al. (Fluid Phase Equilib. 2000, 175, 185-196), and Connors-Wright (Anal. Chem. 1989, 61 (3), 194-198) models to high temperatures for 15 aqueous systems. The best extensions of the Shereshefsky, Li et al., and Connors-Wright models achieve average relative deviations of 2.11%, 1.20%, and 0.62%, respectively, over all systems. We thus recommend the extended Connors-Wright model for predicting the surface tension of aqueous mixtures at different temperatures with the tabulated coefficients herein. An additional outcome of this study is the previously unreported equivalence of the Li et al. and Connors-Wright models in describing experimental data of surface tension as a function of composition at a single temperature.

Thermodynamic Study of the Role of Interface Curvature on Multicomponent Vapor-Liquid Phase Equilibrium.

The effect of interface curvature on phase equilibrium has been much more studied for single-component than multicomponent systems. We isolate the effect of curvature on multicomponent vapor-liquid equilibrium (VLE) phase envelopes and phase composition diagrams using the ideal system methanol/ethanol and the nonideal system ethanol/water as illustrative examples. An important finding is how nanoscale interface curvature shifts the azeotrope (equal volatility point) of nonideal systems. Understanding of the effect of curvature on VLE can be exploited in future nanoscale prediction and design.

Cryoprotectant kinetic analysis of a human articular cartilage vitrification protocol.

We recently published a protocol to vitrify human articular cartilage and a method of cryoprotectant removal in preparation for transplantation. The current study's goal was to perform a cryoprotectant kinetic analysis and theoretically shorten the procedure used to vitrify human articular cartilage. First, the loading of the cryoprotectants was modeled using Fick's law of diffusion, and this information was used to predict the kinetics of cryoprotectant efflux after the cartilage sample had been warmed. We hypothesized that diffusion coefficients obtained from the permeation of individual cryoprotectants into porcine articular cartilage could be used to provide a reasonable prediction of the cryoprotectant loading and of the combined cryoprotectant efflux from vitrified human articular cartilage. We tested this hypothesis with experimental efflux measurements. Osteochondral dowels from three patients were vitrified, and after warming, the articular cartilage was immersed in 3 mL X-VIVO at 4 °C in two consecutive solutions, each for 24 h, with the solution osmolality recorded at various times. Measured equilibrium values agreed with theoretical values within a maximum of 15% for all three samples. The results showed that diffusion coefficients for individual cryoprotectants determined from experiments with 2-mm thick porcine cartilage can be used to approximate the rate of efflux of the combined cryoprotectants from vitrified human articular cartilage of similar thickness. Finally, Fick's law of diffusion was used in a computational optimization to shorten the protocol with the constraint of maintaining the theoretical minimum cryoprotectant concentration needed to achieve vitrification. The learning provided by this study will enable future improvements in tissue vitrification.

Vitrification of particulated articular cartilage via calculated protocols.

Preserving viable articular cartilage is a promising approach to address the shortage of graft tissue and enable the clinical repair of articular cartilage defects in articulating joints, such as the knee, ankle, and hip. In this study, we developed two 2-step, dual-temperature, multicryoprotectant loading protocols to cryopreserve particulated articular cartilage (cubes ~1 mm3 in size) using a mathematical approach, and we experimentally measured chondrocyte viability, metabolic activity, cell migration, and matrix productivity after implementing the designed loading protocols, vitrification, and warming. We demonstrated that porcine and human articular cartilage cubes can be successfully vitrified and rewarmed, maintaining high cell viability and excellent cellular function. The vitrified particulated articular cartilage was stored for a period of 6 months with no significant deterioration in chondrocyte viability and functionality. Our approach enables high-quality long-term storage of viable articular cartilage that can alleviate the shortage of grafts for use in clinically repairing articular cartilage defects.

Osmometric Measurements of Cryoprotective Agent Permeation into Tissues.

Quantification of the amount of cryoprotective agent (CPA) in a tissue is an essential step in the design of successful cryopreservation protocols. This chapter details two inexpensive methods to measure cryoprotective agent permeation into tissues as functions of time. One of the methods to measure the CPA permeation is to permeate a series of tissue samples from a surrounding solution at a specified concentration of CPA, each sample for a different amount of time, and then to quantitate the amount of CPA that was taken up in the tissue during that time period. The quantification is performed by equilibrating the permeated tissue with a surrounding solution and then measuring the osmolality of the solution to determine the amounts of CPAs that have come out of each tissue sample corresponding to each permeation time. An alternative method to measuring the CPA permeation as a function of time, which requires fewer tissue samples, is to measure the CPA efflux as a function of time. In the efflux method, a CPA-permeated tissue sample is placed in a surrounding solution, and solution samples are taken at different time points throughout the efflux to quantitate how much CPA has left the tissue by each time point.

How Surfactants Affect Droplet Wetting on Hydrophobic Microstructures.

Surfactants, as amphiphilic molecules, adsorb easily at interfaces and can detrimentally destroy the useful, gas-trapping wetting state (Cassie-Baxter, CB) of a drop on superhydrophobic surfaces. Here, we provide a quantitative understanding of how surfactants alter the wetting state and contact angle of aqueous drops on hydrophobic microstructures of different roughness (r) and solid fraction (ϕ). Experimentally, at low surfactant concentrations (C), some drops attain a homogeneous wetting state (Wenzel, W), while others attain the CB state whose large contact angles can be predicted by a thermodynamic model. In contrast, all of our high-C drops attain the Wenzel state. To explain this observed transition, we consider the free energy and find that, theoretically, for our surfaces the W state is always preferred, while the CB state is metastable at low C, consistent with experimental results. Furthermore, we provide a beneficial blueprint for stable CB states for applications exploiting superhydrophobicity.

Isobaric Vapor-Liquid Phase Diagrams for Multicomponent Systems with Nanoscale Radii of Curvature.

At any given temperature, pressure, and composition, a compound or a mixture of compounds will exist either in a single phase, whether solid, liquid, or vapor, or in a combination of these phases coexisting in equilibrium. For multiphase systems, it is known that the geometry of the interface impacts the equilibrium state; this effect has been well-studied in single component systems with spherical interfaces. However, multicomponent phase diagrams are usually calculated assuming a planar interface between phases. Recent experimental and theoretical work has started to investigate the effect of curved interfaces on multicomponent phase equilibrium, but these analyses have been limited to isothermal conditions or to a portion of the isobaric phase diagram. Herein, we consider complete vapor-liquid phase diagrams (both bubble and dew lines) under isobaric conditions. We use Gibbsian composite-system thermodynamics to derive the equations governing vapor-liquid equilibrium for systems with a spherical interface separating the phases. We validate our approach by comparing the predicted nitrogen/argon dew points with reported literature data. We then predict complete isobaric phase diagrams as a function of radius of curvature for an ideal methanol/ethanol system and for a nonideal ethanol/water system. We also determine how the azeotropic composition of ethanol/water changes. The effect of curvature on isobaric phase diagrams is similar to that seen on isothermal phase diagrams. This work extends the study of curved-interface multicomponent phase equilibrium to isobaric systems, expanding the conditions under which nanoscale systems, such as nanofluidic systems, shale gas reservoirs, and cloud condensation nuclei, can be understood.