Newtonian fluid
Encyclopedia
A Newtonian fluid is a fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....

 whose stress
Shear stress
A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...

 versus strain
Deformation (mechanics)
Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration. A configuration is a set containing the positions of all particles of the body...

 rate 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. In a Cartesian coordinate system, the origin is the point where the axes of the system intersect...

.
The constant of proportionality is known as the viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

.

Definition

A simple equation to describe Newtonian fluid behaviour is


where is the shear stress
Shear stress
A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...

 exerted by the fluid ("drag
Drag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...

") [Pa] is the fluid viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

 - a constant of proportionality [Pa·s] is the velocity gradient
Gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....

 perpendicular to the direction of shear, or equivalently the strain rate [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. Other examples may be aqueous solutions, emulsions. Contrast this with a non-Newtonian fluid
Non-Newtonian fluid
A non-Newtonian fluid is a fluid whose flow properties differ in any way from those of Newtonian fluids. Most commonly the viscosity of non-Newtonian fluids is not independent of shear rate or shear rate history...

, in which stirring can either leave a "hole" behind (that gradually fills up over time - this behavior is seen in materials such as pudding and oobleck, or, to a less rigorous extent, sand), or climb the stirring rod (the Weissenberg effect
Weissenberg effect
The Weissenberg effect is a common phenomenon that occurs when a spinning rod is placed into a solution of liquid polymer. Instead of being thrown outward, entanglements cause the polymer chains to be drawn towards the rod. It is named after Karl Weissenberg....

) because of shear thinning
Shear thinning
Shear thinning is an effect where a fluid's viscosity—the measure of a fluid's resistance to flow—decreases with an increasing rate of shear stress. Another name for a shear thinning fluid is a pseudoplastic. This property is found in certain complex solutions, such as lava, ketchup, whipped cream,...

, the drop in viscosity causing it to flow more (this is seen in non-drip paint
Paint
Paint is any liquid, liquefiable, or mastic composition which after application to a substrate in a thin layer is converted to an opaque solid film. One may also consider the digital mimicry thereof...

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
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

 and pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

 (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
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length...

, is the tensor
Tensor
Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...




A second tensor, (also written as ), representing the total stress, can be written by combining the shear stress with conventional (thermodynamic) pressure:


where, by the convention of tensor notation, is the shear stress on the th face of a fluid element in the th direction is thermodynamical pressure is the velocity in the th direction is the th 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 differ in any way from those of Newtonian fluids. Most commonly the viscosity of non-Newtonian fluids is not independent of shear rate or shear rate history...

, of which there are several types, including polymer
Polymer
A polymer is a large molecule composed of repeating structural units. These subunits are typically connected by covalent chemical bonds...

solutions, molten polymers, many solid suspensions and most highly viscous fluids.
The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
x
OK