Calibrated Precision Silica Micro-Capillary Tubes
Provides internal lumen diameters D = 20, 35, 50, 65, 80, and 95 μm with circular cross-sections (±0.5 μm).
Biomedical Engineering / Fåhræus-Lindqvist Effect
FREE TO EXPLORELABORATORY 34 · BIOMEDICAL ENGINEERING
Fåhræus-Lindqvist Effect & Apparent Relative Blood Viscosity in Micro-Capillaries
Quantify the Fåhræus-Lindqvist reduction in apparent relative blood viscosity η_rel in micro-capillary glass tubes as lumen diameter D narrows from 95 μm to 20 μm. Explore interactive physiological instrumentation simulation, biomechanics, and biomedical engineering telemetry.
BIOINSTRUMENTATION · BIOSIGNALS · BIOMECHANICS · IMAGING
Your virtual biomedical engineering laboratory.
APPARENT RELATIVE BLOOD VISCOSITY Η_REL—
PHYSIOLOGICAL & TEST CELL TELEMETRY
Ready to sample with Diameter D = 50.0 μm.
Adjust Diameter D, then execute biomedical trial.
Biomedical engineering telemetry and physiological states are evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity biological and physiological modeling.
Biomedical assumptions and boundary condition limits
The linear relation applies across the classic microvascular range (20 to 100 μm); below 7 μm, the curve inverts sharply upward. Evaluated on calibrated silica micro-capillary tubes (diameters D = 20, 35, 50, 65, 80, 95 μm; length L = 30 mm) perfused with human blood (feed hematocrit H_F = 45%, plasma viscosity η_p = 1.20 mPa·s) at high shear rates (γ̇_w > 500 s⁻¹) at 37.0 °C. Apparent relative viscosity slope k_d = 0.0125 μm⁻¹ with baseline η_0 = 1.2500 (η_rel = 1.500 at 20 μm, rising to 2.438 at 95 μm).
Biomedical apparatus & physiological sensors.
Pneumatic Micro-Perfusion Driving Pressure Controller
Applies regulated driving pressure drops ΔP from 1 to 50 kPa with 0.01 kPa stability.
High-Speed Fluorescent Micro-PIV Microscope
Visualizes red cell axial migration and measures cell-free marginal plasma layer thickness δ.
Sub-Micron Electronic Catch Microbalance
Determines volumetric flow rate Q by timed gravimetric catch with anti-evaporation cover.
Thermostatically Controlled Perfusion Chamber (37.0 °C)
Maintains blood and capillary tubes at constant physiological temperature.
Cone-and-Plate Plasma Viscometer
Measures baseline dynamic viscosity of cell-free blood plasma (η_p = 1.20 mPa·s).
FOLLOW THE METHOD
A reason behind every step.
Quantify the Fåhræus-Lindqvist reduction in apparent relative blood viscosity η_rel in micro-capillary glass tubes as lumen diameter D narrows from 95 μm to 20 μm. Standardized parameter settings: 20.0, 35.0, 50.0, 65.0, 80.0, 95.0 μm.
01
Blood Specimen Standardization and Plasma Viscometry
Prepare fresh anti-coagulated human blood (Hct = 45.0%); centrifuge an aliquot to isolate plasma and measure plasma viscosity η_p on cone-plate viscometer (1.20 mPa·s).
02
Micro-Capillary Alignment and Pre-Wetting
Mount 20 μm silica micro-capillary into the perfusion manifold, pre-wet with plasma to prevent bubble entrapment, and seal pressure ports.
03
Driving Pressure Application
Apply pneumatic pressure drop ΔP to achieve high wall shear rate (γ̇_w > 500 s⁻¹), ensuring fully dispersed non-rouleaux flow.
04
Volumetric Flow Rate Measurement
Determine steady volumetric flow rate Q via timed micro-gravimetric collection on ultra-microbalance over 180 seconds.
05
Apparent Viscosity Computation
Calculate apparent blood viscosity from Poiseuille's formula: η_app = [π · D⁴ · ΔP] / [128 · L · Q], and compute relative viscosity η_rel = η_app / η_p.
06
Capillary Diameter Progression Sequence
Repeat standardized perfusion across tube diameters D = 35, 50, 65, 80, and 95 μm, recording apparent relative viscosity η_rel at each diameter.
07
Fåhræus-Lindqvist Linear Regression
Plot apparent relative viscosity η_rel against capillary diameter D and extract slope k_d and baseline intercept η_0 via linear regression.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into biomedical engineering insight.
Points are your recorded observations. The solid regression line validates Fåhræus-Lindqvist Effect mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
η_rel = k_d · D + η_0 = 0.0125 · D + 1.2500
| # | Micro-Capillary Lumen Diameter D (μm) | Apparent Relative Blood Viscosity η_rel (ratio) | Capillary lumen diameter D (μm) | Apparent relative blood viscosity η_rel (ratio) | Remove |
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