Viscosity of Ionic Liquids: Theories and Models

Ionic liquids (ILs) offer a wide range of promising applications due to their unique and designable properties compared to conventional solvents. Further development and application of ILs require correlating/predicting their pressure-viscosity-temperature behavior. In this review, we firstly introduce methods for calculation of thermodynamic inputs of viscosity models. Next, we introduce theories, theoretical and semi-empirical models coupling various theories with EoSs or activity coefficient models, and empirical and phenomenological models for viscosity of pure ILs and IL-related mixtures. Our modelling description is followed immediately by model application and performance. Then, we propose simple predictive equations for viscosity of IL-related mixtures and systematically compare performances of the above-mentioned theories and models. In concluding remarks, we recommend robust predictive models for viscosity at atmospheric pressure as well as proper and consistent theories and models for P-η-T behavior. The work that still remains to be done to obtain the desired theories and models for viscosity of ILs and IL-related mixtures is also presented. The present review is structured from pure ILs to IL-related mixtures and aims to summarize and quantitatively discuss the recent advances in theoretical and empirical modelling of viscosity of ILs and IL-related mixtures.

Prediction of Dead Oil Viscosity: Machine Learning vs. Classical Correlations

Dead oil viscosity is a critical parameter to solve numerous reservoir engineering problems and one of the most unreliable properties to predict with classical black oil correlations. Determination of dead oil viscosity by experiments is expensive and time-consuming, which means developing an accurate and quick prediction model is required. This paper implements six machine learning models: random forest (RF), lightgbm, XGBoost, multilayer perceptron (MLP) neural network, stochastic real-valued (SRV) and SuperLearner to predict dead oil viscosity. More than 2000 pressure–volume–temperature (PVT) data were used for developing and testing these models. A huge range of viscosity data were used, from light intermediate to heavy oil. In this study, we give insight into the performance of different functional forms that have been used in the literature to formulate dead oil viscosity. The results show that the functional form f(γAPI,T), has the best performance, and additional correlating parameters might be unnecessary. Furthermore, SuperLearner outperformed other machine learning (ML) algorithms as well as common correlations that are based on the metric analysis. The SuperLearner model can potentially replace the empirical models for viscosity predictions on a wide range of viscosities (any oil type). Ultimately, the proposed model is capable of simulating the true physical trend of the dead oil viscosity with variations of oil API gravity, temperature and shear rate.

Comparison of different models to calculate the viscosity of biogas and biomethane in order to accurately measure flow rates for conformity assessment

The study presents an optimised method to correct flow rates measured with a LFE flowmeter pre-set on methane while used for gas mixtures of unknown composition at the time of the measurement. The method requires the correction of the flow rate using a factor based on the viscosity of the gas mixtures once the composition is accurately known. The method has several different possible applications inclusive for the sampling of biogas and biomethane onto sorbent tubes for conformity assessment for the determination of siloxanes, terpenes and VOC in general. Five models for the calculation of the viscosity of the gas mixtures were compared and the models were used for ten binary mixtures and four multi-component mixtures. The results of the evaluation of the different models showed that the correction method using the viscosity of the mixtures calculated with the model of Reichenberg and Carr showed the smallest biases for binary mixtures. For multi-component mixtures, the best results were obtained when using the models of Lucas and Carr.

Temperature Dependence of Protein Solution Viscosity and Protein-Protein Interactions: Insights into the Origins of High-Viscosity Protein Solutions

Protein solution viscosity (η) as a function of temperature was measured at a series of protein concentrations under a range of formulation conditions for two monoclonal antibodies (MAbs) and a globular protein (aCgn). Based on theoretical arguments, a strong temperature dependence for protein-protein interactions (PPI) indicates highly anisotropic, short-ranged attractions that could lead to higher solution viscosities. The semi-empirical Ross-Minton model was used to determine the apparent intrinsic viscosity, shape, and "crowding" factors for each protein as a function of temperature and formulation conditions. The apparent intrinsic viscosity was independent of temperature for aCgn, while a slight decrease with increasing temperature was observed for the MAbs. The temperature dependence of solution viscosity was analyzed using the Andrade-Eyring equation to determine the effective activation energy of viscous flow (E_a,η). While E_a,η values were different for each protein, they were independent of formulation conditions for a given protein. PPI were quantified via the osmotic second virial coefficient (B₂₂) and the protein diffusion interaction parameter (k_D) as a function of temperature under the same formulation conditions as the viscosity measurements. Net interactions ranged from strongly attractive to repulsive by changing formulation pH and ionic strength for each protein. Overall, larger activation energies for PPI corresponded to larger activation energies for η, and those were predictive of the highest η values at higher protein concentrations.

A New Machine-Learning Tool for Fast Estimation of Liquid Viscosity. Application to Cosmetic Oils

The viscosities of pure liquids are estimated at 25 °C, from their molecular structures, using three modeling approaches: group contributions, COSMO-RS σ-moment-based neural networks, and graph machines. The last two are machine-learning methods, whereby models are designed and trained from a database of viscosities of 300 molecules at 25 °C. Group contributions and graph machines make use of the 2D-structures only (the SMILES codes of the molecules), while neural networks estimations are based on a set of five descriptors: COSMO-RS σ-moments. For the first time, leave-one-out is used for graph machine selection, and it is shown that it can be replaced with the much faster virtual leave-one-out algorithm. The database covers a wide diversity of chemical structures, namely, alkanes, ethers, esters, ketones, carbonates, acids, alcohols, silanes, and siloxanes, as well as different chemical backbone, i.e., straight, branched, or cyclic chains. A comparison of the viscosities of liquids of an independent set of 22 cosmetic oils shows that the graph machine approach provides the most accurate results given the available data. The results obtained by the neural network based on sigma-moments and by the graph machines can be duplicated easily by using a demonstration tool based on the Docker technology, available for download as explained in the Supporting Information. This demonstration also allows the reader to predict, at 25 °C, the viscosity of any liquid of moderate molecular size (M < 600 Da) that contains C, H, O, or Si atoms, starting either from its SMILES code or from its σ-moments computed with the COSMOtherm software.

Two new models for viscosity prediction of binary, ternary and higher order liquid mixtures

Two new equations have been proposed for predicting viscosity of binary, ternary and higher order liquid mixtures.

A modified Frenkel approach for viscometric prediction of binary and multicomponent liquid mixtures

Comparison of absolute average percentage deviations (AAPD) values of modified Frenkel with different approaches for binary, ternary and quaternary systems.

Generalization of the Friction Theory for Viscosity Modeling

The friction theory (FT) approach relates the viscosity of a fluid to its equation of state (EoS), and it is known to give good results for a large number of compounds over wide ranges of temperature and pressure. Previous FT versions were restricted to use EoS of the van der Waals type, i.e., EoS explicitly consisting of a repulsive and an attractive term, which limited the number of usable EoS as well as the accuracy of the viscosity predictions. In this work, the restriction is removed by means of a pragmatic generalized definition of repulsive and attractive terms based on the internal pressure concept. As a result, the FT theory can be extended to practically all types of EoS, from theoretical ones (e.g., EoS based on thermostatistical or renormalization theories) to the highly accurate empirical reference EoS. In combination with the later, the FT is shown to represent experimental viscosity data for several fluids, including water, with an accuracy as high as that required for reference models. Additionally, some relevant phenomena, such as the critical anomaly, appear to follow naturally from the physics already built into the EoS.