Palierne equation connects the

dynamic modulus Dynamic modulus (sometimes complex modulusThe Open University (UK), 2000. ''T838 Design and Manufacture with Polymers: Solid properties and design'', page 30. Milton Keynes: The Open University.) is the ratio of stress to strain under ''vibratory c ...

emulsion An emulsion is a mixture of two or more liquids that are normally immiscible (unmixable or unblendable) owing to liquid-liquid phase separation. Emulsions are part of a more general class of two-phase systems of matter called colloids. Althoug ...

s with the dynamic modulus of the two phases, size of the droplets and the interphase

surface tension Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor blades and insects (e.g. water striders) to f ...

. The equation can also be used for

suspensions In chemistry, a suspension is a heterogeneous mixture of a fluid that contains solid particles sufficiently large for sedimentation. The particles may be visible to the naked eye, usually must be larger than one micrometer, and will eventually ...

of viscoelastic solid particles in viscoelastic fluids. The equation is named after French rheologist Jean-François Palierne, who proposed the equation in 1991. For the dilute emulsions Palierne equation looks like: :

G^*=G^*_m(1+5\phi H^*)

where

G^*

is the dynamic modulus of the emulsion,

G^*_m

is the dynamic modulus of the continuous phase (matrix),

\phi

is the volume fraction of the disperse phase and the

H^*

is given as :

H^*=\frac

where

G^*_d

is the dynamic modulus of the disperse phase,

\sigma

is the surface tension between the phases and

R

is the

radius In classical geometry, a radius ( : radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the ...

of the droplets. For the suspension of solid particles the value of

H^*

is given as :

H^*=\frac

The Palierne equation is usually extended for the finite volume concentrations of the disperse phase

\phi

as: :

G^*=G^*_m\frac

References

{{reflist Non-Newtonian fluids Colloidal chemistry Composite materials