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Complex flows of cellular suspensions in microtubes at different temperatures

Natalya Kizilova Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, Warsaw, Poland Liliya Batyuk Kharkov National Medical University, Kharkov, Ukraine

Experiments in Fluid Mechanics 2017 Warsaw, 23-24.10.2017

Outline

• 1. Microfluidic systems for blood processing
• 2. Blood flows through microtubes

3.1. Experiments 3.2. Fåhræus-Lindqvist effect 3.3. Copley-Scott Blair effect 3.4. Viscoplastic behavior

• 4. Mathematical modeling
• 5. Conclusions

Microfluidic systems for blood processing

) 10 ~ ( m d RBC 

Treatment/separation are based on

• Mechanical properties: density, elasticity,

flexibility;

• Eelectric properties: charge, dielectric

permittivity;

• Magnetic properties: magnetic moment,

magnetic permittivity;

• Biochemical properties: adhesiveness,

biomarkers.

UltraHighFrequency dielectrometry

Erythrocytes of venous blood was washed out in 0.9% NaCl and diluted to 35% suspension. HF dielectrometer with

9.2 , 47   



f HHz T C

Nanodiamonds in medicine

Radioprotective action of NDs

• Experimental rats + X-ray radiation dose 5.8 Gy

+ suspension of NDs (C=0.01 with 0.9% NaCl) 5 days before radiation => blood sampling 30 days after radiation. Results: 1) radiation => dehydration of erythrocyte membranes (by 37%); 2) radiation+NDs => dehydration by 28.6%; 3) NDs without radiation => no changes (non-toxicity)

Blood flow measurements

4

: 100,300,500 , 1,2,3 : 5 43 , 1 cos ( 1.15 ) : ( ) 8 ( )               

  bl

Tubes d m L cm Temperature T C T C Capillary vis imeter d mm T p R q L T q measured volumetric rate

Fåhræus-Lindqvist effect in suspensions

Stokes force, flow non-uniformity, inertia, Magnus force, unsteady viscous phenomena

t 3 3 2 1 2 3 4

d d d F k R(v v ) k v k R (v v ) k R ( ) (v v ) k R (v v ) dt d t          

      

            



           

5 500     m d m

Copley-Scott Blair effect

• Specific material-dependent adhesion at the

inner wall of the tube;

• Double electric layer and related

electrokinetic phenomena;

• Decrease in the apparent viscosity with

decrease in the diameter and electrostatic forces.

Problem formulation

1,2 1,2 1 2 2 1 2 1 1

dv 1 d p r r dr dr L dv r 0 : dr v r R : v (R) (R) r r R : v v dv Bingham fluid dr (T) : d / dT (T) : d / dT h(T) : d h / dT (T) : d / dT (T) : d / dT                                        

• Fåhræus-Lindqvist effect (boundary layer

free of cells)

• Copley-Scott Blair effect (h-layer of

adsorbed molecules/ions)

• Velocity slip boundary conditions (in

microtubes)

• Temperature dependencies of material

parameters

Fåhræus-Lindqvist for Newtonian fluids

2 2 1 2 2 2 1,2 * 1 1,2 * 1 2 1 (1) (2) 4

v (r) (1 2a) (1 )(1 ) r , v (r) (1 2a) r , v R p v , v , , , 4 L R v a , a C Kn, Kn / R. R q v rdr v rdr (1 4a) ( 1)(1 ) q(T) q( (T), (T),a( For a Boltzmann gas ) K ) n T               

 

                             

 

            

B 2

k T , 2 d pR 0, 0, a 0.         

h

Copley-Scott Blair + Fåhræus-Lindqvist for Newtonian fluids

4 3 2 2 3 4 1 2

q (1 h) 4( a)(1 h) 6 (1 )(1 h) 4 ( 1)(1 h) (1 ) , H h , , , a , a C Kn, Kn / R. R R R                                      

Copley-Scott Blair + Fåhræus-Lindqvist

for Bingham fluids

2 1 1

v (r), r [R h ,R h] v(r) v (r), r [R*,R h ] v (R*), r [0,R*]                

Conclusions

• Dielectric properties of red blood cells vary with

temperature and their surfaces are influenced by serious diseases (cancer, stroke)

• Steady flow of cellular suspensions through

microtubes differs from those described by Poiseuille law

• Among possible factors the transition to

viscoplastic state may explain the experimentally

• bserved temperature dependencies