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The following formula describes the viscous stress tensor for the special case of Stokes flow. It is needed in the calculation of the force acting on the particle. In Cartesian coordinates the vector-gradient is identical to the Jacobian matrix. The matrix I represents the identity-matrix.
The Reynolds and Womersley Numbers are also used to calculate the thicknesses of the boundary layers that can form from the fluid flow’s viscous effects. The Reynolds number is used to calculate the convective inertial boundary layer thickness that can form, and the Womersley number is used to calculate the transient inertial boundary thickness that can form.
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.
This is often used to relate to free surface fluid dynamics such as dispersion of liquids in gases and in spray technology. [3] [4] In inkjet printing, liquids whose Ohnesorge number are in the range 0.1 < Oh < 1.0 are jettable (1<Z<10 where Z is the reciprocal of the Ohnesorge number). [1] [5]
Multiphase flows forms when two or more partially or immiscible fluids are brought in contact. [7] The capillary number in multiphase flow has the same definition as the single flow formulation, the ratio of viscous to surface forces but has the added(?) effect of the ratio of fluid viscosities: [clarification needed]
There is general formula for friction force in a liquid: The vector differential of friction force is equal the viscosity tensor increased on vector product differential of the area vector of adjoining a liquid layers and rotor of velocity: = where is the viscosity tensor.
It is a dimensionless expression of the pulsatile flow frequency in relation to viscous effects. It is named after John R. Womersley (1907–1958) for his work with blood flow in arteries. [1] The Womersley number is important in keeping dynamic similarity when scaling an experiment. An example of this is scaling up the vascular system for ...
Hence a force decomposition according to bodies is possible. General three-dimensional viscous flow For general three-dimensional, viscous and unsteady flow, force formulas are expressed in integral forms. The volume integration of certain flow quantities, such as vorticity moments, is related to forces.