Biofluid Mechanics Computational Dashboard

Viscosity & Flow Regimes

Governing Eq: $\tau = \mu \dot{\gamma}$ (Newtonian) vs $\tau = K\dot{\gamma}^n$ (Power Law)

Analytical Breakdown

Newtonian Model (Plasma): Viscosity ($\mu$) is constant regardless of shear rate. Graph shows a linear relationship between shear stress and shear rate.
Non-Newtonian (Whole Blood): Exhibits shear-thinning (pseudoplastic) behavior. At low shear rates, RBCs form rouleaux, increasing apparent viscosity. At high shear rates (large arteries), cells align and viscosity drops.
🚨 Fåhræus–Lindqvist Effect: In microvessels (< 300 $\mu$m), RBCs migrate to the center, creating a cell-free plasma layer at the wall. Apparent viscosity dramatically decreases, violating bulk continuum assumptions.

Arterial Hydrostatic Pressure

Governing Eq: $P_{total} = P_{heart} + \rho g h$

Parameters

Fluid Density ($\rho$) [kg/m³]: 1060 Gravity ($g$) [m/s²]: 9.81

Physiological Consequence

Gravity significantly influences transmural pressure. When standing, hydrostatic pressure adds up to ~100 mmHg to the baseline mean arterial pressure (MAP) at the feet, forcing the venous system to utilize one-way valves and the skeletal muscle pump to return blood to the right atrium.

Jurin's Law: Capillary Rise

h = 0.00 mm

System Variables

Surface Tension ($\sigma$) [N/m]: 0.0728 Tube Radius ($R$) [mm]: 1.0 Contact Angle ($\theta$) [deg]: 0

Governing Eq: $h = \frac{2\sigma\cos\theta}{\rho g R}$

At the microscale (e.g., organ-on-a-chip, alveoli), interfacial forces dominate over inertial forces (Capillary Number, $Ca < 1$). Surfactants lower $\sigma$, directly preventing lung alveolar collapse.