4 - Mechanical Properties of Blood Whole blood WB fibrin...

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1 Mechanical Properties of Blood Whole blood WB - fibrin RBCs + Saline η γ Non-Newtonian Newtonian Repulsion from wall of test chamber Mechanical Properties of Blood • To get close to the zero shear rate and determine if blood could be an “elastic solid,” it was proposed in 1963 that blood could a Casson fluid: γ    y   A * Shear Yield Stress: 0.05 dyn/cm 2 V i,j ij - p ij 2 J 2 V ij Tensor Notation for Biofluids: w/ J 2 = ½ V ij V ij Only non-zero Strain invariant V ij = ½(v i,j + v j,i ) Recall from the simple parallel plate example:   y/h = 2(½(v i,j + v j,i )) = 2 V 12 = 2 J 2 . . J 2 = (V 12 ) 2 ( J 2 ) = [( 2 J 2 ) ¼ + 2 y ½ ] 2 J 2 ½ Tensor Notation of Stokes: 12 - p 12 2 J 2 V 12 . Substitute into Casson’s Eq: 12   y    .    y    . . ij - p ij 2 J 2 V ij
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