Experimental Viscosity Data Research Articles

Liquid Viscosity and Surface Tension of Cyclohexane Between 280 and 473 K by Surface Light Scattering

The present study provides experimental data for the liquid viscosity and surface tension of cyclohexane at or close to saturation conditions by surface light scattering between (280 and 473) K. By applying the hydrodynamic theory for surface fluctuations at the vapor–liquid phase boundary, which could be verified experimentally, the liquid viscosity and surface tension were determined simultaneously at macroscopic thermodynamic equilibrium with average relative expanded (k = 2) uncertainties of Ur(η′) = 0.020 and Ur(σ) = 0.012. For both properties, the present measurement results agree well with reference values in the literature which are restricted to a maximum temperature of 393 K for viscosity and 337 K for surface tension. The experimental results from this work contribute to an improved database for the viscosity and surface tension of cyclohexane over a wide temperature range from a temperature close to the melting point up to 473 K.

Thermophysical properties: Viscosity, density, and excess properties of 2-propanol and n-Decane mixtures from 283.15 K to 343.15 K under atmospheric conditions

To study the effects of temperature as well as molecular interaction of a fluid system on the thermophysical properties of 2-propanol and n-Decane binary mixture, the density (ρ), dynamic viscosity (η), speed of sound (u), and refractive index (nD) of pure 2-propanol and n-Decane, along with their binary mixtures, were experimentally measured across the entire compositional range at temperatures from 283.15 to 343.15 K and atmospheric pressure. These experimental measurements helped in the evaluation of various thermophysical properties, such as excess molar volume (vE), coefficient of thermal expansion (αE), and isentropic compressibility (κsE). The experimental dynamic viscosity (η) and density (ρ) data were used to evaluate kinematic viscosity (v) and Gibbs free energy (ΔG) of flow with an equation based on Eyring's absolute state theory, and their corresponding excess properties. The excess properties of the binary mixtures were correlated using a Redlich-Kister type polynomial equation via the least-squares regression method, with fitting parameters determined for the binary system. Moreover, the Prigogine–Flory–Patterson theory (PFP) was utilized to identify the primary molecular interactions contributing to the excess molar volume at 293.15, 308.15, and 323.15 K for the binary mixtures. Additionally, the capability of the Eyring-NRTL model was tested to predict the viscosity as well as vapor-liquid equilibrium (VLE) of the binary system, and the correlated model results agreed with literature data.

Synthesis of Linoleic Acid of Conjugated Isomers from Sesame (Sesamum Indicum) Seed Oil: Its Use and Effect in a Microstructured Product Type Oil-in-Water Emulsion

The development of functional foods is an area of great interest and innovation in the food industry. The use of conjugated linoleic acid (CLA) in food formulations has been growing in recent years due to its multiple health benefits. In this study, conjugated linoleic acid was obtained from sesame oil, and its use in the formulation of oil-in-water food emulsions was evaluated. Conjugated linoleic acid (CLA) was synthesized from the linoleic acid present in sesame oil using the alkaline isomerization method using proplyeneglycol as a solvent. The effect of alkali concentration (NaOH) and reaction time on the conversion of linoleic acid to CLA was evaluated. A 96.6% conversion of CLA was obtained with a NaOH concentration of 7% and a reaction time of 2 h. Emulsions were prepared using CLA as oil phase and soy lecithin, tween 80, carboxymethylcellulose as emulsifying agents. Emulsions with mixtures of carboxymethylcellulose and tween 80 were stable, presenting a non-Newtonian fluid behavior of pseudoplastic type (n<1). The Ostwald-de-Waele model shows an optimal fit to the experimental data of apparent viscosity (R2>0.99 ), and its microstructural characterization shows a homogeneous particle distribution. These results show that the alkaline isomerization process using propylene glycol as a solvent is an excellent alternative for the synthesis of CLA from vegetable oils such as sesame oil and its application in the development of microstructured products such as functional emulsions, and their subsequent application in the development of new food products with beneficial health characteristics.

Rheological Changes in Bio-Based Filaments Induced by Extrusion-Based 3D Printing Process.

In this work, the authors investigated the impact of extrusion-based printing process on the structural characteristics of bio-based resins through rheological measurements. Two commercially available filaments made from unfilled and wood-filled polylactide (PLA) polymers were considered. Three-dimensional specimens were prepared by printing these filaments under various operating conditions, i.e., changing the extruder temperature and printing rate, and examined using time sweep tests. Specific cycle rheological testing was conducted on pelletized filaments to simulate temperature changes in the printing process. The rheological characteristics of unprocessed materials, in terms of storage (G') and loss (G″) moduli, were found to be slightly affected by temperature changes. For a pure polymer, the G' slope at a low frequency decreased over time, showing that the polymer chains evolved from a higher to a lower molecular weight. For wood-filled materials, the G' slope rose over the testing time, emphasizing the formation of a percolated network of structured filler within the matrix. On the other side, the rheological parameters of both materials were strongly impacted by the printing extrusion and the related conditions. At lower nozzle temperatures (200 °C), by decreasing the printing speed, the G' and G″ curves became increasingly different with respect to unprocessed resin; whereas at higher nozzle temperatures (220 °C), the influence of the printing speed was insignificant, and all curves (albeit distant from those of unprocessed matrix) mainly overlapped. Considerations on degradation kinetics of both materials during the printing process were also provided by fitting experimental data of complex viscosity with linear correlation over time.

Proof of concept for a nonadditive stochastic model of supercooled liquids.

The recently proposed nonadditive stochastic model (NSM) offers a coherent physical interpretation for diffusive phenomena in glass-forming systems. This model presents nonexponential relationships between viscosity, activation energy, and temperature, characterizing the non-Arrhenius behavior observed in supercooled liquids. In this work, we fit the NSM viscosity equation to experimental temperature-dependent viscosity data corresponding to 25 glass-forming liquids and compare the fit parameters with those obtained using the Vogel-Fulcher-Tammann (VFT), Avramov-Milchev (AM), and Mauro-Yue-Ellison-Gupta-Allan (MYEGA) models. The results demonstrate that the NSM provides an effective fitting equation for modeling viscosity experimental data in comparison with other established models (VFT, AM, and MYEGA), characterizing the activation energy in fragile liquids, presenting a reliable indicator of the degree of fragility of the glass-forming liquids.

Rheology of Suspensions Thickened by Cellulose Nanocrystals.

The steady rheological behavior of suspensions of solid particles thickened by cellulose nanocrystals is investigated. Two different types and sizes of particles are used in the preparation of suspensions, namely, TG hollow spheres of 69 µm in Sauter mean diameter and solospheres S-32 of 14 µm in Sauter mean diameter. The nanocrystal concentration varies from 0 to 3.5 wt% and the particle concentration varies from 0 to 57.2 vol%. The influence of salt (NaCl) concentration and pH on the rheology of suspensions is also investigated. The suspensions generally exhibit shear-thinning behavior. The degree of shear-thinning is stronger in suspensions of smaller size particles. The experimental viscosity data are adequately described by a power-law model. The variations in power-law parameters (consistency index and flow behavior index) under different conditions are determined and discussed in detail.

Transferable Anisotropic Mie Potential Force Field for Alkanediols.

The development of force fields for polyfunctional molecules, such as alkanediols, requires a careful account of different average intramolecular conformations for gas states compared to dense liquid states, where intra- and intermolecular hydrogen bonds compete. In the present work, the transferable anisotropic Mie (TAMie) potential is extended to 1,n-alkanediols. Using the convention that intramolecular nonbonded interactions up to and including the third neighbor are excluded, all force field parameters developed previously for 1-alcohols were transferred to 1,5-pentanediol and beyond, with good agreement with experimental phase equilibrium data. To obtain trans-gauche ratios of 1,2-ethanediol and 1,3-propanediol that are consistent with experimental results, the propensities for intra- and intermolecular hydrogen bonds had to be balanced. This was achieved by parameterizing the intramolecular dihedral energy functions governing the O-C-C-O and O-C-C-C angles while intramolecular charge-charge interactions were active. All partial charges belonging to a functional group are collected in a charge group and all interactions among two charge groups are evaluated even if they are separated by less than three bonds. With this approach, it is possible to apply the nonbonded parameters from 1-alcohols to alkanediols without further refinement. The agreement with experimental phase equilibrium and shear viscosity data is of similar quality as for the 1-alcohols and the trans-gauche ratio agrees with literature results from spectroscopic measurements and ab initio calculations.

Viscosities and Densities of Binary and Ternary Mixtures of Aliphatic and Polyaromatic Hydrocarbons: Pyrene +1-Methylnaphthalene + Dodecane at T = (293.15 to 343.15) K. Experiment and Modeling.

This work presents new experimental viscosity and density data for aromatic and polyaromatic compounds in binary and ternary pyrene, 1-methylnaphthalene, and dodecane mixtures. The lack of experimental viscosity data for these mixtures requires the development of a new database, which is vital for understanding the behavior of mixtures in more complex systems, such as asphaltenes and fuels. The mixtures proposed in this work have been measured over a temperature range of (293.15 to 343.15) K at atmospheric pressure. Several mixture compositions have been studied at these conditions: 1.0, 2.5, 5.0, 7.5, 10.0, 12.5, and 15.0% pyrene mass fraction. The concentration of pyrene correlates with an increase in the viscosity and density values. At the lowest temperature in binary mixtures, the corresponding values reach 4.4217 mPa·s for viscosity and 1.0447 × 103 kg·m-3 for density, respectively. In ternary mixtures, the introduction of dodecane leads to the lowest maximum values of 3.5555 mPa·s for viscosity and 1.0112 × 103 kg·m-3 for density at the same temperature. The experimental data have been employed for the specific modification of viscosity models. These modifications could facilitate the prediction of the viscosity of mixtures that are more complex than those presented in this work. Various viscosity models have been employed, such as Linear, Ratcliff and Khan, modified UNIFAC-Visco, and Krieger-Dougherty. The settings in the models used reliably reproduce the experiment reliably. However, the Ratcliff model agrees excellently with the experiment, having a low standard deviation (2.0%) compared to other models. Furthermore, a model based on the equation of state of Guo is proposed to predict the viscosity values by modifying the specific parameters and adjusting them to the mixtures proposed in this work. The results from this study are compared to previous work, where pyrene, toluene, and heptane mixtures were analyzed. In this case, we find that the decrease of aggregation grade in the present systems is predicted by the model fixed in this work.

Measurements of density and viscosity of carbon dioxide-loaded and -unloaded nano-fluids: Experimental, genetic programming and physical interpretation approaches

In the present study, the density and viscosity of the CO2-loaded and –unloaded base solution and nano-fluid were experimentally measured and investigated from an intermolecular point of view. Nano-fluids are composed of nano-particles such as Al2O3 (0.1 wt.%), Silica-2-methylimidazole, zinc salt (Si-ZIF-8) (0.02 wt.%), and super activated carbon (SAC) (0.1 wt.%) dispersed in aqueous and hybrid Methyl diethanolamine context (MDEA, 40 wt.%) +Sulfolane (SFL), 30 wt.%) +H2O) Experimental measurements were carried out at the low-temperature ranges 303.15–315.15 K, atmospheric pressure, and three different CO2 loadings. The results show that nanomaterials do not have a significant effect on the density and viscosity of the unloaded suspension; however, the density and viscosity of loaded suspensions and base solvent become more by increasing CO2 concentration. In the case of CO2-loaded fluids, the comparison of the results in the presence and absence of nanoparticles shows that the density of the solution is not much different in the two cases, but the viscosity of CO2-loaded in Si-ZIF-8, SAC, and γ-Al2O3 base nano-fluids in comparison with base solvent shows an increase of 35 % in high CO2 loading, ∼0.3 mol CO2 per mol MDEA. Density and viscosity experimental data were modeled using the Genetic Programming approach. The highest values of absolute average relative deviation (AARD) and root mean square error (RMSE) parameters obtained for modeling data are 3.04 and 0.317, respectively, and the lowest value of regression coefficient (R2) is 0.995, which indicates the appropriate fitting of the results.

Density, Surface Tension, and Viscosity of Molten Ni‐Based Superalloys Using the Maximum Bubble Pressure and Oscillating Crucible Methods

Accurate data on the high‐temperature thermophysical properties, which are density, surface tension, and viscosity, are indispensable for performing high‐precision casting simulations of Ni‐based superalloys. Viscosity is the most important thermophysical property for thermofluidic analysis. However, measuring the viscosity of an alloy, which is lower than that of molten glass, is difficult, and experimental viscosity data are limited. Herein, the density of Ni‐based superalloys is measured using the maximum bubble pressure (MBP) method to determine viscosity. The viscosity is evaluated using the oscillating crucible method. The surface tension is simultaneously measured using the MBP method. In these results, the average density values [kg m−3] of Alloy 65, Alloy 718, Alloy WA, and Alloy 720 are 7.52 × 103, 7.43 × 103, 7.82 × 103, and 7.52 × 103, respectively. The average surface tension values [N m−1] of Alloy 65, Alloy 718, Alloy WA, and Alloy 720 are 1.55, 1.54, 1.47, and 1.51, respectively. The fitting equations of the molten Ni‐based superalloys are as follows. 1) Alloy 65: ; 2) Alloy WA: ; 3) Alloy 720: ; 4) Alloy 718: .

Combined thermodynamic and theoretical study on ether-functionalized ionic liquid mixture systems of [MOEmim][TFSI] with ACN/GBL

Ether-functionalized ionic liquids (ILs) have a higher fluidity and are widely used in a variety of applications due to the introduction of the ether group. In order to better understand the relationship between properties and internal interactions of ether-based ILs, we prepared two ether-functionalized ILs 1–2-methoxyethyl-3-methylimidazolium bis((trifluoromethyl)sulfonyl)imide ([MOEmim][TFSI]) with acetonitrile (ACN) or γ-butyrolactone (GBL) mixture systems, and investigated the changes of their thermodynamic properties and internal interaction behaviors over the entire concentration range. First, the thermodynamic properties such as dynamic viscosity, density and electrical conductivity of the two mixture systems were measured from 288.15 K to 343.15 K. The excess molar volume (VE), and viscosity deviation (Δη) were calculated by using the measured experimental density and dynamic viscosity data, which can provide microscopic information on the interactions. Further, the intermolecular interactions of the mixture systems were evaluated by density functional theory (DFT) calculations. The sigma–profile (σ–profile) provided insight into the hydrogen bonds (H-bonds) and molecular surfaces interactions. We also used molecular dynamics simulations (MD) to study ILs mixtures in many different solvent concentrations, thereby providing a microscopic and macroscopic characterization of fluid structure, molecular aggregation, and intermolecular forces.

Reply to the 'Comment on "Dynamics and rheology of vesicles under confined Poiseuille flow"' by G. Coupier and T. Podgorski, Soft Matter, 2024, 20, DOI: 10.1039/D3SM01679J.

In this answer, we provide our arguments in support of the possibility to observe the single file-organization of red blood cells in microvessels and the resulting unexpectedly weak increase of blood viscosity with increasing hematocrit, the physiological relevance of which was questioned in the comment. The key element is that the equivalent diameter in 3D for the maximal hematocrit corresponding to a single file of red blood cells is about 10 µm and not 20 µm, as in 2D. In addition, the viscosity contrast (ratio between the cell internal and external viscosities) value must be chosen in our 2D simulation in a such a way that the effective viscosity (a linear combination of the internal, external and membrane viscosities) be close to that of a real RBC. Taking these two facts into account, we find a reasonable agreement between our 2D viscosity simulations data and experimental data, despite the crude 2D assumption.

Density and viscosity of choline chloride/ethylene glycol deep eutectic solvent based nanofluid

In the present work, the effects of the SiO2, TiO2 and Al2O3 nanoparticles and temperature on the density and viscosity of choline chloride/ethylene glycol deep eutectic solvent based nanofluids were investigated. The choline chloride/ethylene glycol deep eutectic solvents with 1:2, 1:3 and 1:4 M ratio were used as the base fluid, and the nanofluids with different concentrations of nanoparticles were synthesized. All the nanofluids demonstrated Newtonian behavior. The density and viscosity of the nanofluids were measured from 303.15 K to 353.15 K and at atmospheric pressure. The experimental density and viscosity data were correlated using the model proposed by Sharifpur and Masoumi, respectively. In addition, the density and viscosity enhancement rate of different nanofluids were compared and discussed.

Viscosity, Interfacial Tension, and Density of 2-Propanol and Acetone up to 423 K by Surface Light Scattering and Conventional Methods

Despite the extensive use of 2-propanol and acetone in a wide range of applications in the chemical industry and in energy engineering, there is a lack of experimental data in the literature for their thermophysical properties including viscosity, interfacial tension, and density, especially at elevated temperatures beyond the respective normal boiling points. In the present study, the liquid viscosity and interfacial tension were determined simultaneously by surface light scattering (SLS) with average expanded uncertainties of (1.7 and 0.9)% at or close to saturation conditions for temperatures between (273 and 403) K. Furthermore, capillary viscometry (CV) and vibrating-tube densimetry were employed to measure the liquid viscosity at ambient pressure of 0.1 MPa from (283 to 353) K and the liquid density close to saturation conditions between (278 and 423) K. The obtained density data were used for the evaluation of both SLS and CV experiments. In comparison with literature data, the present density data show agreement for 2-propanol over the entire temperature range. In contrast, deviations of up to 0.5% at the maximum temperature can be found for acetone. For the viscosity and interfacial tension at low temperatures, agreement of the measurement results among each other and with literature data is mostly found. At elevated temperatures, the increasing deviations of the present experimental viscosity and interfacial tension data from recommended correlations indicate a lack of reliable data needed for their development. Overall, this work contributes to an improvement of the database for viscosity, interfacial tension, and density of 2-propanol and acetone over a wide temperature range up to 423 K.

Experimental study on the viscosity of trifluoroiodomethane (R13I1) with polyol ester and polyvinylether lubricating oils

Trifluoroiodomethane (R13I1) has attracted extensive attention because of its excellent environmental protection performance, and can be used as a component of environmentally friendly refrigerant blends. To better understand the cycle performance of R13I1 as a refrigerant, it is necessary to study the thermodynamic properties of the R13I1/lubricating oil mixture. In this work, the viscosities of polyol ester (POE) oil (RL 32H) and polyvinylether (PVE) oil (FVC 32D) saturated with R13I1 were measured at temperatures ranging from 293.15 to 353.15 K and pressures up to 0.6 MPa using a custom equilibrium viscosity system. The viscosities of R13I1/RL 32H and R13I1/FVC 32D showed similar trends with temperature, pressure, and solubility. With the increase of the solubility of R13I1 in the oil, the viscosity of the mixture decreased sharply at first and then tended to be flat. The dissolved R13I1 in oil greatly reduced the viscosity of lubricating oil, and the effect of R13I1 on the viscosity of RL 32H was greater than that of FVC 32D. The experimental viscosity data were correlated using the modified Setchenow-type equation, the Eyring-NRTL model, and the Eyring-MTSM model, and the calculated results of the models were in good agreement with the experimental data.

Viscosity Measurements on Natural Gas: Re-evaluation

Previous experimental viscosity data for natural gas, published by Schley et al. (Int J Thermophys 25:1623, 2004) and originally obtained using a vibrating-wire viscometer in the temperature range between 260 K and 320 K, were re-evaluated after an improved re-calibration. For this purpose, a new reference value for the viscosity of argon at 298.15 K and at zero density, proposed by Vogel et al. (Mol Phys 108:3335, 2010) and further updated by Hellmann (Private communication, University of the Federal Armed Forces Hamburg, Hamburg, 2020), was applied. In addition, the density computed from the measured temperatures and pressures was determined using the equation of state by Kunz and Wagner (J Chem Eng Data 57:3032, 2012) instead of employing a calculation according to the International Standard ISO 12213 nowadays out of date.

Ultrasound and salt reduction effect on physicochemical and rheological properties of meat emulsions.

Power ultrasound and salt reduction effects on meat emulsions' physicochemical and rheological properties were determined. Therefore, meat emulsions with different NaCl concentrations (1, 1.5, 2, and 2.5%) were treated in an ultrasonic bath (40kHz, 200W, & 9.34W/cm2 ) at different times (0, 15, and 45min). Results showed that salt reduction and ultrasound time significantly (p<0.05) affected the cooking loss, water holding capacity, water activity, pH, color, hardness, viscosity, storage modulus (G'), loss modulus (G″), and phase angle δ. Meat emulsions with low salt content (1 and 1.5% NaCl) showed significantly higher values of cooking loss than standard emulsions (2.5% NaCl), while ultrasound duration of 15min reduced the cooking loss (12 to 27%). Hardness, color, pH, and water activity (aw) decreased with salt reduction. Ultrasounds increased the hardness, viscosity, G', and G'' values in reduced-salt meat. The experimental data of apparent viscosity were properly fitted to the mathematical model of Ostwald-de-Waele. Ultrasound increased consistency (k) and decreased flow behavior index (n) in emulsions with 1.5 to 2.5% NaCl. Ultrasound at 15min induced gelation in emulsions with 1.5 and 2.0% NaCl (40 and 20% NaCl reduction). The formulation with 2.0% NaCl was found to be the maximum concentration that did not sacrifice meat emulsion quality. When combined with 15 min of ultrasound, this formulation yielded results comparable to the standard formulation. PRACTICAL APPLICATION: Results contribute to developing reduced-salt meat emulsions using power ultrasounds. Therefore, using ultrasounds allows for a 20% reduction in salt content while maintaining the quality of the meat emulsion.

Thermodynamic evaluation of viscosity behavior for CaO–SiO2–Al2O3–MgO slag systems examined at the temperatures range from 1500 to 1700 °C

This work showed an application of computational tools to understand systematically the behavior of viscosity on CSAM systems relevant to industrial uses. Consequently in this study, the viscosity experimental data obtained from the literature were compared with the thermodynamic calculated results via the software FactSage v.7.3 for melts in CaO–SiO2–Al2O3–MgO slag system with the range of compositions slags cover 0–100 wt% CaO, 0–100 wt% SiO2, 0–100 wt% Al2O3 and 0–15 wt% MgO at temperature ranges of 1500–1700 °C. Using open-source software in Python, the results of viscosity, liquid, and solid fraction of the slag, as a function of composition and temperature, are represented by multiple color maps and by iso-viscosity contours. The results of the viscosity values indicated that the effect of all the oxides in the CSAM slag system follows the well-known behavior trend observed in the literature. Viscosities of the slag were found to increase with increasing SiO2 contents and decrease with increasing basicities (high CaO). The increase in Al2O3 content increases the viscosity values. An increase of 0–15% MgO depolymerized the slag melt and decreases the viscosity. However, above 5% MgO content occur a decrease in the liquid zone (single phase) and a liquid fraction (two-phase region) of the slag. For a constant MgO concentration, the increase in temperature generates an expansion of low-viscosity zones associated with an increase in the liquid phase of the slag. From the comparison between the calculated and experimental viscosities data keeps up within 30% average relative deviation (Δ), the predictions are considered acceptable for viscosity in the CSAM slag system at high temperatures.

Viscosity database for ternary Cu–Cr–X (X=Ni, Si, Zr) alloys based on CALPHAD-type modeling

A viscosity model with composition and temperature dependence for the liquid alloys of the Cu–Cr–X (X = Ni, Si, Zr) systems was developed using the CALPHAD (CALculation of PHAse Diagrams) approach. Based on the critical review of the available experimental data for pure metal viscosity, the viscosities of pure liquid Cu, Cr, Zr, Ni and Si were simulated with the Arrhenius formula. The viscosities of the binary liquid alloys of the Cu–Ni, Cu–Si, Cu–Zr, Cr–Ni, Cr–Si and Ni–Zr systems at different temperatures were evaluated using the CALPHAD-type formalism. The non-linear viscosity behavior resulting from chemical short-range order was described using temperature-dependent binary interaction parameters. The viscosities of the Cu–Cr and Cr–Zr liquid alloys were predicted employing the Hirai equation. The viscosities of the Cu–Cr–Zr, Cu–Cr–Ni and Cu–Cr–Si ternary liquids were directly extrapolated using the Redlish-Kister-Muggianu equation from the parameters of the binary systems. A comprehensive understanding of the temperature-composition-solidification phase-viscosity relationship was established for ternary melts. The satisfactory agreement observed between calculations and experimental data validates the use of CALPHAD-type viscosity modeling, supporting the suitability of the constructed viscosity database for predicting the viscosity of high-performance Cu-based alloys.

Recent Developments in the Viscosity Modeling of Concentrated Monodisperse Emulsions.

Emulsions form a large group of food materials. Many foods are either partly or wholly emulsions or are in the form of emulsion at some stage of the production process. A good understanding of the rheological properties of emulsions, especially their shear viscosity, is essential in the design, formulation, and processing of food emulsions. The texture and mouthfeel of food emulsions are also largely influenced by emulsion viscosity. Therefore, it is of practical importance to be able to correlate and predict emulsion viscosity as a function of droplet concentration and other relevant variables. In this article, the recent developments made in the viscosity modeling of concentrated emulsions are reviewed. The viscosity models for concentrated emulsions published in the twenty-first century are discussed, compared, and evaluated using a large body of experimental viscosity data available on emulsions. The effects of droplet size distribution and capillary number on the viscosity of concentrated emulsions are also discussed in detail. A new generalized viscosity model is developed for concentrated emulsions that includes the effect of capillary number and is accurate with small average percent relative error (within 3%).