## Cure Terms Glossary

Viscosity

The viscosity of a fluid is a measure of its resistance to flow. It is a measure of the internal friction within the fluid (i.e. the friction between the molecules themselves). Increasing intermolecular bonding or increasing molecular weight (which multiplies the intermolecular associations) increases the viscosity. Strictly speaking the measure is the coefficient of viscosity although common usage reduces it to just viscosity.

The (coefficient of) viscosity is the tangential force per unit area between two horizontal planes, unit distance apart, within the fluid. In SI, the basic unit of this coefficient is that where a force of one Newton is required to maintain a velocity differential of 1 m/s between surfaces of 1 m square positioned 1 m apart.

Coefficient of viscosity η = (shear stress) / (shear rate)

The shear stress is 1 N/m2 and the shear rate is in reciprocal seconds (s-1), and thus the SI unit for coefficient of viscosity (equivalent to 1 Ns/m2) is the Pascal.second (Pa.s).

In the c.g.s. system, the basic unit is the Poise which is equivalent to 0.1 Ns/m2. Thus the conversions factors are,

1 Pa.s = 10 Poise (P)
1 Pa.s = 1000 centiPoise (cP), or 1 cP = 1 mPa.s

The viscosity of water at 20°C is 1.002 mPa.s (1.002 cP). Examples of liquids with a viscosity in the region of 1 Pa.s could include an unsaturated polyester resin for hand lay-up or a polyether triol for flexible slabstock foam.

In real systems the shear rate may not be consistent across the moving liquid (e.g. see figure below), and the absolute viscosity may be defined according to the equation,

τ = ηdν/dh

where τ is the shear stress and ν the laminar velocity at height h in the flowing liquid.

Absolute viscosity is also called dynamic viscosity. Dynamic viscosity is important in oscillating systems (i.e. where v varies with time). In oscillating systems, the dynamic viscosity is frequency dependent (decreases with increasing frequency).

Steady-flow viscosity can also show rate dependencies. The intermolecular associations can take several forms (e.g., dipolar associations, entanglements, etc.) and, if these cannot reform as fast as they are disrupted by the flow, then the viscosity will become dependent on the shear rate (decreases with increasing shear rate). Where the viscosity is independent of the shear rate, the behaviour is called Newtonian: where dependent on the shear rate the behaviour is non-Newtonian. In the non-Newtonian (shear thinning) region, the basic equations take on a power-law relationship, e.g.,

shear stress = m(shear rate)n

where m has units of Pa.sn and is called the consistency index.

At any given shear rate, the ratio (shear stress) / (shear rate) is still a viscosity - but this is now termed an apparent viscosity. With non-Newtonian materials, common practice is to extrapolate the (shear stress) / (shear rate) plot back to zero shear rate and quote a hypothetical zero-shear viscosity. Most polymers exhibit non-Newtonian behaviour - the higher the molecular weight the earlier the likely onset.

At gelation, the steady-flow viscosity becomes infinite.