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Abstract: Some suspensions in nature have a complex structure and demonstrate a yield shear stress and a non- linear relationship between the shear rate and the shear stress. Kaolin clay suspension is such an example in engineering, whereas in nature it is blood. This study represents an innovative approach to simulate bioliquid flow, similar to that of blood when the solid concentration is high. The objective of this study is to examine the influence of high solid concentration of bioliquid, similar to blood, on energy losses and velocity profiles in turbulent and transitional flow in a narrow tube. Using the analogy between the suspension of kaolin clay and blood, the physical model and the mathematical model were formulated. The mathematical model comprises continuity and time-averaged momentum equations, a two-equation turbulence model for low Reynolds numbers, and a specially developed wall damping function, as such suspensions demonstrate the damping of turbulence. Experimental data on blood rheology for solid concentrations equal to 43% and 70% by volume, gathered from the literature, were used to establish a rheological model. The results of the simulations indicated that an increase of solid concentration in bioliquid suspension from 43% to 70% causes an increase in wall shear stress to approximately 10% and 6% for transitional and turbulent flow, respectively, and changes in velocity profiles. Such simulations are important if an inserted stent or a chemical additive to the bioliquid suspension is considered, as they can influence the shear stress. The results of the simulations are presented in graphs, discussed, and conclusions are formulated.
B I B L I O G R A F I A[1] Shook, C.A. and Roco, M.C., Slurry Flow: Principles and Practice, Ed. Brenner, H., Butterworth-Heinemann, Boston, 2015, p. 324.
[2] Dohnalova, Z., Svoboda, L., Šulcová, P., Characterization of kaolin dispersion using acoustic and electroacoustic spectroscopy. Journal of Mining and Metallurgy, 2008, 44 B, pp. 63-72.
[3] Alexander, D.E., Nature’s Machines. An Introduction to organismal biomechanics, Academic Press. Elsevier, 2017, p. 425.
[4] Earl, E. and Mohammadi, H., Biomechanics of Human Blood, 2018.
[5] Tomschi, F., Bizjak, D., Bloch, W., Latsch, J., Predel, H. G., Grau, M., Deformability of different red blood cell populations and viscosity of differently trained young men in response to intensive and moderate running, Clin. Hemorheol. Microcirc., 2018, vol. 69, pp. 503–514.
[6] Lapoumeroulie, C., Connes, P., El Hoss, S., Hierso, R., Charlot, K., Lemonne, N., New insights into red cell rheology and adhesion in patients with sickle cell anaemia during vaso-occlusive crises, Br. J. Haematol., 2019, vol. 185, pp. 991–994.
[7] Ellsworth, M.L., The red blood cell as an oxygen sensor: what is the evidence? Acta Physiol. Scand., 2000, vol.168, pp.551–559.
[8] Lanotte, L., Mauer, J., Mendez, S., Fedosov, D. A., Fromental, J. M., Claveria, V., Red cells’ dynamic morphologies govern blood shear thinning under microcirculatory flow conditions, Proc. Natl. Acad. Sci. USA., 2016, vol.113, pp.13289–13294.
[9] Ugurel, E., Piskin, S., Aksu, A.C., Eser, A., Yalcin, O., From experiments to simulation: shear-induced responses of red blood cells to different oxygen saturation levels, Frontiers in Physiology, 2019, vol. 10, 1559.
[10] Pop, G. A., Duncker, D. J., Gardien, M., Vranckx, P., Versluis, S., Hasan, D., The clinical significance of whole blood viscosity in cardio-vascular medicine, Neth. Heart J. 2002, vol. 10, No.12, pp.512–516. PMC2499821.
[11] Formaggia, L., Lamponi, D., Quarteroni, A., One-dimensional models for blood flow in arteries. J. Engineering Mathematics, 2003, vol. 47, pp.251-276.
[12] Shipkowitz, T., Rodgers V.G., Frazin L.J., Chandran K.B., Numerical study on the effect of secondary flow in the human aorta on local shear stresses in abdominal aortic branches, J. Biomech., 2000, vol.33 No. 6, pp. 717-728.
[13] Miyazaki, S., Itatani, K., Furusawa, T., Nishino, T., Validation of numerical simulation methods in aortic arch using 4D flow MRI, Heart and Vessels. 2017, vol. 32, No.8, pp.1032–44.
[14] Xu, D., Warnecke, S., Song, B., Transition to turbulence in pulsating pipe flow, J. of Fluid Mechanic, 2017, vol. 831, pp. 418–32.
[15] Xu, D. and Avila, M., The effect of pulsation frequency on transition in pulsatile pipe flow, J. of Fluid Mechanics, 2018, vol. 857, pp. 937–51.
[16] Alasakani, K., Tantravahi, R.S.I., Kumar P.T.V., On refining the input data set to mathematical models simulating arterial blood flow in humans, WSEAS Transactions on Fluid Mechanics, 2021, vol. 16, pp.63-78.
[17] Nader, E., Skinner, S., Romana, M., Fort, R., Lemonne, N., Guillot, N., Gauthier, A., Antoine-Jonville, S., Renoux, C., Hardy-Dessources, M.D., Stauffer, E., Joly, P., Bertrand, Y., Connes, P., Blood rheology: Key parameters, Impact on blood flow, Role in sickle cell disease and effects of exercise, Front Physiol., 2019, vol. 10, pp.1-14.
[18] Lemonne, N., Connes, P., Romana, M., Vent-Schmidt, J., Bourhis, V., Lamarre, Y., Increased blood viscosity and red blood cell aggregation in a patient with sickle cell anemia and smoldering myeloma, Am. J. Hematol., 2012, vol.87, E129.
[19] Vandewalle, H., Lacombe, C., Lelièvre, J. C., Poirot, J.C., Blood viscosity after a 1-h submaximal exercise with and without drinking. Int. J. Sports Med., 1988, vol.09, No.2, pp.104-107.
[20] Abbasi, M., Farutin, A., Ez-Zahraouy, H., Benyoussef, A., Misbah, C., Erythrocyte - erythrocyte aggregation dynamics under shear flow. Physical Review Fluids, 2021, vol. 6, 023602.
[21] Wu, Y., Hsu, P., Tsai, C., Pan, P., Chen, Y., Significantly increased low shear rate viscosity, blood elastic modulus, and RBC aggregation in adults following cardiac surgery. Scientific Reports, 2018, vol. 8, No. 7173, pp. 1–10.
[22] Lee, CA. and Paeng, DG., Numerical simulation of spatiotemporal red blood cell aggregation under sinusoidal pulsatile flow. Scientific Reports, 2021, vol. 11, No. 9977.
[23] Thomas, D.G., Turbulent disruption of flocs in small particle size suspensions. AIChE J., 1964, vol. 10. No. 4, pp. 517-523.
[24] Michaels, A.S. and Bolger, J.C., The plastic flow behavior flocculated kaolin suspensions, Industrial & Engineering Chemistry Fundamentals, 1962. Vol. 1, No. 3, pp. 153-162.
[25] Zimmermann, J., Demedts, D., Mirzaee, H., Ewert, P., Stern, H., Meierhofe, C., Menze, B., Henne, A., Wall shear stress estimation in the aorta: Impact of wall motion, spatiotemporal resolution, and phase noise, J. Magn. Reson. Imaging, 2018, 48, pp. 718-728.
[26] Masutani, E.M., Contijoch, F., Kyubwa, E., Cheng, J., Alley, M.T., Vasanawala, S., Hsiao, A., Volumetric segmentation-free method for rapid visualization of vascular wall shear stress using 4D flow MRI, Magn. Res. Med., 2018, 80(2), pp. 748-755.
[27] Szajer, J. and Ho-Shon, K., A comparison of 4D flow MRI-derived wall shear stress with computational fluid dynamics methods for intracranial aneurysms and carotid bifurcations — A review, Magnetic Resonance Imaging, 2018, 48, pp. 62-69.
[28] Shokina, N., Bauer, A., Teschner, G., Buchenberg, W.B., Tropea, C., Egger, H., Hennig, J., Krafft, A.J., MR-based wall shear stress measurements in fully developed turbulent flow using the Clauser plot method. J. Magn. Reson., 2019, 305, pp. 16-21
[29] Chandra, K., Dalai, I.S., Tatsumi, K., Muralidhar, K., Numerical simulation of blood flow modeled as a fluid- particulate mixture. Journal of Non-Newtonian Fluid Mechanics, 2020, vol.285, No. 104383, pp.1-8,
[30] Yahaya, S., Jikan, S.S., Badarulzaman, N.A., Adamu, A.D., Chemical composition and particle size analysis of kaolin, Int. Electronic Scientific Journal, 2017, vol. 3, No. 10, pp. 1001-1004.
[31] Liepsch, D.W., Thurston, G., Lee, M., Studies of fluids simulating blood-like rheological properties and applications in models of arterial branches. Biorheology, 1991, vol. 28 No. 1-2, pp. 39-52.
[32] Bartosik, A., Modelling of a turbulent flow using the Herschel-Bulkley rheological model. Chemical and Process Engineering, 2006, vol. 27, pp. 623-632.
[33] Wilson, K.C. and Thomas, D.G., A new analysis of the turbulent flow of non-Newtonian fluids. Can. J. Chem. Eng., 1985, vol. 63, pp. 539-546.
[34] Thomas, D.G. and Wilson, K.C., New analysis of non-Newtonian turbulent flow—yield-power-law fluids, Can. J. Chem. Eng., 1987, vol. 65, No. 2, pp. 335-338.
[35] Bartosik, A., Simulation and Experiments of Axially-Symmetrical Flow of Fine- and Coarse-Dispersive Slurry in Delivery Pipelines
Monograph M-11
Kielce University of Technology: Kielce, Poland, 2009.
[36] Bartosik, A., Application of rheological models in prediction of turbulent slurry flow, Flow, Turbulence and Combustion, 2010, vol. 84, No. 2, pp. 277-293.
[37] Wagner, C., Steffen, P., Svetina, S., Aggregation of red blood cells: From rouleaux to clot formation, Comptes Rendus Physique, 2013, vol. 16, No. 6, pp. 459-469.
[38] Baskurt O.K. and Meiselman, H.J., Erythrocyte aggregation: basic aspects and clinical importance. Clinical Hemorheology and Microcirculation. 2013
vol.53, No. 1-2, pp. 23-37 PMID: 22975932,
[39] Sandgren, T., Sonesson, B., Ahlgren, A.R., Lanne, T., The diameter of the common femoral artery in healthy human: Influence of sex, age, and body, J. Vascular Surgery, 1999, vol.29, No. 3, pp. 503-510.
[40] Wells, R.E. and Merrill, E.W., Influence of flow properties of blood upon viscosity - Hematocrit relationship, J. Clinic Investigation, 1962, vol.41, No.8, pp.1591-1598.
[41] Kenner, T., The measurement of blood density and its meaning, Basic Research in Cardiology, 1989, vol.84, No. 2, pp.111-124.
[42] Burstain, J.M., Brecher, M.E., Halling, V.W., Pineda, A.A., Blood volume determination as a function of Hematocrit and mass in three preservative solutions and Saline, A.J.C.P. Coagulation and Transfusion Medicine, 1994, vol.102, No. 6, pp.812-815.
[43] Shibeshi, S.S. and Collins, W.E., The rheology of blood flow in a branched arterial system, Applied Rheology, 2005, vol. 15, No. 6, pp. 398-505.
[44] Lee, B.K., Xue S., Nam J., Lim H., Shin S., Determination of the blood viscosity and yield stress with a pressure-scanning capillary hemorheometer using constitutive models, Korea-Australia Rheology J. 2011, vol. 23, No. 1, pp. 1-6.
[45] Ruef, P., Gehm, J., Gehm, L., Felbinger, C., Pöschl, J., Kuss, N., The new low shear viscosimeter LS300 for determination of viscosities of Newtonian and non-Newtonian fluids, General Physiology and Biophysics, 2014, vol.33, No. 3, pp.281-284.
[46] Ruef, P., Gehm, J., Gehm, L., Felbinger, C., Pöschl, J., Kuss, N., Determination of whole blood and plasma viscosity by means of flow curve analysis, General Physiology and Biophysics, 2014, vol. 33, No.3, pp.285-293.
[47] Casson, N., A flow equation for pigment-oil suspensions of the printing ink type rheology of dispersed systems. London Pergamon Press, 1959, pp. 84-104.
[48] Metzner, A.B. and Reed, J., Flow of non-Newtonian fluids - correlation of the laminar, transition and turbulent flow regions, AIChEJ. 1955, pp.434-440.
[49] Ramanathan, T. and Skinner, H., Coronary blood flow, Continuing Education in Anaesthesia Vritical Care & Pain, 2005, vol.5, No. 2, pp.61-64.
[50] Saqr, K.M., Tupin, S., Rashad, S., Physiologic blood flow is turbulent. Nature, Scientific Reports, 2020, vol. 10, No. 15492.
[51] Boussinesque, J., Theorie de l’ecoulement tourbillant, Mem. Acad. Sci., 1897, vol. 23 46.
[52] Cotas, C., Silva, R., Garcia, F., Faia, P., Asendrych D., Rasteiro, M.G., Application of different low-Reynolds k-ε turbulence models to model the flow of concentrated pulp suspensions in pipes, Procedia Engineering, 2015, No. 102, pp. 1326-1335.
[53] Cotas, C., Asendrych, D., Garcia, F., Faia, P., Rasteiro, M.G., Turbulent flow of concentrated pulp suspensions in a pipe – numerical study based on a pseudo-homogeneous approach. COST Action FP1005 Final Conference, EUROMECH Colloquium 566, Trondheim, Norway, 2015, pp. 31-33.
[54] Mathur, S. and He, S., Performance and implementation of the Launder–Sharma low-Reynolds number turbulence model. Comput. Fluids, 2013, vol.79, pp. 134–139.
[55] Abir, I.A. and Emin, A.M., A comparative study of four low-Reynolds-number k-e turbulence models for periodic fully developed duct flow and heat transfer. Numer. Heat Transf. Part B Fundam. 2016, vol. 69, No. 234–248.
[56] Hedlund, A., Evaluation of RANS Turbulence Models for the Simulation of Channel Flow
Teknisk-naturvetenskaplig Fakultet UTH-enheten: Upsala, Sweden, 2014
p. 26.
[57] Davidson, L., An Introduction to Turbulence Models, Chalmers University of Technology: Goteborg, Sweden, 2018.
[58] Bartosik, A., Simulation of a yield stress influence on Nusselt number in turbulent flow of Kaolin slurry, Proc. of the ASME Summer Heat Transfer Conf., 2016, HTFEICNMM2016, No.2, pp. 1-7.
[59] Launder, B.E. and Sharma B.I., Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc, Letters in Heat and Mass Transfer, 1974, No.1 pp.131-138.
[60] Reynolds, O., On the dynamical theory on incompressible viscous fluids and the determination of the criterion, Philosophical Transactions of the Royal Society of London, 1895, vol. 186, pp.123–164.
[61] Roache, P.J., Computational Fluid Dynamics, Hermosa Publ., Albuquerque, 1982.
[62] Silva, R.C., Experimental characterization techniques for solid-liquid slurry flows in pipelines: A review, Processes, 2022, vol. 10, No. 597, pp. 1-44.
[63] Javed, K., Vaezi, M., Kurian, V., Kumar, A., Frictional behaviour of wheat straw-water suspensions in vertical upward flows, Biosystems Engineering, 2021, vol. 212, pp. 30-45.
[64] DiCarlo, A. L., Holdsworth, D. W., Tamie L., Poepping, T.L., Study of the effect of stenosis severity and non-Newtonian viscosity on multidirectional wall shear stress and flow disturbances in the carotid artery using Particle Image Velocimetry, Medical Engineering and Physics, 2019, vol.65, pp. 8–23.