where:
h = coefficient of viscosity
| Definition of Terms |
| Hooke's and Newton's Laws |
Elasticity is the ability of a material to store deformational energy, and can be viewed as the capacity of a material to regain its original shape after being deformed. Viscosity is a measure of the ability of a material to resist flow, and reflects the ability of the material to dissipate deformational energy through flow. Material will respond to an applied force by exhibiting either elastic or viscous behavior, or more commonly, a combination of both mechanisms. The combined behavior is termed viscoelasticity.
In rheological measurements, the deformational force is expressed as the stress, or per unit area. The degree of deformation applied to a material is called the strain. Strain may be expressed as sample displacement (after deformation) relative to pre-deformation sample dimensions. Sample deformations can be in the form of either simple shear (where the material is deformed in a plane while confined between two surfaces), or linear deformations (where the material is either compressed or extended).
Hooke's law describes the mechanical behavior of an ideal solid. Hooke's law for shear deformations states that if a shear strain g is applied to an ideal solid, a shear stress g develops in the material in direct proportion to the strain:
s = G g
The proportionality constant in equations for shear (G) is known as the modulus of the material. The modulus of a material is a measure of its stiffness, or ability to resist deformation. Linear stress-strain behavior is characterized by the modulus remaining unchanged as strain is varied. The region where the modulus remains constant as strain is changed is called the linear region. The linear region is also referred to as the Hookean region of the material.
Newton's law describes the mechanical behavior of an ideal viscous fluid. When a fluid moves by virtue of being pushed through a pipe, or dragged through a screw in an extruder, etc., the movement is termed shear. Newton's law relates the shear stress (t) to the rate of strain (or shear rate) dg/dt:
where:
h = coefficient of viscosity
A fluid is said to be Newtonian if the viscosity does not depend upon the strain rate. An analogous equation can be written for tensile testing, where the tensile stress (e) is related to the tensile strain (e) by:
In a non-Newtonian fluid, the viscosity is not constant, but is a function of strain rate. Many polymer solutions are non-Newtonian in behavior because their viscosity decreases as shear rate is increased. This is called shear thinning or pseudoplasticity. In the opposite effect, shear thickening or dilatancy, the viscosity increases with increasing shear rate. This is seen in some concentrated aqueous dispersions of clays and sands.
