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Honey was serially diluted with different percentages of glucose, fructose and water and each was analysed rheologically at room temperature of 27 °C. Pure honey exhibits thixotropic time-dependent rheological behaviour, the behaviour of glucose and fructose solutions in water (a Newtonian solvent) tends towards near Newtonian. The rheological profiles of pure and adulterated honey samples were determined using RV DV-III Ultra Programmable Rheometer at low rates of share. A Structural Kinetic Model was developed which provided good correlations with the rheological data. The new model was used to classify samples using their average molecular weights as one of the distinguishing parameters. Also the order of the kinetics in the new model suggests the number of active components in the “honey” undergoing deformation as 3. Carreau-Yasuda model was also improved upon to provide an independent assessment of average molecular weight of samples.

Honey is a sweet fluid produced by honey bees (Apis Mellifera) from the nectar of flowers [

Rheology is the study of deformation and flow of fluids. The goal is to employ it to understand and predict the behaviour of fluids undergoing deformation. The rheological responses of fluid materials are obtained in terms of the dependence of their apparent viscosities on shear rate, and shear stress. A good understanding of rheology is essential to understanding many processes in engineering and other areas of research. All materials are made up of molecules under relative motion. These molecular motions are influenced by interaction potentials arising from the presence of the molecules. The same molecular motions and interactions are responsible for rheology [

There are many types of fluids in nature―pure substances, mixtures, dispersions and solutions, which fall into categories of either simple or structured fluids [

The objective of this study is firstly to explore the efficacy of utilizing honey rheology to assess its purity and to extract structural and compositional information from the theological data.

The essence of this section is to develop a structural kinetic model that can distinguish pure from adulterated honey using average molecular weight as one of its major distinguishing properties. Also, to improve upon Carreau-Yasuda model so that it can be used independently to assess the molecular weight of samples from the rheograms.

The structural kinetic approach assumes that the change in the rheological behaviour is associated with shear-induced breakdown of internal structure of pure honey. We use the analogy of a chemical reaction to express the structural breakdown process in the following form:

Structured state → Non Structured state (1)

Honey is at rest at its structured state but undergoes deformation at its unstructured state. This model will assume in accordance with the above expression that the structure of honey changes under the effect of imposed shear but restores itself upon the withdrawal of shear.

This study suggests that pure honey exhibits thixotropic time dependent flow pattern. The structured state of the thixotropic structure at any time t and under applied shear rate, γ , can be represented by a dimensionless structural parameter ( θ ) as given in Equation (2):

θ = θ ( γ , t ) (2)

This was defined, according to [

θ ( γ , t ) = η − η ∞ η o − η ∞ (3)

where η o , is the initial apparent viscosity at t = 0 (structured state) and η ∞ , is the equilibrium apparent viscosity as t → ∞ (non-structured state). Both η o and η ∞ are functions of applied shear rate only. The dimensionless structured parameter, θ is subjected to the following conditions: at the fully structured state, t = 0 and θ = θ o , and at non-structured state, as t → ∞, θ = θ ∞ .

The rate of structural breakdown can be expressed as:

− d θ d t = k ( θ − θ ∞ ) n (4)

where k = k ( γ ) is the rate constant, and n is the order of the structural breakdown reaction.

Integrating Equation (4) between t = t and t = 0 , we have:

∫ d θ ( θ − θ ∞ ) n = ∫ A o d t (5)

which yields:

( θ − θ ∞ ) 1 − n = t k ( n − 1 ) + C (6)

Solving for C at and θ = θ o , t = t o (initial value problem) we obtain:

( θ o − θ ∞ ) 1 − n = C (7)

Putting back C into Equation (6) at t_{0} = 0 gives:

( θ − θ ∞ ) 1 − n − ( θ o − θ ∞ ) 1 − n = t k ( n − 1 ) (8)

Putting back Equation (3) into Equation (8)

gives: η = η ∞ + ( η o − η ∞ ) [ t k ( n − 1 ) + 1 ] 1 / 1 − n (9)

Equation (9) is designated as the Structural Kinetic Model (SKM) which, in this study, would be applied to honey. This equation should answer the need to have a model that can give an insight into the composition of honey. One way to make this connection is through appropriate introduction of the average molecular weight of the honey sample. A good relationship has been found for polymeric materials in the Mark Houwink relation as given in Equation (10).

η o = K M A (10)

where η_{o} is the zero shear Viscosity of the fluid, K_{ }and A, are Mark Houwink constants. A is generally in the range of 0.5 to 0.8 [

Putting Equation (10) into Equation (9) gives:

η = η ∞ + ( K M A − η ∞ ) [ k t ( n − 1 ) + 1 ] 1 / 1 − n (11)

Equation (11) is designated as SKM for molecular weight Correlation in Honeys.

The Carreau-Yasuda model [

η ( γ ˙ ) = η ∞ + ( η o − η ∞ ) [ 1 + ( γ ˙ λ ) a ] n − 1 a (12)

This empirical model has five adjustable parameters, α, λ, n,_{ η o } and η ∞ .

This model describes non-Newtonian time dependent flow with asymptotic viscosities at zero ( η o ) and infinite ( η ∞ ) shear rates, and with no yield stress. The parameter λ is the viscous relaxation time. The viscous relaxation time defines the location of the transition from shear-thickening to shear-thinning behaviour. The 1 / λ is the critical shear rate at which viscosity begins to decrease. The power-law slope is (n − 1). The value of n (consistency index) changes with the composition of the fluid. The parameter, “α” is the dimensionless parameter (sometimes called “the Yasuda constant” since it is a parameter added to Carreau equation by Yasuda). It describes the transition region between η o _{ }and the power-law region and it is inversely related to the breath of the zone.

Putting Equation (10) into Equation (12) yields:

η ( γ ˙ ) = η ∞ + ( K M A − η ∞ ) [ 1 + ( γ ˙ λ ) a ] n − 1 a (13)

Equation (13) is the Amended Carreau-Yasuda model (ACYM). A comparison shall be made on the molecular weight obtained using this equation and that from SKM.

The experimental methods involve samples preparation, rheological characterization and curve fitting.

Sample A is pure honey or control sample harvested and processed for the purpose of this work. Glucose G1 (produced by dissolving three parts of glucose in one part of distilled water), fructose F1 (produced by dissolving three parts of fructose in one part of distilled water) and distilled water sample named H_{0} were used to serially adulterate the control sample A. Samples G2, G3, G4 and G5 are 10%, 50%, 70% and 90% adulteration with sample G1. Likewise, Samples F2, F3, F4 and F5 are 10%, 50%, 70% and 90% adulteration of pure honey with sample F1. Also Samples H1, H2, H3, H4, H5 and H6 are 5%, 10%, 15%, 20%, 30% and 50% adulteration with water.

The rheological tests of the samples were carried out using Brookfield RV DV-III Ultra Programmable Rheometer. The analyses were done at room temperature of 27˚C. The equipment thermometer was kept dipped into the fluid before the analyses began for temperature control. The DV III Program mode was used. The shear rates, from 0.0 to 3.4 s^{−1} at incremental steps of 0.01 s^{−1} were used. The time interval for each speed was sixty seconds, and readings were taken every ten seconds. Step time was not allowed in order not to allow the recovery of the sample from the shearing of the initial speed. The samples were allowed to stand in the container for at least 30 minutes before the analysis to allow for the complete structural equilibrium. Coaxial spindle was chosen which is appropriate for the rheology of viscous non-Newtonian fluids. The geometries of coaxial cylinder are needed for application where extremely well-defined shear rate and shear stress are required. The spindle number “00” was chosen which would enable the Rheometer to calculate the shear stress (N/m^{2}), viscosity (mPa.s), and torque (%) for every shear rate (s^{−1}).The experimental procedure was repeated after 24 hours to determine if the results were reproducible.

For the Carreau-Yasuda model, curve fitting was carried out using the method of Morrison [

k = { [ ( η − η ∞ ) / ( η o − η ∞ ) ] 1 − n − 1 } / t ( n − 1 ) (14)

Also, if Γ is defined by, Γ = ( η − η ∞ η o − η ∞ ) 1 − n (15)

Then Γ = t k ( n − 1 ) + 1 (16)

Since k is expected to depend only on rate of shear rate [

This study focused on the effect of fructose, glucose and water adulteration on the rheological behaviour of honey. The ACYM and the new Structural Kinetic Model were used in the study. The rheological characterization of polymers and polymers in dilute solutions are well established [

Pure honey first exhibited shear thickening behaviour at the inception of flow and at low shear rate but later assumed an essentially shear thinning behaviour at higher rate of shear. Kurzberck and coworkers, [

increase in shear rate over time was caused by inducing changes in the network entanglement of the fluid. This kind of flow behaviour was also reported by Fan and coworkers, [

^{−1}. The zero shear viscosity was applied in Mark-Houwink Equation (Equation (10)) to obtain the molecular weight at that shear rate. The average molecular weight of the fluid was then

determined for all the rates of shear used. Since this study was done at low shear rate, the fluid would not have deformed for a long time to obtain the infinite time viscosity. ^{−1}. From the plot, the minimum value (best value) of infinite time viscosity was obtained. It was observed during the iterations that the infinite (time) shear viscosities at different rates of shear that satisfied the SKM for pure honey were negative. This shall be discussed in details under

The parameters of the structural kinetic model, M, is the molecular weight of honey, the Mark Houwink constants, K and A, introduced into the equation via the Mark Houwink equation, the infinite time viscosity, η ∞ , which gives an indication of the viscosity of honey at knife edge (high shear) conditions, the zero time viscosity, η 0 , and n, the order of structural breakdown kinetics which depends on the composition of the fluid.

S/N | Sample Code | Sample Identity | Molecular Weight(g/mol) | n | k (S^{−1}) | t(s) |
---|---|---|---|---|---|---|

1. | A | Ijebu Mushin | 252.07 | 3.00 | 0.83 | 4.16 |

2. | G1 | Glucose | 145.60 | 1.50 | 3.69 | 1.70 |

3. | G2 | 10% Glucose Adulteration | 232.05 | 2.50 | 10.69 | 0.05 |

4. | G3 | 50% Glucose Adulteration | 189.25 | 2.00 | 13.16 | 5.56 |

5. | G4 | 70% Glucose Adulteration | 174.19 | 2.00 | 2.83 | 18.03 |

6. | G5 | 90% Glucose Adulteration | 160.19 | 1.50 | 3.29 | 391.25 |

7. | F1 | Fructose | 148.60 | 1.50 | 3.26 | 1071.14 |

8. | F2 | 10% Fructose Adulteration | 230.36 | 2.50 | 4.12 | 0.19 |

9. | F3 | 50% Fructose Adulteration | 198.25 | 2.50 | 5.18 | 0.0005 |

10. | F4 | 70% Fructose Adulteration | 176.19 | 2.00 | 1.59 | 30.00 |

11. | F5 | 90% Fructose Adulteration | 160.13 | 1.50 | 4.06 | 17.49 |

12. | H1 | 5% Water Adulteration | 241.71 | 2.50 | 1.05 | 0.00003 |

13. | H2 | 10% Water Adulteration | 222.20 | 2.00 | 0.94 | 0.42 |

14. | H3 | 15% Water Adulteration | 212.15 | 1.50 | 0.61 | 22.66 |

15. | H4 | 20% Water Adulteration | 200.91 | 1.50 | 0.63 | 16.24 |

16. | H5 | 30% Water Adulteration | 178.42 | 1.50 | 0.69 | 8.60 |

17. | H6 | 50% water Adulteration | 132.44 | 1.50 | 0.75 | 5.31 |

S/N | Sample Code | Sample Identity | Molecular Weight | λ | n |
---|---|---|---|---|---|

1. | A | Ijebu Mushin | 250.00 | 1.600 | −0.0013 |

2. | G1 | Glucose | 147.00 | 0.887 | 0.9000 |

3. | G2 | 10% Glucose Adulteration | 243.88 | 1.297 | 0.3700 |

4. | G3 | 50% Glucose Adulteration | 214.00 | 2368.94 | 0.5600 |

5. | G4 | 70% Glucose Adulteration | 200.88 | 11.48 | 0.8000 |

6. | G5 | 90% Glucose Adulteration | 187.00 | 43.37 | 0.9447 |

7. | F1 | Fructose | 149.81 | 13.08 | 0.9967 |

8. | F2 | 10% Fructose Adulteration | 241.27 | 1.51 | 0.5532 |

9. | F3 | 50% Fructose Adulteration | 216.91 | 0.85 | 0.7948 |

10. | F4 | 70% Fructose Adulteration | 200.21 | 0.60 | 0.8787 |

11. | F5 | 90% Fructose Adulteration | 187.00 | 0.005 | 0.8884 |

12. | H1 | 5% Water Adulteration | 239.06 | 0.55 | 0.8494 |

13. | H2 | 10% Water Adulteration | 226.68 | 2.15 | 0.9908 |

14. | H3 | 15% Water Adulteration | 215.20 | 0.06 | 1.0078 |

15. | H4 | 20% Water Adulteration | 200.12 | 0.06 | 0.5107 |

16. | H5 | 30% Water Adulteration | 169.08 | 0.06 | -1.6938 |

17. | H6 | 50% water Adulteration | 130.00 | 0.06 | 0.1418 |

used in the adulteration here have lower molecular weight than honey and reductions in the molecular weight of adulterated samples explain why their behaviour tends toward Newtonian.

The best results were obtained for the pure honey samples at third order deformation kinetics. The essence of this is that three components of the honey constituents are active during deformation. It suggests that melezitose and other oligosaccharides and polymerized materials serve as the first, water as the second, and monosaccharides as the third active component. In the study of effect of water adulteration in honey, the results of curve fitting were best at second order deformation. It again suggests that the kinetic model views the entire honey as one component and the water as another during deformation.

The results of the rate of deformation of samples in

Rheology is a consistent tool for honey characterization deriving from the correlation between flow behaviour and compositional changes in honey. Honey exhibited thixotropic rheological behaviour, glucose and fructose exhibited near Newtonian behaviour while water is Newtonian. The adulteration of honey with glucose, fructose or water pushes their viscosities towards Newtonian behaviour. The new Structural Kinetic Model followed well the experimental results and predicted the molecular weight of different samples as a means of discrimination of pure from adulterated honey and served to determine the degree of adulteration. The Carreau Yasuda model was amended to improve its performance as a tool for the determination of molecular weight of fluids from the rheological data. The amended Carreau Yasuda model compared relatively well with our new model except on honey adulterated with water where the empirical model failed.

We wish to thank the Tertiary Education Trust Fund (TETFUND) of Nigeria for sponsoring, at the University of Lagos, the Ph.D. program in Chemical Engineering that produced this article.

Nwalor, J.U., Babalola, F.U. and Anidiobu, V.O. (2018) Rheological Modeling of the Effects of Adulteration on Nigerian Honey. Open Journal of Fluid Dynamics, 8, 249-263. https://doi.org/10.4236/ojfd.2018.83016