5 - RBC Mechanics: Linear Viscoelasticity RBCs are neither...

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1 RBC Mechanics: Linear Viscoelasticity • RBCs are neither an elastic solid, e.g. σ ij ~ ε ij , nor a viscous fluid, e.g. σ ij ≈∂ε ij / t. Rather, they are somewhere in between • Consider the 1-D elements for –E las t ic ma te r ia l σ = E ε – Viscous material σ = με • Maxwell Fluid σ = με and σ = E ε in series (add) ε 1 + ε 2 = εσ /E + σ / μ = ε . σ σ . . . μ RBC Mechanics: Linear Viscoelasticity • Voigt Model σ = με and σ = E ε in series (parallel) σ 1 + σ 2 = σ E ε + με = σ • Kelvin Model (Standard Linear Solid) ε 1 = ε 2 + ε μ (A); σ = σ 1 + σ 2 (B) σ 2 = E 2 ε 2 (C); σ 2 = με μ (D); σ 1 = E 1 ε 1 (E) – Plug in C, E, and A into B: σ = E 1 ε 1 + E 2 ( ε 1 ε μ ) = (E 1 + E 2 ) ε 1 –E 2 ε μ σ = (E 1 + E 2 ) ε 1 –E 2 ε μ – Combine and plug in D as well: σ + ( μ /E 2 ) σ = E 1 ε 1 + μ (1+E 1 /E
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5 - RBC Mechanics: Linear Viscoelasticity RBCs are neither...

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