Fluid Viscosity

Fluid viscosity is a measure of the ability of fluids to flow - fluids with low viscosity flow readily and fluids with high viscosity flow sluggishly. ^[1] Viscosity is one of the two fundamental physical properties of fluids - alongside density - that most strongly govern sediment transport. Together they determine how readily a fluid can erode sediment, how quickly particles settle through it, and whether flow will be smooth or chaotic.

Familiar examples span a wide range: air has very low viscosity, ice has very high viscosity, water has low viscosity, and honey has high viscosity. ^[1] The viscosity of water at 20°C is almost 55 times greater than that of air. ^[1] This large difference - between two fluids that both move particles in natural sediment transport - is one reason why water can transport particles of much larger size than those transported by wind. ^[1]

Like density, viscosity increases with decreasing temperature of the fluid. ^[1] This temperature dependence has real consequences for sediment transport: a cold mountain stream in winter carries more viscous water than the same stream in summer, which modifies settling velocities and the threshold current speed needed to entrain sediment from the bed.

Molecular (Dynamic) Viscosity

Molecular (dynamic) viscosity is the measure of resistance of a substance to change in shape taking place at finite speeds during flow. ^[1] It is the proportionality factor that links shear stress to the rate of strain - defined as the ratio of shear stress to the rate of deformation (du/dy) sustained across the fluid. ^[1] In other words, dynamic viscosity μ is a single number that describes how hard you have to push - per unit area - to make a fluid shear at a given rate.

The concept becomes clearest in a controlled experiment: imagine a fluid trapped between two parallel plates, with the lower plate stationary and the upper plate moving at a constant velocity V. ^[1] The fluid between the plates forms parallel sheets; as the upper plate moves, velocity varies linearly from zero at the lower plate to V at the upper plate. ^[1] Each layer moves slightly faster than the one below it, and the shear stress τ is the force per unit area required to sustain that velocity gradient. Dynamic viscosity is the constant that links shear stress to the velocity gradient du/dy: higher viscosity means greater shear stress is needed to achieve the same velocity gradient.

Shear stress is the shearing force per unit area exerted across the shearing surface at some point in a fluid, acting parallel to the surface of the fluid body. ^[1] It is generated at the boundary of two moving fluids and is a function of the extent to which a slower moving mass retards a faster moving one. ^[1]

The shearing force per unit area needed to produce a given rate of shearing or a given velocity gradient normal to the shear planes is determined by the viscosity - the greater the viscosity the greater the shear stress must be. ^[1] Viscosity decreases with higher temperature, so a given fluid flows more readily at higher temperatures. ^[1]

Newtonian vs. Non-Newtonian Fluids

A fluid that does not undergo a change in viscosity as the shear rate increases is called a Newtonian fluid - ordinary water is a prime example. ^[1] Most geologically important fluids that transport sediment - rivers, tidal currents, wind - behave as Newtonian fluids under normal conditions. Mud flows and debris flows with high clay content, however, behave as non-Newtonian fluids: their apparent viscosity changes with shear rate, and they require an initial yield stress before they begin to flow at all. This distinction fundamentally changes how they transport and deposit sediment compared to water.

Kinematic Viscosity

Because both density and dynamic viscosity strongly affect fluid behaviour, fluid dynamicists commonly combine them into a single parameter called kinematic viscosity ν, which is the ratio of dynamic viscosity to density. ^[1] Kinematic viscosity is an important factor in determining the extent to which fluid flows exhibit turbulence. ^[1]

The reason for combining both properties is that in natural flow systems, neither density nor dynamic viscosity acts alone - their ratio determines the balance between inertial forces and viscous forces, which is the ultimate control on whether flow is turbulent or laminar. Kinematic viscosity enters the Reynolds number formula directly, making it the key viscosity parameter for predicting flow regime.

Significance in Sediment Transport

Viscosity has a particularly important influence on water turbulence. ^[1] Increasing viscosity tends to suppress turbulence - the random movement of water molecules - thereby slowing the rate at which particles settle through water, a significant factor in transport of suspended sediment. ^[1] Decreased turbulence also reduces the ability of running water to erode and entrain sediment. ^[1]

These three linked effects - suppressed turbulence, slower settling, reduced erosion - mean that viscosity actively controls every stage of the sediment transport process. Higher viscosity at a given velocity means less sediment eroded, slower settling, and finer grain sizes remaining in suspension longer. Understanding viscosity is therefore a prerequisite for understanding the mechanics of rivers, wind transport, and density currents.

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