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For a compressible fluid in a tube the volumetric flow rate Q(x) and the axial velocity are not constant along the tube; but the mass flow rate is constant along the tube length. The volumetric flow rate is usually expressed at the outlet pressure. As fluid is compressed or expanded, work is done and the fluid is heated or cooled.
where the surface tension-to-viscosity ratio [] represents the speed of ink penetration into the substrate. In reality, the evaporation of solvents limits the extent of liquid penetration in a porous layer and thus, for the meaningful modelling of inkjet printing physics it is appropriate to utilise models which account for evaporation effects ...
A Newtonian fluid is a power-law fluid with a behaviour index of 1, where the shear stress is directly proportional to the shear rate: = These fluids have a constant viscosity, μ, across all shear rates and include many of the most common fluids, such as water, most aqueous solutions, oils, corn syrup, glycerine, air and other gases.
Where: , , and are material coefficients: is the viscosity at zero shear rate (Pa.s), is the viscosity at infinite shear rate (Pa.s), is the characteristic time (s) and power index. The dynamics of fluid motions is an important area of physics, with many important and commercially significant applications.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
By introducing the tensors (matrices) , and (where e is a scalar called dilation, and is the identity tensor), which describes crude shear flow (i.e. the strain rate tensor), pure shear flow (i.e. the deviatoric part of the strain rate tensor, i.e. the shear rate tensor [14]) and compression flow (i.e. the isotropic dilation tensor), respectively,
The dilute gas viscosity contribution to the total viscosity of a fluid will only be important when predicting the viscosity of vapors at low pressures or the viscosity of dense fluids at high temperatures. The viscosity model for dilute gas, that is shown above, is widely used throughout the industry and applied science communities.
A large limiting viscosity means that the fluid will only flow in response to a large applied force. This feature captures the Bingham -type behaviour of the fluid. It is not entirely possible to capture rigid behavior described by the constitutive equation of the Herschel-Bulkley model using a regularised model.