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Offline methods for rheological measurements such as cylindirical coquette, cone and plate geometries (conventional rheometries) generally used for the study of fluid motion in shear. However, obtained results from these types of geometries need to be verified with suitable online or inline methods. Especially, many industrial processes, such as extrusion, transfer processes involve established or developing flows in pipes or tubes. Therefore, online techniques based on the measurement of the velocity profile in a pipe flow using Magnetic Resonance Imaging (MRI), which is a noninvasive method, and simultaneously determining the pressure drop, are promising for use a product quality or rheology control tool during the fluid flow. Magnetic resonance imaging (MRI) can be used as a viscometer, based on analysis of a measured velocity profile of fluid flowing in a tube coupled with a simultaneous measurement of the pressure drop driving the flow (Arola et al., 1997 and Arola et al., 1999).

This type of measurement is well suited for rheological characterization of non-Newtonian fluids (Choi et al., 2002 and Tozzi et al., 2012).

To evaluate shear viscosity in tube (or capillary) flow, an incompressible fluid must undergo steady pressure-driven flow in the laminar regime. The conservation of linear momentum, which equates pressure forces to viscous forces, provides the relationship between the shear stress, s, and radial position, r:

[sigma](r) = [[-[DELTA]P]/2L]r (1)

where [DELTA]P is the pressure drop over the tube length L. The shear rate is obtained at the same radial position using the velocity profile obtained from a flow image. The expression for the shear rate in tube flow is:

[gamma](r) = [dV(r)]/dr (2)

Where V is the axial velocity. Using Equations 2 and 3, the apparent viscosity ? is determined by the ratio of shear stress to shear rate:

[eta](r) = [[sigma](r)]/[[gamma](r)] (2)

Graphical User Interface (GUI) programs are used to analyze data and display rheological results (Choi et al., 2005 and Tozzi et al., 2012). Main step in the data processing procedure include calculating the shear stress as a function of radial position in the pipe, processing the velocity profile image to obtain a velocity profile, calculating the shear rate as a function of radial position from the velocity profile, and generating the rheogram by plotting the shear stress against the shear rate (Arola et al., 1997, Callaghan 1999 and Tozzi et al., 2012). Calculating the shear stress is straightforward as in Equation 1.

In this study, Carboxymethyl cellulose (CMC) was used as test fluid. CMC is widely used as thickener especially in food and pharmaceutical industries (Benchabane and Bekkour, 2008). This is also known as complex fluid due to no linear relationship between stress and shear rate in simple shear during the flow.


2.1. Materials

The CMC, with nominal molecular weight of 250,000 g/mol was supplied from Sigma. Aqueous solutions of CMC were prepared by dissolving the appropriate amount of CMC powder in distilled water. The high CMC concentration solutions (0.5%, 1.0%, 1.5%, 2% w/w.) were prepared by using water heated at 50 oC by gentle stirring with the sufficient time < 24 h.

Online and offline measurements were performed with an MRI (Magnetic Resonance Imaging) at Food and Science Technology Department at University of California, Davis, USA using flow loop depicted in Fig. 1. At 25 oC, MRI Flow Imaging Tests were done for 0.5, 1, 1.5, 2% (w/w) CMC solutions to determine rheological constitutive equations parameters. Inlet diamater of PVC tube was 38.1 mm. The test fluid was recirculated using Moyno pump (Integrated Motor Drive System, Franklin Electric) Pressure drop was obtained at the ends of pipe with a constant length of 1.68 m using pressure transducer (Siemens Company).

2.2. Methods

In Fig. 2, flow image for an example of 0.5% CMC flow, can be seen with data processing window. The velocity profile is used to obtain shear rate distribution, while the pressure drop is used to calculate the shear stress distribution. By taking the ratio of these quantities at a radial position, local viscosity can be obtained within the shear rate range in the flow, zero at the center, and maximum at the wall, within minutes. There is not observed slip effect on the wall as in Fig. 2.

Fig. 2 shows the flow curves of the CMC solutions at different concentrations. Instrument CVO rheometer (Bohlin Insturements) with a cone and plate rheometer (with a cone angle 4o and diameter 40 mm) at 25 oC was used for offline measurement. A steady state shear rate ramp from 0.085 to10 [s.sup.-1] was performed in logarithmic mode with 10 points/ decade.


For MRI measurements at the different pump speed of flow loop and also measured using a conventional technique and the agreement between the results is satisfactory shown in Figure 3. MRI measurement results of CMC solutions are also listed in the Table 1 with changing pump speed of flow loop shown in Fig. 3.

All obtained rheograms for different CMC solutions are as listed in Table 1. Rheological properties are independent of flow velocity. Hence, zero shear viscosities are nearly constant during the flow. As Reynolds number and concentration of flow increased, fluid shear stress acting on the pipe wall also increased as seen in Table 1.

Rheological parameters for CMC solutions are also listed in Table 2. Depending on CMC concentration, Power law or H.Bulkley models give the best fit according to MRI flow result using Equations 4 and 5 respectively. Power Law model is valid for 0.5% and 1.0% CMC. On the other hand, 1.5% and 2.0% CMC solutions flow are well described by Herschel-Bulkley model.

[sigma] = K[[gamma].sup.n] (4)

[sigma] = [sigma]o + K[[gamma].sup.n] (5)

In Equations 4 and 5, consistency index, K, and power law index, n, and yield stress, s0 , data values are obtained from shear stress v.s. shear rate data using online (MRI Rheometry) method and offline (CVO Rheometry) method. R2 values of the fittings are also satisfactory. As CMC concentration increased, yield stress gets larger and elastic forces dominates the viscoelastic flow medium (Nguyen & Boger, 1992).


MRI velocity measurements with a pressure drop measurements allows a relationship between shear rate and shear stress and yields a rheological parameters measurements. A rheological investigation of CMC flow of 0.5%, 0.10%, 0.15%, 0.20% w/w concentrations in MRI and CVO was presented. The following conclusions can be highlighted from the results of the study:

* Rheological parameters are independent of flow conditions.

* Online and offline measurement results are good agreement with each other.

* MRI flow imaging is suitable for evaluations of rheological parameters of CMC solutions even in high concentration of 1.5 and 2.0% w/w CMC.

* MRI flow imaging is suitable for evaluations of rheological parameters of CMC solutions even in high concentration of 1.5 and 2.0% w/w CMC.


Arola, D.F., Barrall, G.A., Powell, R.L., McCarthy, K.L. and McCarthy, M.J., (1997). "Use of nuclear magnetic imaging as a viscometer for process monitoring." Chem. Eng. Sci., Vol. 52, No. 13, pp 2049-2057.

Arola, D. F., Powell, R. L., Barrall, G. A. and McCarthy, M. J. (1998). "A simplified method for accuracy estimation of nuclear magnetic resonant imaging." Rev. Sci. Instrum. Vol. 69, No. 13, pp. 3300-3307.

Arola, D. F., Powell, R. L., Barrall, G. A. and McCarthy, M. J. (1999) "Pointwise observation for rheological characterization using nuclear magnetic resonance imaging." J. Rheol. Vol. 43, No. 1, pp. 9-30.

Benchabane, A. and Bekkour, K. (2008). "Rheological properties of carboxymethyl cellulose (CMC) solutions." Colloid Polym. Sci. Vol. 286, No. 10, pp.1173-1180.

Callaghan, P. T. (1999). "Rheo-NMR: nuclear magnetic resonance and the rheology of complex fluids." Reports Prog. Phys. Vol. 62, No. 4, pp. 599-670.

Choi, Y. J., McCarthy, K. L. and McCarthy, M. J. (2005) "A MATLAB graphical user interface program for tomographic viscometer data processing." Comput. Electron. Agric. Vol. 47, No. 3, pp.59-67.

Nguyen, Q. D. and Boger, D. V. (1992). "Measuring the flow properties of yield stress fluids." Annu. Rev. Fluid Mech. Vol. 24, No. 1, pp. 47-88.

Tozzi E.J., Bacca L.A., Hartt W.H., McCarthy, K.L. and M.J. McCarthy (2012). "Robust processing of capillary velocimetry data via stress-rescaled velocity functions." J. Rheol., Vol. 56, No. 6, pp. 1464-1499.


Authors would like to thank Prof. Dr. Micheal J. McCarthy for his help and open his laboratory in Food Science and Technology Department, UC, Davis, USA.

G. Bengusu Tezel (*1)

(1) Abant Izzet Baysal University, Faculty of Engineering and Architecture, Department of Chemical Engineering, Bolu, Turkey ORCID ID 0000-0002-0671-208X

(*) Corresponding Author

Received: 07/12/2017 Accepted: 20/01/2018

DOI: 10.31127/tuje.363596
Table 1. MRI flow measurement for CMC-water solutions

         Pump   V(m/s)  Re      Wall     Zero Shear
         Speed                  stress   Viscosity
         (rpm)                  (Pa)     (Pa.s)

0.5%CMC   330   0.023    2.176    4.371  0.412
          400   0.039    4.020    4.940  0.411
          700   0.078    8.940    7.590  0.411
         1000   0.121   14.445   11.730  0.413
1.0%CMC  1500   0.196   25.013   15.240  0.415
          330   0.032    1.620    7.230  1.002.
          430   0.043    2.312    9.350  1.003
          600   0.060    3.390   12.780  1.001
         1000   0.122    7.870   20.670  1.002
         1500   0.193   13.590   29.605  1.001
1.5%CMC   330   0.035    0.970   16.800  2.001
          460   0.047    1.400   21.560  1.989
          600   0.055    1.950   27.770  2.012
         1000   0.094    3.300   42.540  2.014
         1500   0.183    7.690   55.550  2.001
2.0%CMC   330   0.031    0.180   53.651  9.012
          500   0.053    0.360   77.670  9.022
          800   0.077    0.580   95.431  8.912
         1000   0.095    0.760  106.071  8.993
         1500   0.147    1.340  127.350  8.912

Table 2. Rheological Parameters for CMC-water solutions

         MM                   CVO                   Goodness of the fit
         Rheometer            Rheometer             [R.sup.2](MRI-CVO)

0.5%CMC  K=0.550              K=0.512               0.9993-0.9987
         n=0.753              n=0.730
1.0%CMC  K=0.825              K=0.863               0.9983-0.9985
         n=0.653              n=0.670
1.5%CMC  [[tau].sub.0]=0.436  [[tau].sub.0]=0.424   0.9994-0.99996
         K=2.116              K=2.640
         n=0.607              n=0.608
2.0%CMC  [[tau].sub.0]=9.054  [[tau].sub.0]=9.150   0.9986-0.9991
         K=14.131             K=13.120
         n=0.495              n=0.507
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Author:Tezel, G. Bengusu
Publication:Turkish Journal of Engineering (TUJE)
Article Type:Report
Date:Sep 1, 2018

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