Newtonian fluid

Newtonian fluid
Name	Newtonian fluid
Type	Fluid mechanics concept
Introduced	18th century
Named after	Sir Isaac Newton

Newtonian fluid A Newtonian fluid is a class of fluid in which the shear stress is linearly proportional to the rate of strain; this proportionality produces a constant viscosity independent of shear rate. The concept was formalized in the 17th and 18th centuries and is central to classical continuum mechanics, hydrodynamics, and engineering analyses involving laminar and turbulent flows. Newtonian behavior serves as a baseline for comparing complex rheological responses observed in polymers, suspensions, and biological materials.

Definition and constitutive relation

The constitutive relation for a Newtonian fluid states that the Cauchy stress tensor depends linearly on the rate-of-deformation tensor, with proportionality given by the dynamic viscosity and the second viscosity (bulk viscosity) for compressible cases. This linear relation was inspired by experimental and theoretical work from figures associated with the Royal Society era and subsequent developments in Cambridge and Edinburgh mathematics and physics circles. The Newtonian constitutive model contrasts with non-Newtonian models developed in later work at institutions such as the Max Planck Society, Brown University, and Imperial College London, which introduced shear-thinning, shear-thickening, viscoelastic, and thixotropic terms. In compressible Newtonian fluids the volumetric stress is handled using bulk viscosity concepts employed in formulations used by researchers at California Institute of Technology, Massachusetts Institute of Technology, and Stanford University.

Rheological properties and viscosity

Viscosity in a Newtonian fluid is a material constant independent of shear rate and time, a property measured and tabulated by laboratories at organizations such as the National Institute of Standards and Technology, National Physical Laboratory, and industrial research centers like Dow Chemical Company and Shell plc. The shear viscosity governs laminar boundary layers described in classical studies at Princeton University and ETH Zurich, while kinematic viscosity (dynamic viscosity divided by density) is used in aerodynamics and hydrology research at NASA, NOAA, and university groups at University of Cambridge. Temperature dependence follows empirical or theoretical laws developed by researchers in thermal fluids at Argonne National Laboratory and Los Alamos National Laboratory, often referenced alongside standards from bodies like the International Organization for Standardization and American Society of Mechanical Engineers.

Examples and non-examples

Common examples of Newtonian fluids include pure water, air, many simple hydrocarbons such as hexane and n-hexane used in chemical engineering at BP plc, and low-concentration aqueous solutions studied at University of Oxford and Yale University. Industrially relevant Newtonian fluids include lubricants in baseline regimes at General Motors, Siemens, and Toyota Motor Corporation research centers, and process fluids in petrochemical operations at ExxonMobil and Chevron. Non-Newtonian examples—studied extensively at University of Geneva, Tokyo University, and McGill University—include polymer melts investigated by researchers affiliated with I. G. Farben (historical context), blood examined at Cleveland Clinic, and concentrated suspensions researched at Lawrence Berkeley National Laboratory. Classic non-Newtonian models include the power-law model developed in academic work at University of Pennsylvania and viscoelastic models advanced at Columbia University and Princeton University.

Mathematical formulation and governing equations

The governing equations for a Newtonian fluid combine the linear constitutive relation with conservation laws—mass, momentum, and energy—yielding the incompressible Navier–Stokes equations used in studies at Courant Institute of Mathematical Sciences and computational implementations developed at Los Alamos National Laboratory and Sandia National Laboratories. The linear stress-strain relationship simplifies analytical solutions derived in classical problems such as Couette flow, Poiseuille flow, and Stokes flow examined historically at Sorbonne University and University of Göttingen. Compressible Newtonian flow formulations are central to high-speed aerothermodynamics research at California Institute of Technology and CERN computational groups. Numerical methods—finite element method (FEM), finite volume method (FVM), and spectral methods—were refined by teams at Imperial College London, ETH Zurich, and Princeton University to solve Newtonian flow problems in complex geometries.

Experimental measurement and rheometry

Viscosity measurement for Newtonian fluids is standardized with instruments such as capillary viscometers, rotational rheometers, and falling-ball viscometers developed and calibrated at National Institute for Occupational Safety and Health, Rheosystems commercial labs, and university facilities like University of Minnesota. Classical viscometry techniques originated in experimental programs associated with Royal Institution and were expanded by industrial laboratories at DuPont and BASF. Modern rheometers capable of assessing near-Newtonian behavior are produced by manufacturers linked to research programs at ETH Zurich and Massachusetts Institute of Technology, with protocols aligned to standards from International Electrotechnical Commission committees and national metrology institutes.

Applications and industrial relevance

Newtonian fluids underpin models used in aerospace design programs at NASA, European Space Agency, and Boeing, and in civil engineering hydraulics projects overseen by organizations such as United Nations-linked agencies and municipal engineering departments influenced by research at University of California, Berkeley. Chemical process simulations at companies like Shell plc, BASF, and Dow Chemical Company rely on Newtonian approximations for many base oils and solvents. Biomedical device flows, diagnostic instruments, and laboratory protocols at hospitals such as Mayo Clinic and Johns Hopkins Hospital often assume Newtonian properties for saline and buffer solutions. Computational fluid dynamics (CFD) software packages from firms such as ANSYS, Siemens PLM Software, and research groups at Lawrence Livermore National Laboratory implement Newtonian constitutive laws as default models for engineering analysis.

Category:Fluid dynamics