HagenPoiseuillekaavan

HagenPoiseuillekaavan is a theoretical framework in fluid dynamics that extends the classical Hagen-Poiseuille model of laminar flow in circular pipes by incorporating a Kaavan correction. It is used to analyze steady and slowly varying flows in microchannels and small biological vessels where viscosity, wall elasticity, and pulsatile pressure deviate from ideal conditions. The term combines the names of Hagen and Poiseuille with "Kaavan," a fictional or generalized parameter that captures non-Newtonian behavior, wall compliance, and flow pulsatility.

In its mathematical form, the standard Hagen-Poiseuille relation Q = (π ΔP r^4) /(8 μ L) is modified to include effective viscosity μ_eff and an adjustment factor Φ_Kaavan that accounts for temporal changes and wall mechanics: Q = (π r^4 ΔP_eff) /(8 μ_eff L) × Φ_Kaavan(Kaavan, Re, Wi). Here ΔP_eff may reflect time-averaged or pulsatile pressure, μ_eff represents non-Newtonian or temperature-dependent viscosity, and Φ_Kaavan is a dimensionless correction function. For a Newtonian, rigid-walled, steady flow, Kaavan returns Φ_Kaavan = 1 and μ_eff = μ, recovering the classical formula.

The Kaavan parameter is a composite, often defined to include wall compliance, pulsatility (via a Womersley-like factor), and non-Newtonian shear-thinning or thickening behavior. Researchers may calibrate Φ_Kaavan experimentally or numerically for specific fluids and geometries.

Applications include microfluidic device design, biomedical modeling of capillaries and artificial vessels, and soft robotics where flexible conduits are common. The framework remains a theoretical tool; practical deployment depends on reliable characterization of Kaavan-related effects.