Shear-dependent Viscosity Research Articles

FSI modeling and simulation of blood viscosity impacts on cavitation in mechanical heart valves

Heart valve replacements are critical for patients with valve malfunctions, and the tri-leaflet mechanical heart valve (tMHV) is one of the most durable options available. The tMHV is used to replace malfunctioning heart valves, restoring normal blood flow with exceptional durability, often lasting up to 20 years without needing replacement. This durability makes tMHVs particularly suitable for patients under 60. However, mechanical issues like cavitation can undermine the valve's functionality, posing risks to both its longevity and the overall efficacy of cardiovascular treatments. While previous studies have investigated some aspects of cavitation in these valves, the combined effects of blood viscosity and fluid-structure interaction (FSI) on cavitation dynamics remain insufficiently explored.This work models and numerically simulate the influence of blood viscosity on cavitation within tMHVs, using FSI principles. A detailed geometric model of the tMHV was developed, incorporating experimental data and non-Newtonian fluid behaviour to accurately replicate blood flow. Simulations were conducted in ANSYS Fluent R1® using a transient solver to capture the dynamic FSI, with the Carreau-Yasuda model representing blood's shear-dependent viscosity. Cavitation was observed at pressures as low as 4.5 Pa—well below the 15-20 Pa range typically reported—indicating a higher vulnerability than previously recognized. The simulations further showed significant vapour bubble formation, with the maximum vapour volume fraction reaching 0.953. High-speed leakage flows, peaking at 11 m/s during valve closure, were also noted, considerably exceeding velocities observed in earlier studies.These findings demonstrate that cavitation occurs when blood pressure drops below vapour pressure, causing vapour bubbles to form. These bubbles generate shock waves that can damage the valve surfaces and surrounding tissue. Insights from this study will aid in the design of next-generation tMHVs with optimised flow dynamics, potentially reducing cavitation risks and enhancing patient outcomes by minimising valve-associated complications.

Effects of a typical shear dependent viscosity on analytical elastohydrodynamic lubrication film thickness predictions: A critical issue for the classical approach

Many engineering estimates of the film thickness in the concentrated contacts of real machines have come from extrapolations of measurements of elastohydrodynamic lubrication film thickness performed in glass on steel elastohydrodynamic rigs. Such estimates are likely to have large errors due to shear dependence of viscosity. The classical film thickness formulas employed have not been validated except for some Newtonian reference liquids at room temperature because the real pressure-viscosity response measured in viscometers has been ignored. A blend of polyalpha olefin base oils with mild shear-thinning has been employed in a line contact calculation to assess the effects of shear-dependent viscosity on the power-law exponents of the classical film thickness formula. The exponents on the pressure-viscosity coefficient and on the elastic modulus of the solids are not sensitive to the non-Newtonian effect. The exponents on ambient pressure viscosity and velocity are slightly reduced by shear-thinning. The exponents on pressure and scale are substantially increased by the shear dependence. The usual practice of measuring film thickness in an elastohydrodynamic rig to obtain an effective “[Formula: see text]-value” to use in a classical Newtonian film thickness formula will overstated the film thickness of a liquid which is shear dependent in the elastohydrodynamic lubrication inlet.

Lattice Boltzmann method for studying dynamics of single rising bubble in shear-thickening power-law fluids

Bubble motion in non-Newtonian fluids is widely present in various industrial processes such as crude oil extraction, enhancement of boiling heat transfer, CO<sub>2</sub> sequestration and wastewater treatment. System containing non-Newtonian liquid, as opposed to Newtonian liquid, has shear-dependent viscosity, which can change the hydrodynamic characteristics of the bubbles, such as their size, deformation, instability, terminal velocity, and shear rate, and ultimately affect the bubble rising behaviors. In this work, the dynamic behavior of bubble rising in a shear-thickened fluid is studied by using an incompressible lattice Boltzmann non-Newtonian gas-liquid two-phase flow model. The effects of the rheological exponent <i>n</i>, the Eötvös number (<i>Eo</i>), and the Galilei number (<i>Ga</i>) on the bubble deformation, terminal velocity, and the shear rate are investigated. The numerical results show that the degree of bubble deformation increases as <i>Eo</i> grows, and the effect of <i>n</i> on bubble deformation degree relates to <i>Ga</i>. On the other hand, the terminal velocity of the bubbles increases monotonically and nonlinearly with <i>Ga</i> for given <i>Eo</i> and <i>n</i>, and the effect of <i>n</i> on the terminal velocity of the bubbles turns stronger as <i>Ga</i> increases. When <i>Ga</i> is fixed and small, the terminal velocity of the bubble increases and then decreases with the increase of <i>n</i> at small <i>Eo</i>, and increases with the increase of <i>n</i> when <i>Eo</i> is large; but when <i>Ga</i> is fixed and large, the terminal velocity of the bubbles increases with the increase of <i>n</i> in a more uniform manner. In addition, regions with high shear rates can be found near the left end and right end of the bubble. The size of these regions grows with <i>Eo</i> and <i>Ga</i>, exhibiting an initial increase followed by a decrease as <i>n</i> increases. Finally, the orthogonal experimental method is used to obtain the influences of the aforementioned three factors on the shear rate and terminal velocity. The order of influence on shear rate is <i>n</i>, <i>Ga</i> and <i>Eo</i> which are arranged in descending order. For the terminal velocity, <i>Ga</i> has the greatest influence, followed by <i>n</i>, and <i>Eo</i> has the least influence.

Abstract 12955: Shear-Dependent Changes in Blood Viscosity Negatively Affect Energetic Efficiency in Patient-Specific Models of the Fontan Circulation

Introduction: Since blood flow through the lungs is passive in patients with the Fontan circulation, cardiac output is sensitive to power loss through the pulmonary vasculature. Prior small in vitro studies of how changes in blood viscosity at venous shear rates (“non-Newtonian behavior”) affect power loss have yielded conflicting results. The purpose of this study was to evaluate the extent to which non-Newtonian behavior contributes to power loss in a large number of pediatric patient-specific models of the Fontan circulation. Hypothesis: Shear-dependent changes in blood viscosity cause increased power loss in the low-shear Fontan circulation. Methods: Pulmonary vascular geometry was segmented from clinical cardiac MRI images. Pressure and velocity fields were then calculated using computational fluid dynamic simulations. Cardiac index was set at 2 L/min/m2 to simulate a low cardiac output state. A constant viscosity model (“Newtonian”) was compared to a shear-dependent viscosity model (“non-Newtonian”). Power loss was calculated by simplified power loss (using bulk flow and pressure changes) and viscous dissipation rate (using element-wise shear rates and viscosities). Both metrics were indexed to adjust for cardiac output and body surface area. Wilcoxon signed-rank test was used to compare differences between the two viscosity models. Results: Twenty patients (mean 10.9 years, 35% female) were included. Mean viscosity was nearly 10-fold higher in the non-Newtonian vs. Newtonian simulations (mean non-Newtonian to Newtonian viscosity ratio 9.7, SD 0.6). Accordingly, power loss by both metrics was significantly larger for the non-Newtonian simulations ( Figure ). Conclusions: Shear-dependent increases in blood viscosity cause increased power loss in computational models of the Fontan circulation under low cardiac output conditions. Further studies are needed to evaluate the degree to which this correlates with clinical outcomes.

Comment on Neupert, T.; Bartel, D. Evaluation of Various Shear-Thinning Models for Squalane Using Traction Measurements, TEHD and NEMD Simulations. Lubricants 2023, 11, 178

The field of EHL (elastohydrodynamic lubrication) may be the only one in science in which a model for shear-dependent viscosity would be evaluated by means other than viscometer measurements [...]

Observation of a Large Slip Effect in the Nanoscale Flow of Highly Viscous Supercooled Liquid Metals.

Understanding and controlling the flow of materials confined in channels play important roles in science and engineering. The general no-slip boundary condition will result in it being more challenging to drive the flow as the channel size decreases to the nanoscale, especially for highly viscous liquids. Here, we report the observation of a large boundary slip in the nanoscale flow of highly viscous supercooled liquid metals (with viscosities of ≲108 Pa s), enabled by the hydrophobic treatment of smooth nanochannels. The slip length significantly depends on the pressure, which can be rationalized by the shear-dependent viscosity. Our findings provide not only new insights into the field of nanofluidics but also a practical technique for resolving the challenge in the net formation of highly viscous supercooled liquid metals at the nanoscale.

Flow modeling and in situ viscosity monitoring for a combined rotational and pressure-driven flow of a non-Newtonian fluid through a concentric annulus

Based on the energy dissipation rate, we proposed a systematic method for quantifying the effective viscosity, effective shear rate, and flow characteristics in a drilling flow of non-Newtonian fluids in a concentric annulus subjected to a combined pressure-driven and rotational flow. Two flow parameters, i.e., the energy dissipation rate coefficient and the effective shear rate coefficient, were introduced to quantify flow characteristics, such as the relationship between pressure drop, flow rate, torque, and rotational speed, which are nearly independent of rheological behaviors. In this work, we began with flow quantification of the individual flow problem in a concentric annulus, i.e., pressure-driven flow and rotational flow, and derived expressions of two flow parameters analytically in each case. Then, we established the flow quantification method for the combined pressure-driven and rotational flow. The proposed flow modeling scheme was derived analytically with a power-law fluid and was validated for various non-Newtonian fluids, such as Carreau and Herschel–Bulkley fluids, through extensive numerical simulations. The method can be employed for the in situ viscosity measurement of drilling muds in terms of shear rate, as well as for the estimation of torque, pressure drop, and power consumption. Maximum errors between theoretical prediction and numerical simulation results in estimating torque, pressure drop, and shear-dependent viscosity were found to be 5.5%, 7.3%, and 6%, respectively.

On the flow of a bubble pair rising in temperature-sensitive gel propellants

The gel propellant is a novel type of propellant created by introducing gelling agents to the liquid propellant. Similar to other types of propellants, the occurrence of air bubbles in the gels is common and unavoidable during the manufacturing and casting process. The presence of bubbles can adversely impact the stable combustion of the engine and may even pose safety hazards when they enter the combustion chamber. In order to gain a better understanding of the bubble interaction within the gel propellant, we have conducted a study on the motion of a pair of bubbles rising in a quiescent water-gel. In this study, the volume of fluid (VOF) method is adopted for modeling the multiphase feature of the flow. The shear and temperature dependent viscosity of the gel has been modeled using the temperature-coupled Carreau–Yasuda model. The effects of various factors, including the initial distance between the bubble pair, bubble diameters, and the temperature, on the motion characteristics of the bubble pair are studied. It is found that an increase in the initial distance leads to a reduction in the bubble interaction; for side-by-side bubble pairs, the bubbles exhibit slower ascent rates and reduced lateral displacement; for inline bubble pairs, the coalescence of the bubble pair becomes slower. Increasing the diameter of the dominant bubble accelerates the coalescence of the bubble pair and the ascent. Elevating the temperature results in a decrease in viscosity, thereby accelerating the coalescence and ascent of inline bubble pairs and producing viscosity reduction around the bubble pair.

Temperature gradient focusing of bio-analyte in a microfluidic channel dealing with non-Newtonian electrolyte considering temperature-dependent zeta potential.

Temperature gradient focusing (TGF) relies on establishing a precise balance between the electrophoretic motility of a target analyte and the advective flow of the background electrolyte (BGE) to locally concentrate the analyte in a microfluidic configuration. This paper presents a finite-element-based numerical analysis where the coupled electric field and the transport equations are solved to describe the effects of the shear-dependent apparent viscosity of a non-Newtonian BGE on the localized concentration buildup of a charged bio-sample inside a microchannel by TGF via Joule heating. Effects of the temperature-dependent nature of the wall zeta potential and the flow behavior index (n) of BGE on the flow, thermal, and species concentration profiles inside the microchannel have been investigated. Study using a fluorescein-Na analyte sample shows that the maximum normalized analyte concentration (Cmax /C0 ) reduces as the zeta potential increases linearly with temperature. The maximum concentration enhancement is achieved when the BGE displays the Newtonian rheology. For example, Cmax /C0 increases 134- to 280-fold when n is increased from 0.8 to 1 (pseudoplastic regime) and again reduces to 190-fold when n increases further from 1 to 1.2 (dilatant regime).

Physical quality of gluten-free doughs and fresh pasta made of amaranth.

Pasta is one of the most consumed foods in the world. Therefore, the development and investigation of the quality parameters of fresh gluten-free pasta made from amaranth was the subject of this study. For this purpose, different doughs (amaranth flour: water 1:2, 1:4, 1:6, 1:8, 1:10) were heat-treated and sodium alginate (1.0 and 1.5%) was added. The pasta was produced by extrusion into a 0.1M calcium L-lactate pentahydrate-containing bath. Both the dough and the pasta were examined. The doughs for its viscosity properties, water content, and color and the pasta for its firmness, color, water content, water absorption, cooking loss, and swelling index. The pasta was cooked for 5, 10, and 15 min for the cooking quality study. A higher alginate content of 1.5% and a higher proportion of amaranth flour resulted in a significant difference in color, water content, and shear-dependent viscosity of the dough (p < .001). It was also found that both doughs with amaranth flour-water content of 1:2 and 1:10 had significant effects on processing properties and pasta quality, especially on firmness, swelling index, and cooking loss. For the doughs with a 1:2 ratio, the high flour content resulted in very soft pasta, and for the doughs with a 1:10 ratio, the high-water content resulted in very firm pasta with a smooth, watery surface. Overall, cooking loss, swelling index, and water absorption were low for the pasta with 1.5% alginate. Even with cooking times of 15 min, the pasta retained its shape.

Thickening Properties of Carboxymethyl Cellulose in Aqueous Lubrication

Increasingly restricted availability and environmental impact of mineral oils have boosted the interest in sustainable lubrication. In this study, the thickening properties of sodium carboxymethyl celluloses (CMCs) were investigated in order to assess their potential as viscosity modifiers in aqueous gear and bearing fluids. The pressure, temperature and shear dependence of viscosity was studied at different concentrations and molecular weights MW. The tribological properties were investigated at different viscosity grades in both sliding and rolling contact, and compared to rapeseed oil and polyethylene glycol 400. The viscosity of the CMC solutions was adjustable to all application-relevant viscosity grades. Viscosity indices were similar or higher compared to the reference fluids and mineral oil. Temporary and permanent viscosity losses increased with MW. Permanent viscosity loss was highest for high MW derivatives, up to 70%. The pressure-viscosity coefficients α were low and showed a high dependency on shear and concentration. In rolling contact, low MW CMC showed up to 35% lower friction values compared to high MW, whereas no improvement of lubricating properties was observed in sliding contact. The results suggest that low MW CMC has great potential as bio-based thickener in aqueous lubrication.

Hofmeister series: An insight into its application on gelatin and alginate-based dual-drug biomaterial design

Alginate and gelatin are bio-polymers widely used in drug delivery. A range of salts can be used to achieve the required flexibility in biomaterial design. Hofmeister series gives an idea about the behaviour of salts with proteins. However, its application for the design of biomaterials and their specific effect on high-viscosity polymers and polymer mixtures has not quite been explored. Firstly, this work proposes a strategic interaction-based approach for designing a dual-drug ocular biomaterial. Secondly, the impact of different salt anions on gelatin and alginate mixture for the developed protocols is studied by a proposed method of determining shear-dependent general intrinsic viscosity. Thirdly, shear-dependent intrinsic viscosity is used to determine the interaction amongst the polymers in their mixture, which is then correlated to the release profiles and hydrodynamic radii of polymer mixtures. It is observed that Hofmeister anions behave reversely for high-viscosity negatively charged polymers and depends on the charge densities of the anions. For the polyelectrolyte/polyampholyte complex/mixture, the interactions depend on the addition sequence. It is inferred that the kosmotropes are preferred for protocols where salt is added between gelatin and alginate and chaotropes for protocols where salt is added to the gelatin and alginate complex/mixture in terms of release profiles.

Rheology dictated spreading regimes of a non-isothermal sessile drop

In the present work, within the framework of thin film theory, we delineate the interaction between the interfacial dynamics of thermal Marangoni flow and non-Newtonian rheology by considering a spreading droplet over a non-isothermal substrate. The numerical simulations, performed at different equilibrium contact angles $(\theta _e)$ , dimensionless thermocapillary strengths $(\beta )$ and shear-dependent viscosities $(n)$ , reveal that the fluid rheology nonlinearly influences the mechanisms of disjoining pressure and Marangoni stress. Accordingly, three distinct spreading regimes for non-Newtonian drops arise. Results indicate that the Marangoni film regime, having an approximate linear drop shape, sustains at lower $\theta _e$ , higher $\beta$ and $n$ ranges. Also, shear-thickening drops display an early onset of thermocapillary time scale and a steeper advancing front, while their shear-thinning counterparts retain a significant curvature for a much longer time. Contrastingly, the droplet regime is identified by fixed shape and uniform speed $(U)$ at higher $\theta _e$ and lower $(\beta$ , $n)$ combinations. Here, an intricate interplay between $\beta$ and $n$ realizes a sharp increase in $U$ for shear thinning compared with its invariance for shear-thickening droplets. The transition regime appears as an intermediate regime between the other two and involves multiple ruptured droplets. In all the regimes, we observe slower (faster) spreading of shear-thinning (thickening) droplets than the Newtonian droplets. In addition, the variations in $n$ cause intense characteristic modulations to spreading attributes like droplet morphology and transient spreading behaviour, and also act as a switching mechanism between different spreading regimes. These unique results may be utilized for superior control of non-isothermal biofluid droplets in microfluidics.

The role of liquid rheological properties on the injection process of a spring-driven autoinjector

Accurate injection time prediction is essential in developing spring-driven autoinjector devices since the drug delivery is expected to finish within seconds to bring convenience, reduce the risk for early lift-off, and provide a consistent experience to users. The Carreau model captures the liquid’s shear-dependent viscosity measured in our experiments. Thus, a quasi-steady model, which uses the Carreau model to describe the liquid’s viscosity, is developed to predict the injection time of spring-driven autoinjectors. Analytical relations between the flow rate and the pressure drop in the needle are also obtained. The Carreau number in the spring-driven autoinjector is greater than one and smaller than a critical value; in this region, using the power-law model to describe the liquid viscosity accurately predicts the injection time, which agrees with the current literature findings. Additionally, a force threshold is identified for the friction force between the plunger and the syringe barrel, beyond which the injection time is infinite. Appreciation of this force threshold can help avoid device stalling and reduce the risk of underdosing. Moreover, the role of liquid’s shear-thinning index on the injection time of spring-driven autoinjectors is quantified. Understanding the shear-thinning index allows formulators to experiment with excipients and pH to enhance confidence in drug/device combination product design and integration. Our experimental and theoretical results can help drug product and device developers with integrated product design and improve the patient experience.

Heat Transfer and Flow of a Gel Fuel in Corrugated Channels

For propulsion systems using gel fuels, reducing the gel fuel viscosity is essential for achieving better atomization and combustion. In this paper, we investigate the flow and heat transfer in a water-gel with a temperature and shear dependent viscosity. We consider several different channels, mimicking the transport of gelled fuels in propulsion systems, and we also look at corrugation, which is a way of enhancing fluid mixing and thus improving the heat transfer characteristics. The rheological parameters in the constitutive model of the gel are fitted with experimental data. The influence of different corrugation profiles, corrugation configuration parameters and the Reynolds number on the mean apparent viscosity and the pressure drop are investigated. It was found that the flow recirculation formed in the valley of the corrugations enhances the heat transfer and thus the temperature of the main flow. We also noticed an increase in the pressure drop due to the stronger viscous dissipation. Furthermore, it was observed that the sinusoidal corrugation can achieve lower viscosity with a lower pressure drop compared with triangular and trapezoidal corrugations. A shorter wavelength and a deeper wave amplitude of the corrugation seemed to be better for reducing the gel fuel viscosity, while we must consider the adverse consequence of increased pressure drop. A larger Reynolds number was helpful for both lowering the pressure drop and for reducing the viscosity. In addition, compared with a smooth straight pipe, a Y-shape corrugated channel with a constant inlet velocity reduced the mean apparent viscosity by 70.8%, and this value increased to 72.6% by further applying a pulsed inlet velocity, which can greatly enhance the gel fuel atomization and thus improve the combustion efficiency.

A discussion of Yu, M., Zhang, J., Joedicke, A., & Reddyhoff, T. (2021). Experimental investigation into the effects of diesel dilution on engine lubrication. Tribol. Int., 156, 106828

The recent rapid progress in the understanding and prediction of film thickness in elastohydrodynamic lubrication (EHL) has been the result of a shift in method from the classical treatment of viscosity as an adjustable parameter to measuring viscosity in viscometers. See for example, Hooke et al. (2021) [1]. For researchers outside of EHL the latter method would appear to be the obvious best approach. However, measuring shear-dependent viscosity in lubricating oils is fraught with great difficulty because there are other phenomena which appear to be constitutive behavior. For example, viscous heating appears in viscometers as the decrease in viscosity with increasing shear rate and in many viscometers this was accurately described by the sinh-law model. The lack of understanding of thermal feedback in viscometers resulted in much wasted effort in EHL friction.

Weak solution of a stochastic 3D nonlocal Cahn–Hilliard–Navier–Stokes systems with shear-dependent viscosity

We consider the stochastic nonlocal Cahn–Hilliard–Navier–Stokes system with shear-dependent viscosity on a bounded domain , d = 2, 3, driven by a multiplicative noise of Lévy and Gaussian types. The velocity u is governed by a Navier–Stokes system with a shear-dependent viscosity controlled by a power p>2. This system is nonlinearly coupled through the Korteweg force with a convective nonlocal Cahn–Hilliard equation for the order parameter φ. The existence of a global weak martingale solution is proved. In the 2D case, we prove the pathwise uniqueness of the weak solution, when .

Computational analysis of one-dimensional models for simulation of blood flow in vascular networks

The paper is devoted to the comparison of one-dimensional models, used for the simulation of blood flow in elastic vessels. The inviscid, Newtonian, and non-Newtonian models of blood are considered. The one-dimensional non-Newtonian models, corresponding to widely-used rheological models with shear-dependent viscosity (Power Law, Carreau, Carreau–Yasuda, Cross, simplified Cross, modified Cross, Powell–Eyring, modified Powell–Eyring, Yeleswarapu, modified Yeleswarapu, and Quemada) are presented.The attention is focused on the investigation of the influence of viscosity, shape factor, velocity profile, non-Newtonian viscosity, and hematocrit. In the numerical experiments, the models of arterial systems with twenty and thirty-seven vessels are considered. It is demonstrated, that for the vessels near the heart the effect of viscosity can be considered as inessential, and an inviscid model can be used. The main effect on the relative deviations of solutions, obtained by different models, is realized by the velocity profile. The effect of non-Newtonian viscosity is not so essential, but can be taken into account for the models with peripheral vessels.

Cartesian grid method with a consistent direct discretization approach for numerical simulation of non-Newtonian fluid flow

This paper proposes an extended version of the discretization scheme for a consistent direct discretization approach in a Cartesian grid method for flow simulations of incompressible non-Newtonian fluids. Based on the concept of the original method, which was developed for Newtonian fluid flow, the Navier–Stokes and the pressure Poisson equations are discretized directly in the vicinity of a solid boundary while maintaining the consistency between the velocity and pressure fields. The main difficulty in the discretization arises from the evaluation of the velocity gradients on the fluid–solid interface, which is necessary for handling the viscous term for spatially distributed shear-dependent viscosity. In the extended method, a new procedure for the calculation of the velocity gradient using the relation that holds on a rigidly moving solid surface is proposed. The validity of the method is ascertained in fundamental test problems of non-Newtonian fluids: laminar Poiseuille/Couette flows in a concentric annulus and flows around a circular cylinder. It is found that a second-order spatial accuracy with the desired numerical stability is achieved in both the shear-thinning and shear-thickening viscous properties, and the numerical error is considerably decreased compared with some conventional methods. As a realistic application of the extended method, a polymer mixing simulation inside a co-rotating twin-screw extruder is demonstrated by applying the method to the moving boundary problem. In a screw arrangement with a sequential combination of a kneading disk (KD), a cylindrical ring (CR), and a backward mixing screw (BMS), large- and small-scale structures of bifurcating and converging flows are respectively formed in the KD and BMS zones, whereas elongational flow structures and velocity fluctuations are still maintained in the CR zone due to flow interaction with the upstream and downstream screw elements, which presumably contributes to moderate mixing at low shear stress. • A Cartesian grid method for non-Newtonian fluid flow is developed. • The present method extends a consistent direct discretization approach. • A procedure for evaluating velocity gradients on an immersed boundary is proposed. • Second order spatial accuracies for velocity and its derivatives are ascertained. • A polymer mixing simulation in a co-rotating twin-screw extruder is demonstrated.

Modeling the shear-dependent viscosity of nonionically stabilized waterborne dispersions

The performance of a rheological model that accounts for the effect of the volume fraction, the particle size distribution, and shear rate on the viscosity of water-borne dispersions stabilized with conventional nonionic surfactants and polymeric stabilizers is assessed. The model that contains three parameters fitted well the experimental data. The parameters were independent of the volume fraction, the particle size distribution, and the shear rate. Furthermore, two of them were not affected by the surfactant type and concentration, and temperature. The other parameter increased with the surfactant molecular weight and surface covering, but decreased with increasing temperature.Graphical