Abstract
It is essential to formulate a refractive index (RI)-matched fluid to use in silicone phantom models for particle image velocimetry (PIV) experiments. In this work, an extensive effort to develop a non-Newtonian human milk-mimicking fluid (HMMF) with different concentrations of sodium iodide (NaI), glycerol (Gly), xanthan gum (XG), and distilled water (DW) is conducted. Measurements of RI and density are fitted onto a linear empirical expression relating to the NaI and Gly concentration. The Cross model was utilized to find the nonlinear viscosity model of raw human milk. HMMF solution is generated from a multi-constrained optimization. The matched HMMF, suitable for use in the lactating human breast phantom with bifurcated ductal structures, is achieved with composition of 15.69% NaI, 30.27% Gly, 54.02% water and 0.02% XG by weight percentage resulting in a non-Newtonian viscosity matched with that of human milk.
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Notes
For any parametric model, the relationship of its model outputs and experimental measurements can be expressed as:
$$ y_E(x)=y_R(x,\theta )+\delta (x)+\epsilon ,$$(2)where \(\theta \) stands for empirical parameters and x stands for design variables. \(y_E(x)\) is the experimental measurement, \(y_R(x,\theta )\) is the results from the predicted model (fitted equation in this work), \(\delta (x)\) is the model uncertainty, and \(\epsilon \) is the measurement uncertainty (Arendt et al. 2012).
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Acknowledgements
The authors wish to thank the mothers who donated breast milk for this study and Paige Clark of Anton Paar for the use of their Thermo-optical Oscillating Refraction Characterizer (TORC) 5000.
Funding
This material is based upon work supported by the National Science Foundation under Grant nos. 1454334 and 1707063, National Science Foundation Graduate Research Fellowship Program under Grant no. 1746053, and Eugene McDermott Graduate Fellowship no. 201701.
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Jiang, L., Alatalo, D.L. & Hassanipour, F. A human milk-mimicking fluid for PIV experiments. Exp Fluids 61, 224 (2020). https://doi.org/10.1007/s00348-020-03052-z
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DOI: https://doi.org/10.1007/s00348-020-03052-z