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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.
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]
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.
The Womersley numbers tend to 1 at the level of the terminal arteries. In the arterioles, capillaries, and venules the Womersley numbers are less than one. In these regions the inertia force becomes less important and the flow is determined by the balance of viscous stresses and the pressure gradient. This is called microcirculation. [4]
Flux F through a surface, dS is the differential vector area element, n is the unit normal to the surface. Left: No flux passes in the surface, the maximum amount flows normal to the surface.
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).
Dynamic viscosity is a material property which describes the resistance of a fluid to shearing flows. It corresponds roughly to the intuitive notion of a fluid's 'thickness'.