On the oscillatory tube flow of healthy human blood
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1 On the oscillatory tube flow of healthy human blood Miguel A. Moyers-Gonzalez Department of Mathematics and Statistics, University of Canterbury, New Zealand Robert G. Owens Département de mathématiques et de statistique, Université de Montréal, Canada Jiannong Fang ENAC-ICARE-GEOLEP EPFL, Switzerland 1
2 Outline Blood rheology rouleaux, linear viscoelastic properties and modelling, validation Oscillatory tube flow Results linear viscoelastic fluid W<<1 and W>>1 non-homogeneous model small volume flow rate amplitude high frequency oscillations quadrature component of pressure gradient phase shift, flow enhancement and loss angle leading order behaviour of macroscopic variables Conclusions 2
3 Blood rheology: composition of blood 3
4 Blood rheology: yield stress (Picart et al. (1998)) 4
5 Blood rheology: aggregation and disaggregation 5
6 Blood rheology: shear and complex viscosity 6
7 Blood rheology: modelling of rouleaux (From Y. Liu and W. K. Liu, Rheology of red blood cell aggregation by computer simulation J. Comput. Phys. 220 (2006) ) 7
8 Blood rheology: a non-homogeneous model 8
9 Blood rheology: a non-homogeneous model 9
10 Blood rheology: a non-homogeneous model + (i,k-i) k k+j (k,j) k (i,k-i) (k,j) k+j 10
11 Blood rheology: a non-homogeneous model 11
12 Experimental validation. 1: triangular shear-rate 12
13 Experimental validation. 1: triangular shear-rate 13
14 Experimental validation. 1: triangular shear-rate 14
15 Experimental validation. 1: triangular shear-rate 15
16 Experimental validation. 1: triangular shear-rate 16
17 Experimental validation. 2: peripheral cell-free layer 17
18 Oscillatory tube flow: parameters 18
19 Oscillatory tube flow: basic equations 19
20 Oscillatory tube flow: linear viscoelastic fluid 20
21 Oscillatory tube flow: linear viscoelastic fluid 21
22 Oscillatory tube flow: non-homogeneous model 22
23 Oscillatory tube flow: MTSE: leading order variables 23
24 Oscillatory tube flow: MTSE: leading order variables 24
25 Oscillatory tube flow: MTSE: leading order variables 25
26 Oscillatory tube flow: MTSE: leading order variables 26
27 Oscillatory tube flow: MTSE: leading order variables 27
28 Oscillatory tube flow: MTSE: leading order variables 28
29 Oscillatory tube flow: MTSE: complex viscosity η 29
30 Oscillatory tube flow: MTSE: complex viscosity η 30
31 Results: PM rms A>0 A<0 31
32 Results: PM rms A<0 A>0 32
33 Results: PM rms and flow enhancement 33
34 Results: PM rms and flow enhancement 34
35 Results: A and ϕ 35
36 Results: N0De at 4π rads /s 36
37 Results: N0De at 4π rads /s 37
38 Results: N0De at 400π rads /s 38
39 Results: N0De at 400π rads /s 39
40 Conclusions An extensively tested sticky dumbbell model has been developed, allowing for aggregation and fragmentation of rouleaux and the description of non-homogeneous blood flow. The behaviour of healthy human blood in oscillating tube flow has been described via computations of the pressure gradient-volume flow rate relationship. A multiple time scales analysis has shown that red cell number density, average aggregate size and the rrcomponent of the elastic stress are functions of r alone, to leading order. Current work is directed towards correct prediction (with HI) of cell migration the thickness of the cell-free layer and the Fahraeus-Lindqvist effect. 40
41 References RGO, A new microstructure-based constitutive model for human blood, J. Non-Newtonian Fluid Mech., 140 (2006) J. Fang and RGO, Numerical simulations of pulsatile blood flow using a new constitutive model, Biorheology, 43 (2006) M. Moyers-Gonzalez, RGO and J. Fang, A non-homogeneous constitutive model for human blood. Part I: model derivation and steady flow, J. Fluid Mech., 617 (2008) M. Moyers-Gonzalez and RGO, A non-homogeneous constitutive model for human blood. Part II: Asymptotic solution for large Péclet numbers, J. Non-Newtonian Fluid Mech., 155 (2008) M. Moyers-Gonzalez, RGO and J. Fang, A non-homogeneous constitutive model for human blood. Part III: Oscillatory flow, J. Non-Newtonian Fluid Mech., 155 (2008) M. Moyers-Gonzalez, RGO and J. Fang, On the high frequency oscillatory tube flow of healthy human blood, J. Non-Newtonian Fluid Mech. (2009), in press. 41
On the high frequency oscillatory tube flow of healthy human blood
* Revised Manuscript Click here to view linked References On the high frequency oscillatory tube flow of healthy human blood Miguel A. Moyers-Gonzalez a, Robert G. Owens b, Jiannong Fang c a Department
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