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I am studying the Barus effect / Merrington effect / die swell / extrudate swell, which is a characteristic of non-Newtonian viscoelastic liquids (Introduction to the phenomenon in this video) i.e. the medium responds to the stress $\sigma$ of irritator with a strain $\epsilon (= \Delta l/l)$ that increases until the medium ultimately fails in a local pathology

  • blood has both viscous and elastic components which it can apply in pathophysiological condition \begin{equation} \gamma = \gamma_{v} + \gamma_{e}. \end{equation}

#1 Maxwell material model

  • total shear stress if blood behaves like Maxwell material in local pathophysiological regions \begin{equation} \sigma = \sigma_{v} = \sigma_{E} = \eta \frac{d \gamma_{v}}{d t} = G_{M} \gamma_{E}, \end{equation} implying $\sigma = \eta \, d\gamma_{v}/dt$ and $\sigma = G_{M} \gamma_{E}$.

I am thinking when blood is not non-Newtonian etc in muscular pathologies and muscular infections. I want to evaluate how much blood is non-Newtonian in particular situations. I am interested in muscles and their supply with necessities.

How much is local blood non-Newtonian pathophysiologically?

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According to this conference proceeding blood is very nearly newtonian at normal shear rates. More accurately blood is very thick and a shear-thinning fluid, but the shear-thinning effects don't scale with a power law like other non-Newtonian fluids.

In terms of blood changing viscosities, I suspect that in living patients blood viscosity is quite constrained, not only by physiological feedback but by the fact that if the blood viscosity changed very much the patient would become nonliving. Blood circulates constantly, and when it stops circulating it coagulates(which complicates efforts to measure its viscosity, I imagine). Any local effects on blood viscosity would be 'washed away' by the fresh blood arriving every heartbeat. If there's no or very limited blood circulating to the muscular pathology you're interested in the blood viscosity is probably not as significant as the ischemic tissue death that's just about to happen.

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  • $\begingroup$ Thank you for your answer! Your case is general. You cannot assume that all local effects are always washed away after a new heartbeat. Ischemic tissue death happens lastly. I am interested in what happens between the initiator and ischemia i.e. how much local blood is non-Newtonian. $\endgroup$
    – Léo Léopold Hertz 준영
    Dec 4, 2015 at 17:30
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    $\begingroup$ I'm not sure I understand. Between the initiator and ischemia the blood won't move much/at all, so why would it be interesting to study its non-newtonianness? All fluids at rest are perfectly Newtonian. Studies of blood viscosity next to dead or dying tissue would be pretty interesting but under those circumstances blood clots quickly. I'd start with kinematic blood clotting studies like this one but I think most of this research hasn't been done. With the possible exception of people studying angiogenesis and leaky blood vessels in tumors. $\endgroup$
    – Resonating
    Dec 7, 2015 at 21:48
  • $\begingroup$ Yes, exactly. Blood at rest is perfectly Newtonian. But I am not considering cases at rest. Consider etc low BP and low Chol cases. Why CVD? $\endgroup$
    – Léo Léopold Hertz 준영
    Dec 7, 2015 at 22:30

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