Viscosity

Why it matters in anaesthesia

• Determines resistance to flow in tubes and hence affects infusion rates, cannula/needle performance, and work of breathing through airways/ETTs.
  • In laminar flow, resistance is proportional to viscosity: R ∝ η (Poiseuille).
  • In turbulent flow, resistance depends more on density and flow velocity than viscosity (Reynolds).
• Affects gas flow measurement and delivery (rotameters, pneumotachographs) and performance of humidifiers/filters (increased resistance with secretions).
  • Viscosity influences laminar flow elements used in flowmeters; secretions increase effective viscosity and promote turbulence.
• Blood viscosity influences microcirculatory flow and shear stress; clinically relevant in anaemia/polycythaemia, hypothermia, and low-flow states.
  • Blood is non-Newtonian (shear-thinning): apparent viscosity decreases as shear rate increases.

Clinical examples

• Rapid fluid delivery: large-bore, short cannula; warming fluids reduces viscosity and increases flow.
  • For laminar flow: Q ∝ 1/η and Q ∝ r^4 and Q ∝ 1/L.
• ETT/airway resistance: secretions and humidification changes can increase resistance; high flows increase turbulence and pressure requirements.
  • Heliox reduces density and can reduce turbulent resistance (not viscosity-driven).
• Temperature management: hypothermia increases blood viscosity and may worsen microvascular flow; warming reduces viscosity of blood and IV fluids.
  • Most liquids: viscosity decreases with increasing temperature; gases: viscosity increases with increasing temperature.

Core definitions

• Dynamic viscosity (η): measure of internal friction; proportionality constant between shear stress and velocity gradient in Newtonian fluids.
  • Shear stress (τ) = η × (du/dy).
  • Units: Pa·s (N·s·m⁻²). Common: mPa·s (centipoise, cP); 1 cP = 1 mPa·s.
• Kinematic viscosity (ν): dynamic viscosity divided by density.
  • ν = η/ρ.
  • Units: m²·s⁻¹ (Stokes, St); 1 St = 10⁻⁴ m²·s⁻¹; 1 cSt = 10⁻⁶ m²·s⁻¹.
• Newtonian vs non-Newtonian fluids.
  • Newtonian: viscosity constant regardless of shear rate (e.g., water, most simple gases).
  • Non-Newtonian: viscosity varies with shear rate/time (e.g., blood, mucus).

Relationship to flow in tubes

• Poiseuille’s law (steady, incompressible, laminar flow of a Newtonian fluid in a long rigid cylindrical tube):
  • Q = (ΔP · π · r⁴) / (8 · η · L).
  • Resistance R = ΔP/Q = (8ηL)/(πr⁴).
• Reynolds number predicts laminar vs turbulent tendency:
  • Re = (ρ · v · D) / η = (v · D) / ν.
  • Higher viscosity lowers Re (promotes laminar); higher density/velocity/diameter increases Re (promotes turbulence).
• Entrance length and developing flow: Poiseuille applies after fully developed laminar flow; short cannulae may have significant entrance effects.
  • Clinical implication: real-world flow may be less than Poiseuille predicts, especially at high flow rates and with connectors/valves.

Determinants of viscosity

• Temperature dependence:
  • Liquids: viscosity decreases as temperature increases (reduced intermolecular cohesion).
  • Gases: viscosity increases as temperature increases (increased molecular momentum transfer).
• Pressure dependence:
  • Liquids: viscosity increases slightly with pressure (usually small effect clinically).
  • Gases: viscosity relatively independent of pressure at moderate pressures (ideal gas approximation).
• Composition and molecular structure:
  • Higher molecular weight/long-chain molecules increase viscosity; solutions with proteins (e.g., blood plasma) more viscous than water.
• Blood-specific determinants (apparent viscosity):
  • Haematocrit is the major determinant: viscosity rises non-linearly with increasing Hct.
  • Plasma proteins (fibrinogen), RBC deformability, RBC aggregation (rouleaux) affect low-shear viscosity.
  • Shear rate: blood is shear-thinning; at high shear (arteries) apparent viscosity falls; at low shear (venous/microcirculation) apparent viscosity rises.

Measurement of viscosity

• Capillary (Ostwald) viscometer: time for a fixed volume to flow through a capillary under gravity; compares to a reference fluid.
  • Best for Newtonian fluids; temperature control essential.
• Rotational viscometers (cone-and-plate, concentric cylinder): measure torque required to rotate at a set shear rate; can characterise non-Newtonian behaviour.
  • Useful for blood and polymer solutions (shear-dependent viscosity).
• Falling-sphere (Stokes) viscometer: terminal velocity of a sphere in fluid relates to viscosity (assumes laminar flow around sphere).
  • Requires low Reynolds number; sensitive to temperature and sphere size/density.

Typical values (order of magnitude)

• Water at 20°C: ~1 mPa·s (1 cP).
• Blood at 37°C: apparent viscosity ~3–4 mPa·s (varies with Hct and shear rate).
• Air at 20°C: ~0.018 mPa·s (1.8×10⁻⁵ Pa·s).