Modified Cox-Merz Rule Research Articles

Effects of pre-formulation and post-cooking method on the rheological and gelation properties of 3D printed chicken products

This study investigated the influence of oil type (olive, soybean, and peanut oil) and post-cooking methods (oven bake and microwave) on the quality of 3D printed chicken meat products. The Ostwald-de-Waele model was used to describe the flow behavior of chicken meat paste (R2 > 0.995). Oil-fortified groups present significantly lower consistency index (K) and flow behavior index (n), indicating better fluidity. A modified Cox-Merz rule was applied by multiplying angular frequency with shift factors (αSF). Surprisingly, the values of αSF are well-correlated with accuracy parameters of 3D printed cubes (|r| >0.8). For post-heating methods, baking results in higher fluid loss but contributes to a smoother surface. The microwaved gels showed better fluid retention ability and higher accuracy but lost the detail shape of the 3D printing model. Overall, the PO (peanut oil) meat emulsion group presented better textural properties and flat surfaces than other oil-added counterparts.

Rheology and microstructure of discontinuous shear thickening suspensions

We report experimental studies on rheology and microstructure in discontinuous shear thickening of fumed silica suspensions. Formation of particle clusters was observed after the critical shear rate, and their size increases during shear thickening. At higher shear rates, these clusters were found to break down due to strong shear forces, and a continuous decrease in viscosity was observed. The suspension viscosity and the first normal stress difference variation with the shear rate showed similar dependence. The sign of first normal stress difference was negative during shear thickening, which is consistent with the hydrodynamic model of cluster formation. A linear variation of the first normal stress difference with shear rate during shear thickening further indicates its predominant hydrodynamic origin and supports the recent Stokesian dynamics simulation studies on discontinuous shear thickening based on the hydrodynamic model of nonsmooth colloids by Wang et al. [J. Rheol. 64, 379–394 (2020)]. On the other hand, a nonlinear decrease in the first normal stress difference with shear rate in the second shear-thinning region is primarily due to breaking of large clusters into smaller ones and with a possibility of frictional contacts within these hydroclusters. The oscillatory shear measurements were also performed and the samples displayed strain thickening similar to shear thickening. The similarity between the steady and dynamic shear rheology at high strain amplitudes was observed using the modified Cox–Merz rule.

Rheological properties of Indian coffee plum (Flacourtia jangomas) pulp in steady and dynamic shear at different temperatures

ABSTRACT Indian coffee plum (Flacourtia jangomas) is an underutilized fruit with many great nutritional and medicinal value generally available in the northeastern part of India. Although rheological study of different fruit pulps have been studied till now, however no such study has been undertaken on Indian coffee plum. The present study was aimed to evaluate the steady-state shear and viscoelastic rheological properties of Flacourtia jangomas (F. jangomas) pulp as function of temperature in the range 20 to 80°C using dynamic oscillatory viscometry, as well as applicability of Cox-Merz rule. Under steady-state shear tests, the shear stress versus shear rate data were adequately fitted to the Bingham model (R2 = 1) for too low shear rate (0.1to 1.0 s−1) and Power law model (R2 > 0.83) for moderate shear rate (1.0 to 100 s−1). Oscillatory shear data of the fruit pulp showed weak gel behavior where loss modulus exceeded the value of storage modulus. The power modified Cox-Merz rule was tested for all temperature and found applicable for lower temperatures. These results could be beneficial for future studies on food properties and industries.

Pickering emulsion fabricated smart polyaniline/clay composite particles and their tunable rheological response under electric field

Conducting polyaniline (PANI)/attapulgite (ATP) nanocomposite particle was fabricated via Pickering emulsion polymerization and adopted as a candidate material for a polymer/inorganic -based electrorheological (ER) fluid. Scanning electron microscope and transmission electron microscope demonstrated that the PANI were covered compactly with rod-shaped ATP. Flow, viscoelastic, and yielding characteristics of the PANI/ATP ER fluid, where the synthesized particle was dispersed evenly in silicone oil, were assessed by a rotational rheometer under applied external electric field. The PANI/ATP ER fluid was found to exhibited typical ER characteristics, and the flow curves were scaled appropriately using a modified Mason number for a qualitative description of the rheological behavior of the ER fluid. All three different yield stresses measured from different methods showed a conduction mechanism with a slope of 1.5. In addition, complex viscosity determined by both Cox-Merz rule and its modified Cox-Merz rule were compared with shear viscosity measured under a steady-shear condition. The equivalence between the shear and complex viscosities was also appeared in a strain sweep test for this ER fluid.

Applicability of Modified Cox-Merz Rule to Concentrated Suspensions

The present work studied the rheological properties of concentrated non-colloidal aqueous suspensions of graphite particles together with carboxymethyl cellulose (CMC) having various molecular weights, especially focusing on the applicability of the modified Cox-Merz rule. These suspensions were investigated as model slurries to produce anode electrodes of lithium ion batteries. In the case of suspensions containing high molecular weight CMC, the complex viscosity resulting from the measurements of frequency dependence of the viscoelastic moduli at high strain values was in good agreement with the steady state viscosity. That is, the data conformed to the modified Cox-Merz rule. However, the data obtained from suspensions containing low molecular weight CMC did not agree with the modified Cox-Merz rule. The difference in the applicability of this model is considered to be attributed to variations in the ability of the suspensions to recover to a stable state during the application of cyclic strain.

New analysis and correlation between steady and oscillatory tests in fumed silica-based shear thickening fluids

In recent years, the non-Newtonian behavior of shear thickening fluids (STFs) has motivated a sharp increase in the number of studies related to their use for engineering applications. For this reason, rheological characterization of STFs is crucial in order to develop and design new devices based on these novelsmart fluids. Typically, different experiments have been carried out for the rheological characterization of STFs to prove their shear/strain thickening behavior. In order to find an empirical relationship between steady and oscillatory experiments, the modified Cox-Merz rule has been recently used to correlate the results with enormous controversy between authors due to the disparity in the correlations achieved. In this paper, we present an improvement in the correlation between the results obtained in steady and oscillatory tests in STFs using fumed silica-concentrated suspensions. The proposed method with the use of strain sweep oscillatory tests has improved the correlation in all STF regimes (pre-transition, transition, and post-transition) in comparison with the results obtained using the modified Cox-Merz rule, which uses oscillatory frequency sweep tests. This improvement has been experimentally validated using concentrated colloidal suspensions with different concentrations of fumed silica (from 12.5 to 25 wt%). Rheological experiments with shear thickening fluids performed in this article.

Temperature dependence of stability, steady and dynamic rheological properties of oil-in-water emulsions stabilized by gum tragacanth

In this paper, the effects of four different temperatures (5, 25, 37 and 50 °C) on the physical stability and the dynamic and steady-state shear rheological properties of sunflower oil-in-water emulsions prepared with gum tragacanth were investigated. Emulsions showed excellent stability against various instability mechanisms after 150 days storage at 5 and 25 °C. The experimental data had the best fit with power law model (R2 > 0.99). The effect of temperature on power law parameters was determined. The increase of temperature from 5 to 50 °C resulted in 4 times decrease in the flow consistency index, whereas the flow behavior index slightly enhanced with temperature (0.49–0.58). For all samples loss modulus (G″) was higher than the storage modulus (G′) in the low frequency range and G′ increased faster than G″ with frequency enhancement. A modified Cox–Merz rule was valid to emulsion samples using shift factors.

Modeling the rheological properties of currant paste as a function of plasticizers concentration, storage temperature and time and process temperature

The steady and dynamic shear rheological properties of currant paste samples as a function of storage temperature (15, 25 and 35 °C) and time (180 days) and plasticizers content (water and/or glycerol) have been evaluated. Apparent viscosity (ηa) has been found to be significantly increased with prolonged storage, implying possible structural changes, and decreased with the increase in storage temperature and the addition of water or/and glycerol. Flow behavior index and consistency index were determined by fitting the resulting experimental data to a power law equation with high values of correlation coefficients (R2 ≥ 0.912). Furthermore, the combined effect of storage temperature, time and plasticizers concentration on the apparent viscosity was described adequately by a proposed empirical model, with low standard relative errors (SRE ≤ 0.011). Additionally, the viscoelastic properties were significantly affected by all evaluated parameters in the same way as in apparent viscosity while both moduli (G′ and G″) were modeled sufficiently (R2 ≥ 0.884) as power functions of oscillatory frequency. The heat treatment (heating from 25 to 100 °C and cooling back with a rate of 10 °C/min) applied has proved sufficient to reverse the observed storage effects. Moreover, the modified Cox-Merz rule was satisfactorily applied to describe the correlation between the apparent viscosity and the complex viscosity.

Linear viscoelasticity of a dilute active suspension

The linear viscoelasticity of a dilute suspension of active (self-propelled) rigid spheroidal particles is calculated under a small-amplitude oscillatory shear (SAOS) deformation. The imposed shear acts to drive the microstructure of the suspension, as parameterized by the orientational probability distribution function, out of equilibrium. The microstructure relaxes via two independent mechanisms: rotational Brownian motion and correlated tumbling; the combination of which results in an increased rate of stress relaxation, relative to a suspension that relaxes solely by either mechanism. We explicitly calculate the non-equilibrium orientational microstructure due to the SAOS deformation, rotational diffusion, and tumbling. From this, we determine the linear viscoelasticity of the suspension from the orientationally averaged stresslet, which arises from the imposed flow, rotational diffusion, and particle activity (self-propulsion). Next, we demonstrate that a modified Cox-Merz rule is applicable to a dilute, active suspension via a comparison of our linear viscoelasticity results to a theoretical prediction of the steady shear viscosity of active, slender rods (Saintillan, Exp Mech 50(9) 1275–1281, 2010). Finally, through a comparison of our results to experiments on Escherichia coli (Lopez et al., Phys Rev Lett 115(2) 028, 301, 2015), we show that the linear viscoelasticity of an active suspension can be utilized to determine the mechanism of self-propulsion (i.e., pusher or puller), and estimate the strength of self-propulsion and correlation between tumbling events.

Comparison of rheological behaviors with fumed silica-based shear thickening fluids

Shear thickening fluids (STFs) of differing compositions were fabricated and characterised in order to observe the effect of varying chemical and material properties on the resultant rheological behavior. Steady shear tests showed that for a given carrier fluid and particle size exists an optimum weight fraction which exhibits optimal shear thickening performance. Testing also showed that increasing particle size resulted in increased shear thickening performance and its onset whilst altering the carrier fluid chemistry has a significant effect on the thickening performance. An explanation is provided connecting the effect of varying particle size, carrier fluid chemistry and weight fraction to the resultant rheological behavior of the STFs. Two STFs were chosen for further testing due to their improved but contrasting rheological behaviors. Both STFs displayed a relationship between steady and dynamic shear conditions via the Modified Cox-Merz rule at high strain amplitudes (γ≥500%). Understanding the effects of particle and liquid polymer chemistry on the shear thickening effect will assist in ‘tailoring’ STFs for certain potential or existing applications.

Effect of sugar beet fiber concentrations on rheological properties of meat emulsions and their correlation with texture profile analysis

The effect of sugar beet fiber (SBF) concentration on the rheological properties of meat emulsions was determined. In addition, texture profile analysis (TPA) of cooked meat emulsions was carried out to find a possible relationship between the dynamic rheological data and TPA parameters. All studied emulsions exhibited non-Newtonian, pseudoplastic behavior since apparent viscosity decreased with increasing shear rate. The Ostwald–de Waele model was successfully used to describe the flow properties of meat emulsions (R2>0.913). Emulsion systems were characterized as weak gel-like macromolecular dispersions with storage modulus (G′) much greater than loss modulus (G″). A modified Cox–Merz rule was applied by multiplying angular frequency with shift factors (αSF). Material stiffness parameter (Aα) calculated from complex modulus (G*) increased as SBF concentration increased. Significant correlations among the material stiffness data and TPA parameters were observed. It was concluded that TPA parameters could be predicted by using dynamic shear tests, and hence, this will make possible to save time and cost for meat processors when manufacturing a product with acceptable structural or textural characteristics.

The viscoelastic characterisation of thermally-treated waste activated sludge

Compositional change in sewage sludge due to thermal treatment drives rheological changes in the sludge. In this study, the viscoelastic characteristics of waste activated sludge (WAS) was investigated by measuring viscoelastic properties of sludge, the storage (G′) and loss (G″) moduli over 1h thermal treatment at different temperatures ranging from 20 to 80°C as well as after treatment when sludge cooled down to 20°C (thermal history effect). The soluble chemical oxygen demands (COD) was also measured at the same thermal treatment conditions.The results showed a distinctive difference between thermally-treated sludge and raw sludge in transitions from solid-like to liquid-like behaviour. It was observed that thermally induced compositional change in sludge impacted on both viscoelastic properties (G′ and G″) and viscous properties of sludge. Modified Cox-Merz rule (or Rutgers-Delaware) was successfully used to determine the sludge flow curve from the linear viscoelastic measurements of sludge.It was also found that the effect of short-time thermal treatment at high temperature on viscoelastic properties of sludge is similar to the effect of long-time thermal treatment at low temperature. This indicates that the amount of supplied thermal energy was the key controlling parameter of the evolution of rheological properties and the degree of organic matter solubilisation. A linear proportionality was also established between a dimensionless form of the released soluble COD and a dimensionless form of both G′ and G″. This suggests a possibility of controlling thermal treatment processes via rheological measurements.

Bioactive and rheological properties of rose hip marmalade.

In this study, bioactive (total phenolic, antioxidant and antiradical activity) and rheological properties (steady and dynamic) of rose hip marmalade were investigated. Bioactive properties were determined in rose hip marmalade and extract. Extract had higher total phenolic content (38.5mg GAE/g dry extract), antioxidant activity (124mg AAE/g dry extract) and antiradical activity (49.98%) than marmalade. Steady and dynamic rheological properties of the marmalade were determined at different temperature levels (5, 25 and 45°C). Rose hip marmalade exhibited shear thinning behavior and Ostwald de Waele model best described flow behavior of the sample (R (2) ≥0.9880) at different temperature levels. Consistency index and apparent viscosity values (η 50 ) at shear rate 50s(-1) decreased with increase in temperature level. Viscoelastic properties were determined by oscillatory shear measurements and G' (storage modulus) values were found to be higher than G'' (loss modulus) values, indicating that the rose hip marmalade had a weak gel-like structure with solid-like behavior. G', G'', G (*) (complex modulus) and η* (complex viscosity) values decreased with increase in temperature level. Modified Cox-Merz rule was satisfactorily applied to correlate apparent and complex viscosity values of the rose hip marmalade at all temperatures studied.

The effect of starch modification and concentration on steady-state and dynamic rheology of meat emulsions

In this study, the effect of starch modification (NPS, native potato starch; AMS, acid modified starch; DMS, dextrinized modified starch; PGS, pre-gelatinized modified starch) and its concentrations (1, 2, 4 wt%) on steady-state and dynamic rheological properties of meat emulsions were determined. Water-oil binding capacity and intrinsic viscosity of potato starch increased up to 5.07–0.90 g/g, and 14.98 mL/g, respectively, after modifying with pre-gelatinization method. The particle size of starches as average mean diameter ranged between 44.19 μm and 293.06 μm. The maximum solubility was obtained from DMS after heat treatment at 70 °C being 48.22%, which means an increase about 3.06-fold in solubility as compared with NPS. The Ostwald-de Waele model was successfully used to describe the flow properties of meat emulsions (R2 > 0.961). While starch types did not affect the K values of emulsions (p > 0.05), starch concentrations did (p < 0.01). All studied emulsions exhibited non-Newtonian, pseudoplastic behavior since n values were lower than 1. Emulsion systems were characterized as weak gel-like macromolecular dispersions with storage modulus (G′) much greater than loss modulus (G″). A modified Cox–Merz rule was applied by multiplying angular frequency with shift factors (αSF). Frequency dependence of complex modulus (G*) was studied to measure the strength of cross-linking protein network of emulsion systems by calculating a constant order of relaxation function (α) and concentration dependent stiffness parameter (Aα). It was concluded that PGS addition improved rheological properties of meat emulsions due to higher solubility, particle size, intrinsic viscosity, water-oil binding capacity than NPS.

Steady, dynamic, creep/recovery, and textural properties of yoghurt/molasses blends: Temperature sweep tests and applicability of Cox-Merz rule.

In this study, physicochemical, rheological (steady, dynamic, and creep/recovery), and textural properties of yoghurt/molasses blends (0, 5, 10, and 15% molasses) were investigated. The blends showed shear thinning behavior, as described by Ostwald de Waele model (R(2) ( )≥ 0.955). Consistency coefficient value (K) of the blends decreased with increasing molasses concentration in the sample. Storage modulus (G') of blends was higher than loss modulus (G″), exhibiting weak gel-like behavior. Molasses addition decreased G' and G″ values. Temperature sweep tests indicated that blends followed Arrhenius relationship. A modified Cox-Merz rule was applicable using shift factors. Compliance values (J(t)) increased as molasses concentration increased, revealing that deformation stability and internal viscosity (η1) decreased with concentration. Creep behavior was characterized using Burger model. Obtained J data as a function of time could be satisfactorily fitted to Burger model (R(2) ( )≥ 0.994). The final percentage recovery of blends remarkably decreased with the increase of molasses concentration. Firmness, consistency, cohesiveness, and viscosity index values decreased with molasses addition. According to the results of the current study, molasses amount to be added to the yoghurt should be determined regarding rheological properties since resistance of the sample to deformation decreased with increase in molasses concentration.

Microbiological, steady, and dynamic rheological characterization of boza samples: temperature sweep tests and applicability of the Cox–Merz rule

Boza is a beverage produced by lactic acid bacteria (LAB) and yeast, which affects rheological properties. In the present study, boza samples collected from a local market were characterized with reference to microbiological and rheological approaches. The boza samples were characterized with respect to their microbiological population, i.e. the numbers of LAB and yeast. The numbers of LAB and yeast were found to range from 2.88 × 106 to 2.06 × 1010 CFU/mL and from 3.71 × 103 to 9.40 × 105 CFU/mL, respectively. Their steady and dynamic rheological properties were investigated within the temperature range of 0-50 °C. Apparent viscosity values (h) of the boza samples decreased with shear rate, indicating that the samples behaved as a pseudoplastic fluid. The Ostwald-de Waele model satisfactorily described (R2 > 0.99) the flow behavior of the samples at 5 and 20 °C. Storage modulus (G') values were higher than loss modulus (G''), indicating that boza samples had a solid-like structure. Temperature had a remarkable effect on the steady and dynamic properties of the samples; therefore, temperature sweep tests were also conducted to determine temperature dependency of the samples. The h50, G', and G'' values decreased with increase in temperature. The Arrhenius equation could be satisfactorily used to describe changes in these parameters depending on temperature. A modified Cox-Merz rule with shift factors ranging from 1.0 to 2.2 was successfully applied to put forward a relationship between steady shear and dynamic shear viscosity data.

Dynamic Rheological and Textural Characteristics of Low-Calorie Pistachio Butter

The small and large deformation properties of different low-calorie pistachio butter formulas were studied in order to develop a background understanding of the changes in viscoelastic and textural characteristics that occur due to different types of fat replacers and sweeteners. Frequency, temperature, and time sweep analysis and also back extrusion and texture profile analysis tests were performed. The magnitudes of dynamic moduli increased in the frequency sweep test with loss tan values <1. The elastic structure of all samples changed to viscous behavior with increasing temperature (5–65°C), regardless of the type of fat replacers and sweeteners’ level. The temperature sweep test on heating and cooling samples resulted in higher viscoelastic properties and more solid-like behavior. There was no time dependency for loss tan at 45°C. A modified Cox-Merz rule could superimpose the steady and complex viscosity data. There was a good agreement between the results of G′ and hardness in small and large deformation tests.

Mathematical approach for two component modeling of salep–starch mixtures using central composite rotatable design: Part II. Dynamic oscillatory shear properties and applicability of Cox–Merz rule

Dynamic shear rheological properties of salep–corn starch mixture (SCSM), salep–wheat starch mixture (SWSM) and salep–potato starch mixture (SPSM) samples were determined using a 2-factor-5-level Central Composite Rotatable Design (CCRD). Salep increased loss modulus (G″) values, and decreased loss tangent (tan δ) values of only SCSM; however, all starch types increased the storage (G′), loss (G″), complex (G∗) modulus, complex viscosity (η*) values and decreased tan δ values. At various salep and starch combination levels, a remarkable synergistic effect was observed in the dynamic shear properties. Potato starch exhibited completely different rheological performance in terms of G′, G″ and η∗ values. Salep did not obey the Cox–Merz rule; however, a modified Cox–Merz rule was applicable for SCSM and SPSM samples. The ridge analysis revealed that maximum G′, G″, η* and G∗ values for the SCSM, SWSM and SPSM samples would occur at salep = 0.54% and 0.26%, respectively, and each starch type = 2.83%.

Effect of temperature on dynamic and steady-state shear rheological properties of siriguela (Spondias purpurea L.) pulp

The present work has evaluated the dynamic and steady-state shear rheological properties of siriguela (Spondias purpurea) pulp as function of temperature (0–80°C), as well as the applicability of the Cox-Merz rule. The product flow behavior could be well described by the Herschel–Bulkley’s model (R2>0.98), whose parameters were modeled as function of temperature (R2>0.91). The product has shown a weak gel behavior, with storage modulus higher than loss modulus in the evaluated frequency range. The storage and loss modules could be well described by a power function of the oscillatory frequency (R2>0.93), whose parameters were modeled as function of temperature (R2>0.97). Moreover, a power modified Cox-Merz rule could describe the rheological properties of S. purpurea pulp (R2>0.96). The obtained data are potentially useful for future studies on food properties and process design.

Dynamic oscillatory shear properties of O/W model system meat emulsions: Linear viscoelastic analysis for effect of temperature and oil concentration on protein network formation

Effects of oil concentration (57.50%, 58.75%, 60.00% and 61.25%) and temperature (5, 10 and 15 °C) on O/W model system meat emulsions were analyzed using oscillatory dynamic shear tests, allowing all emulsion systems to be characterized as linear viscoelastic solids exhibiting a pseudoplastic flow. The emulsion systems were characterized as weak gel-like macromolecular dispersions with G′ much greater than G″, exhibiting a plateau region. A modified Cox–Merz rule was applicable using shift factors. Frequency dependence of complex modulus ( G ∗) was studied to measure strength of cross-linking protein network of the emulsion systems by calculating a practically constant order of the relaxation function ( α = 0.10) and a concentration dependent stiffness parameter ( A α ) using Friedrich and Heymann theory. It was concluded that the viscoelastic characteristics and strength of the emulsion systems increased with increasing oil level, but decreased with temperature. Different mathematical models were successfully constructed to predict the rheological parameters.