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Newtonian fluid
 
 
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A Newtonian fluid (named for Isaac Newton
Isaac Newton

Sir Isaac Newton, Fellow of the Royal Society was an English people physicist, mathematician, Astronomy, Natural philosophy, Alchemy, and Theology and one of the the 100 in human history....
) is a fluid
Fluid

A fluid is defined as a substance that continually deforms under an applied shear stress. All liquids and all gases are fluids. Fluids are a subset of the Phase and include liquids, gas, Plasma physics and, to some extent, plasticity ....
 whose stress
Shear stress

File:Shear stress.JPGA shear stress, denoted , is defined as a stress which is applied parallel or tangent to a face of a material, as opposed to a normal stress which is applied perpendicularly....
 versus rate of strain
Strain (materials science)

In continuum mechanics, the infinitesimal strain theory, sometimes called small deformation theory, small displacement theory, or small displacement-gradient theory, deals with infinitesimal Deformation s of a Continuum mechanics....
 curve is linear and passes through the origin
Origin (mathematics)

In mathematics, the origin of a Euclidean space is a special Point , usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space....
. The constant of proportionality is known as the viscosity
Viscosity

Viscosity is a measure of the Drag of a fluid which is being deformed by either shear stress or extensional stress. In everyday terms , viscosity is "thickness"....
.
mple equation to describe Newtonian fluid behaviour is

where is the shear stress exerted by the fluid ("drag
Drag (physics)

The term drag is widely used in Physics and Engineering and is central to the field of fluid dynamics. "Drag" refers to forces that oppose the motion of a solid object through a fluid ....
") [Pa] is the fluid viscosity - a constant of proportionality [Pa·s] is the velocity gradient perpendicular to the direction of shear [s-1]

In common terms, this means the fluid continues to flow, regardless of the forces acting on it.






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A Newtonian fluid (named for Isaac Newton
Isaac Newton

Sir Isaac Newton, Fellow of the Royal Society was an English people physicist, mathematician, Astronomy, Natural philosophy, Alchemy, and Theology and one of the the 100 in human history....
) is a fluid
Fluid

A fluid is defined as a substance that continually deforms under an applied shear stress. All liquids and all gases are fluids. Fluids are a subset of the Phase and include liquids, gas, Plasma physics and, to some extent, plasticity ....
 whose stress
Shear stress

File:Shear stress.JPGA shear stress, denoted , is defined as a stress which is applied parallel or tangent to a face of a material, as opposed to a normal stress which is applied perpendicularly....
 versus rate of strain
Strain (materials science)

In continuum mechanics, the infinitesimal strain theory, sometimes called small deformation theory, small displacement theory, or small displacement-gradient theory, deals with infinitesimal Deformation s of a Continuum mechanics....
 curve is linear and passes through the origin
Origin (mathematics)

In mathematics, the origin of a Euclidean space is a special Point , usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space....
. The constant of proportionality is known as the viscosity
Viscosity

Viscosity is a measure of the Drag of a fluid which is being deformed by either shear stress or extensional stress. In everyday terms , viscosity is "thickness"....
.

Definition

A simple equation to describe Newtonian fluid behaviour is

where is the shear stress exerted by the fluid ("drag
Drag (physics)

The term drag is widely used in Physics and Engineering and is central to the field of fluid dynamics. "Drag" refers to forces that oppose the motion of a solid object through a fluid ....
") [Pa] is the fluid viscosity - a constant of proportionality [Pa·s] is the velocity gradient perpendicular to the direction of shear [s-1]

In common terms, this means the fluid continues to flow, regardless of the forces acting on it. For example, water is Newtonian, because it continues to exemplify fluid properties no matter how fast it is stirred or mixed. Contrast this with a non-Newtonian fluid
Non-Newtonian fluid

A non-Newtonian fluid is a fluid whose flow properties are not described by a single constant value of viscosity. Many polymer solutions and molten polymers are non-Newtonian fluids, as are many commonly found substances such as ketchup, starch suspensions, paint, blood and shampoo....
, in which stirring can leave a "hole" behind (that gradually fills up over time - this behaviour is seen in materials such as pudding, starch in water (oobleck
Oobleck

Oobleck is a fictional green precipitation invented by children's author Dr. Seuss in the book Bartholomew and the Oobleck. The word has since been used to describe a mixture of corn starch and water used to demonstrate the dilatant property of non-Newtonian fluids....
), or, to a less rigorous extent, sand), or cause the fluid to become thinner, the drop in viscosity causing it to flow more (this is seen in non-drip paint
Paint

Paint is any liquid, liquifiable, or mastic composition which after application to a Substrate in a thin layer is converted to an opaque solid film....
s, which brush on easily but become more viscous when on walls).

For a Newtonian fluid, the viscosity, by definition, depends only on temperature
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
 and pressure
Pressure

Pressure is the force per unit area applied to an object in a direction surface normal to the surface. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure....
 (and also the chemical composition of the fluid if the fluid is not a pure substance), not on the forces acting upon it.

If the fluid is incompressible and viscosity is constant across the fluid, the equation governing the shear stress, in the Cartesian coordinate system
Cartesian coordinate system

In mathematics, the Cartesian coordinate system is used to determine each Point uniquely in a Plane through two numbers, usually called the x-coordinate or abscissa and the y-coordinate or ordinate of the point....
, is

with comoving stress tensor (also written as )

where, by the convention of tensor
Tensor

A tensor is an object which extends the notion of Scalar , Vector , and Matrix . The term has slightly different meanings in mathematics and physics....
 notation, is the shear stress on the face of a fluid element in the direction is the velocity in the direction is the direction coordinate

If a fluid does not obey this relation, it is termed a non-Newtonian fluid
Non-Newtonian fluid

A non-Newtonian fluid is a fluid whose flow properties are not described by a single constant value of viscosity. Many polymer solutions and molten polymers are non-Newtonian fluids, as are many commonly found substances such as ketchup, starch suspensions, paint, blood and shampoo....
, of which there are several types, including polymer
Polymer

A polymer is a large molecule composed of repeating structural units typically connected by covalent chemical bonds. While polymer in popular usage suggests plastic, the term actually refers to a large class of natural and synthetic materials with a variety of properties....
 solutions, molten polymers, many solid suspensions and most highly viscous fluids.

See also

Non-newtonian fluid
Non-Newtonian fluid

A non-Newtonian fluid is a fluid whose flow properties are not described by a single constant value of viscosity. Many polymer solutions and molten polymers are non-Newtonian fluids, as are many commonly found substances such as ketchup, starch suspensions, paint, blood and shampoo....


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