# Newtonian Fluid

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## Newtonian fluid

A fluid whose stress at each point is linearly proportional to its strain rate at that point. The concept was first deduced by Isaac Newton and is directly analogous to Hooke's law for a solid. All gases are newtonian, as are most common liquids such as water, hydrocarbons, and oils.

A simple example, often used for measuring fluid deformation properties, is the steady one-dimensional flow u(y) between a fixed and a moving wall (see illustration). The no-slip condition at each wall forces the fluid into a uniform shear strain rate ε, given by Eq. (1),

(1) which is induced by a uniform shear stress &tgr;. Here V is the speed of the moving wall, H is the perpendicular distance between the walls, and u is the fluid velocity at distance y from the fixed wall.

If the fluid is newtonian, the experimental plot of &tgr; versus will be a straight line. The constant of proportionality is called the viscosity μ of the fluid, as stated in Eq. (2). (2) The viscosity coefficients of common fluids vary by several orders of magnitude. See Fluid flow, Fluids, Viscosity

## Newtonian Fluid

a fluid that obeys Newton’s law of viscous friction. For rectilinear laminar flow, this law states that the shear stress τ in the planes of contact of layers of the fluid is directly proportional to the derivative of the rate of flow ν in the direction of the normal n to these planes; that is, τ = η(∂ν/∂n) where η is the coefficient of viscosity. In the general case of a three-dimensional flow, for a Newtonian fluid a linear relation holds between the stress tensor and the tensor of the rates of strain. Most liquids, including water and lubricating oil, and all gases have the properties of a Newtonian fluid. The flow of Newtonian fluids is studied in hydrodynamics and aerodynamics.

Non-Newtonian fluids are fluids for which the relations indicated above are not linear, for example, for the rectilinear flow where k ≠ 1. Examples are a number of suspensions and solutions of polymers. Rheology is the study of such flows.

S. M. TARG

## Newtonian fluid

[′nü′tō·nē·ən ′flü·əd]
(fluid mechanics)
A simple fluid in which the state of stress at any point is proportional to the time rate of strain at that point; the proportionality factor is the viscosity coefficient.
References in periodicals archive ?
Their result has two parameters with values depending on the shape of the conduit, and when these are not available the solution of a linear, partial differential equation over the cross-section is required but only for a Newtonian liquid (n=1).
Similar to the results of the LIB slurry, the system pressure of the Newtonian liquid increases during the whole coating phase.
This is similar to the behavior of fibers suspended in a Newtonian liquid where the Trouton ratio varies as the square of the fiber aspect ratio (17).
One important conclusion from the results presented is that deformation of a falling non-Newtonian surfactant covered drop in a Newtonian liquid is mainly controlled by interfacial tension and viscous forces and that inertia and shear-thinning effects are negligible.
Literature review shows that, most of the experimental studies reported in literature are based on either Newtonian liquid flow or gas-Newtonian two-phase flow through coils.
The present authors (19-21) have in earlier manuscripts considered the isothermal (19) and non-isothermal (20) transient startup flow of a Newtonian liquid and output fluctuations with time (surging) (21) in a starved flow modular twin-screw extruder.
Barlow and Langlois (7), Szekely and Martins (8) and Patel (9) developed models for bubble growth in a Newtonian liquid.
A growth model of a large number of spherical bubbles in polymer melts was proposed, which employs a cell model and assumes an ideal gas and a Newtonian liquid .
The model is based on the analysis of flow of a Newtonian liquid inside a rectangular multilayer channel.
A model for flow start-up of a Newtonian liquid in an initially empty modular self-wiping co-rotating twin screw extruder is developed.
This situation is analogous to the thinning of a Newtonian liquid on a rotating disk first derived by Emslie, Bonner, and Peck (4):

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