In this work, we propose a simple method to simultaneously match the refractive index and kinematic viscosity of a circulating blood analog in hydraulic models for optical flow measurement techniques (PIV, PMFV, LDA, and LIF). The method is based on the determination of the volumetric proportions and temperature at which two transparent miscible liquids should be mixed to reproduce the targeted fluid characteristics. The temperature dependence models are a linear relation for the refractive index and an Arrhenius relation for the dynamic viscosity of each liquid. Then the dynamic viscosity of the mixture is represented with a Grunberg-Nissan model of type 1. Experimental tests for acrylic and blood viscosity were found to be in very good agreement with the targeted values (measured refractive index of 1.486 and kinematic viscosity of 3.454 milli-m2/s with targeted values of 1.47 and 3.300 milli-m2/s).

1.
Bitsch, L., Olesen, L. H., Westergaard, C. H., Bruus, H., Klank, H., and Kutter, J. P., 2003, Micro PIV on Blood Flow in a Microchannel, microTAS 2003, Lake Tahoe, USA, proc. vol. 1, pp. 825–828.
2.
Yoon, J. H., and Lee, S. J., 2001, 3-D Stereoscopic PIV Measurements of Flow around an Axial Fan, Proc. 4th International Symposium on Particle Image Velocimetry, Gottingen, Germany, Sept. 17–19, Paper 1045.
3.
Dierksheide, U., Meyer, P., Hovestadt, T., and Hentschel, W., 2001, Endoscopic 2D-PIV Flow Field Measurement in IC Engines, 4th International Symposium on Particle Image Velocimetry, Go¨ttingen, Germany, Sept. 17–19, Paper 1060.
4.
Gang, C., Jing, L., Lianfeng, X., Jianbin, X., Shanghai, J., and Jianzhong, L., 2001, A Review on PIV with Image Techniques, XXIX IAHR Congress, Beijing, China, September 16–21, p. 946.
5.
Lowe
,
M. I.
, and
Kutt
,
P. H.
,
1992
,
Refraction through cylindrical tubes
,
Exp. Fluids
,
10
, pp.
50
54
.
6.
Budwig
,
R.
,
1994
,
Refractive index matching methods for liquid flow investigations
,
Experiments in fluids
,
17
, pp.
350
355
.
7.
Reul, H., 1983, Hydraulic analogue model of the systemic circulation—Designed for fluid mechanical studies in the left heart and systemic arteries, Eds. Ghista, Dhanjoo N., Advances in cardiovascular physics, vol. 5 (Part IV Prostheses, assist and artificial organs.), ISBN 3805536097, pp. 43–54.
8.
Affeld, K., 1998, Intra and Extra-corporeal Cardiovascular Fluid Dynamics Vol. 1: General principles in application. WIT Press, ISBN: 1853125474, Chap. 5, pp. 163–168.
9.
Lim
,
W. L.
,
Chew
,
Y. T.
,
Chew
,
T. C.
, and
Low
,
H. T.
,
1994
,
Particle image velocimetry in the investigation of flow past artificial heart valves
,
Ann. Biomed. Eng.
,
22
, pp.
307
318
.
10.
Hendrik
,
S.
, and
Aviram
,
A.
,
1982
,
Use of Zinc Iodide solutions in flow research
,
Rev. Sci. Instrum.
,
53
(
1
), pp.
75
78
.
11.
MSDS Sodium Iodide, Sigma-Aldrich, CAS number: 7681-82-5 (www.sigmaaldrich.com).
12.
Gijsen
,
F. J. H.
,
van de Vosse
,
F. N.
, and
Janssen
,
J. D.
,
1998
,
The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotic bifurcation model
,
J. Biomech.
,
32
, pp.
601
608
.
13.
Gijsen
,
F. J. H.
,
van de Vosse
,
F. N.
, and
Janssen
,
J. D.
,
1999
,
The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in a 90° curved tube
,
J. Biomech.
,
32
, pp.
705
713
.
14.
Wernicke
,
J. T.
,
Meier
,
D.
,
Mizuguchi
,
K.
,
Damm
,
G.
,
Aber
,
G.
,
Benkowski
,
R.
,
Nose
,
Y.
,
Noon
,
G. P.
, and
DeBakey
,
M. E.
,
1995
,
A fluid dynamic analysis using flow visualization of the Baylor/NASA implantable axial flow blood pump for design improvement
,
Artif. Organs
,
19
(
2
), pp.
161
77
.
15.
MSDS Sodium Thiocyanate, Sigma-Aldrich, CAS number: 540-72-7 (www.sigmaaldrich.com).
16.
MSDS Potassium Thiocyanate, Sigma-Aldrich, CAS number: 333-20-0 (www.sigmaaldrich.com).
17.
Hein
,
J. A.
, and
O’Brien
,
W. D.
,
1992
,
A flexible blood flow phantom capable of independently producing constant and pulsatile flow with predictable spatial flow profile for ultrasound flow measurement validation
,
IEEE Trans. Biomed. Eng.
,
39
, pp.
1111
1122
.
18.
Mikami
,
F.
,
Chen
,
B.
, and
Nishikawa
,
N.
,
2001
,
Visualization and PTV study of natural convection in particle suspensions
,
JSME Int. J., Ser. B
,
44
(
1
), pp.
30
37
.
19.
Uzol
,
O.
,
Chow
,
Y. C.
,
Katz
,
J.
, and
Meneveau
,
C.
,
2002
,
Unobstructed particle image velocimetry measurements within an axial turbo-pump using liquid and blades with matched refractive indices
,
Exp. Fluids
,
33
(
6
), pp.
909
916
.
20.
McAllister
,
R. A.
,
1960
,
The viscosity of liquid mixtures
,
AIChE J.
,
6
(
3
), pp.
427
431
.
21.
Narrow
,
T. L.
,
Yoda
,
M.
, and
Abdel-Khalik
,
I.
,
2000
,
A simple model for the refractive index of sodium iodide aqueous solutions
,
Exp. Fluids
,
28
, pp.
282
283
.
22.
Singh
,
S.
,
1983
,
An exact technique for mixing of immersion fluids
,
Exp. Tech.
,
7
(
1
), pp.
27
29
.
23.
MSDS Zinc Iodine, Sigma-Aldrich, CAS number: 10139-47-6 (www.sigmaaldrich.com).
24.
Oates
,
C. P.
,
1991
,
Towards an ideal blood analogue for Doppler ultrasound phantoms
,
Phys Med Biol.
,
11
, pp.
1433
1442
.
25.
Law
,
Y. F.
,
Johnston
,
K. W.
,
Routh
,
H. F.
, and
Cobbold
,
R. S. C.
,
1989
,
On the design of a steady flow model for Doppler ultrasound studies
,
Ultrasound Med. Biol.
,
15
, pp.
505
516
.
26.
Ramnarine
,
K. V.
,
Nassiri
,
D. K.
,
Hoskins
,
P. R.
, and
Lubbers
,
J.
,
1998
,
Validation of a new blood-mimicking fluid for use in Doppler flow test objects
,
Ultrasound Med. Biol.
,
24
(
3
), pp.
451
459
.
27.
Stewart
,
S. F. C.
,
1999
,
A rotating phantom torus for assessing color Doppler Accuracy
,
Ultrasound Med. Biol.
,
25
(
8
), pp.
1251
1264
.
28.
Liepsch
,
D.
,
2002
,
An introduction to biofluids mechanics-basic models and applications
,
J. Biomech.
,
35
, pp.
415
435
.
29.
Naiki
,
T.
,
Yanai
,
Y.
, and
Hayabashi
,
K.
,
1995
,
Evaluation of high polymer solutions as blood analog fluid
,
J. Jpn. Soc. Biorheology
,
9
, pp.
84
89
.
30.
Pohl
,
M.
,
Wendt
,
M. O.
,
Werner
,
S.
,
Koch
,
B.
, and
Lerche
,
D.
,
1996
,
In vitro testing of artificial heart valves: comparison between Newtonian and non-Newtonian fluids
,
Artif. Organs
,
20
(
1
), pp.
37
46
.
31.
Brookshier
,
K. A.
, and
Tarbell
,
J. M.
,
1993
,
Evaluation of a transparent blood analog fluid: aqueous xanthan gum/glycerin
,
Biorheology
,
30
, pp.
107
116
.
32.
Mann
,
D. E.
, and
Tarbell
,
J. M.
,
1990
,
Flow of non-Newtonian blood analog fluids in rigid curved and straight artery models
,
Biorheology
,
27
, pp.
711
733
.
33.
ABBE-3L Refractometer Operator’s manual and refractive index 1996, University of Richmond (http://web.uccs.edu/bgaddis/chem337/expts/nD/nD.htm).
34.
Barnes, H. A., Hutton, J. F., and Walters, K., 1989, An introduction to rheology, Rheology Series, 3, Elsevier, ISBN 0-444-87140-3, p. 13.
35.
George
,
J.
,
Sastry
,
N. V.
,
Patel
,
S. R.
, and
Valand
,
M. K.
,
2002
,
Densities, viscosities, speeds of sound, and relative permittivities for Methyl Acrylate+1-Alcohols (C1–C6) at T=(308.15 and 318.15 K),
J. Chem. Eng. Data
,
47
(
2
), pp.
262
269
.
36.
Kirk, R. E., and Othmer, D. F., 1984, Kirk-Othmer Encyclopedia of chemical technology (3rd Edition) 1984, John Wiley & Sons, vol. 9, ISBN: 0-471-52677-0, pp. 62–64.
37.
Joram, C., 1998, The distillation plant of the DELPHI Barrel RICH Detector, DELPHI 98-53 RICH 94, (Publications of the CERN laboratory in Geneva, Switzerland (http://delphiwww.cern.ch).
38.
Lide D. R., (Ed), 2001, Handbook of Chemistry & Physics, CRC Press, Inc., ISBN: 0-8493-0482-2, p. 3-161, p. 3-269, p. 3-316, p. 3-224, p. 3-380, and pp. 10-223, 10-224.
39.
Perry, R. H., Green, D. W., and Maloney, J. O. (Eds), 1997, Perry’s Chemical Engineers’ Handbook, McGraw-Hill, 7th edition, ISBN: 0070498415, pp. 2–7 and pp. 2–47.
40.
MSDS Methyl Salicylate, Sigma-Aldrich, CAS number: 119-36-8 (www.sigmaaldrich.com).
41.
MSDS Ethanol, Sigma-Aldrich, CAS number: 64-17-5 (www.sigmaaldrich.com).
42.
MSDS Diethyl Phthalate, Sigma-Aldrich, CAS number: 84-66-2 (www.sigmaaldrich.com).
43.
MSDS D-Limonene, Sigma-Aldrich, CAS number: 5989-27-5 (www.sigmaaldrich.com).
44.
MSDS Glycerin, Sigma-Aldrich, CAS number: 56-81-5 (www.sigmaaldrich.com).
45.
Chemical Resistance of Plexiglas, V-Series Acrylic Resins, Technical report by Atoglas Inc. ADV # 010334/TGI/6-01 (also on www.atoglass.com).
46.
Chemical Resistance of Rigid Geon® vinyls based on immersion test, Technical service report No. 15 by Plastomatic Inc. (also on http://www.plastomatic.com/geom-chemical-resistance.pdf).
47.
Tenite Cellulosic Plastics, Technical reports PP 101, PP 102 and PP 103 by Eastman Inc. (also on http://www.eastman.com/Online̱Publications).
48.
O’Connell
,
P. A.
, and
McKenna
,
G. B.
,
1999
,
Arrhenius-type temperature dependence of the segmental relaxation below Tg
,
J. Chem. Phys.
,
110
(
22
), pp.
11054
11060
.
49.
Helleloid, G. T., 2001, On the computation of viscosity-shear rate temperature master curves for polymeric liquids, Morehead Electronic Journal of Applicable Mathematics, 1, pp. 1–11 (also on http://www.morehead-st.edu/colleges/science/math/mejam/).
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