Estimation of shear in liquids



Shear forces in liquids are a result of velocity differences of fluid layers moving adjacent to one another. The simple representation of shear forces is given by considering an experimental set-up where one plate is moving with a velocity v parallel to a stationary plate with liquid between the plates. Shear forces then develop within the liquid with maximum value at the wall of the moving plate and no shear at the wall of the stationary plate.  One of the main conditions in such set-up is that fluid layers also move parallel to the plates and each other. This is generally the case in laminar flow. The mathematical expression for determining the shear in such model is:


\frac{F}{A} = \mu\frac{dv}{dx}             (1)


The term \frac{F}{A} indicates the force applied to the area to produce the shearing. It is usually referred to as shear stress. The velocity gradient, \frac{dv}{dx}, is a term for change in velocity between adjacent moving layers. It is called shear rate. The term \mu is the viscosity, which is a constant for a given Newtonian fluid.


The flow conditions described above are rather uncommon in the real life processes. Conditions like velocity variations, turbulence and complex flow paths make it impossible to estimate shear force directly. In engineering practice, it is of more interest to determine the effects of shear forces on the fluid flow.



Friction losses


Shear forces present in the process flow result in friction losses due to viscous dissipation. For a fluid flow in a pipe, this is accounted for as a frictional pressure gradient in overall pressure loss over a pipe length. Frictional pressure gradient determines pressure change due to friction forces in the flow. It can be estimated by:


\left ( \frac{dP}{dx} \right )_{{f}}=\frac{1}{D}\cdot f_{{D}}\cdot \frac{\rho u^{2}}{2}              (2)




f_{{D}} is Darcy friction factor, -

D is pipe inside diameter, m

\rho is fluid density, kg/m3

u is fluid velocity, m/s


The Darcy friction factor, f_{D}, describes the friction losses in a pipe flow. This factor takes into account the pipe roughness, diameter, fluid viscosity, density, and velocity. Moody diagram gives a good representation of friction factor as a function of different system parameters.


Figure 1. – Moody Diagram.

Figure 1. – Moody Diagram.




Viscosity changes


As described in detail in shear in non-Newtonian fluids, the viscosity of many fluids is not constant, but is a function of shear rate, as well as a function of temperature. Therefore, when working with these types of fluids, it is important to know their rheological behavior. The observation of viscosity changes during the fluid flow can be used to estimate the level the fluid is exposed to/has been expose to. Depending on the type of fluid, viscosity can decrease or increase with increasing of the shear rate. The knowledge of the fluid behavior under the presence of shear forces can help to make sound process decisions for the optimal operation of the system.





Shear forces present in a mixture of two immiscible liquids will lead to dispersion of one liquid in the other. Emulsions form because of high shear forces. The mechanism of mixing involves both droplet break-up and coalescence. Shear forces therefore affect both coalescence and droplet break-up. Certain level of shear is actually beneficial for promotion of droplet coalescence and increasing in average droplet size. Intense turbulence, though, stimulates strong shear forces and result in highly dispersed mixtures with small average droplet sizes. Pressure reducing elements, such as control valves or orifices, are examples of high shear sources. The smaller the droplets, the more stable the emulsion. The stability of emulsions is a parameter determining how long it takes to separate the emulsion fluid phases. Depending on their stability, emulsions classify as loose, medium and tight emulsions. While loose emulsions can separate in several minutes, it may take hours and, sometimes, day to separate tight emulsions in a still environment.


When dealing with liquid mixtures and multiphase flows, the level of shear force acting on the fluids will result in certain degree of emulsification. The indirect parameter to estimate the emulsification of the fluid can be the necessary residence time in the gravity separator to reach the required level of separation (i.e. product quality).