Transport phenomena in chemical processes part III Michał Araszkiewicz PhD

Momentum transport All systems have a tendency to be in equilibrium state. If something disturbed that situation, whole system seek the way to regain the previous state. To do so, one or more quantities are transported within the system from one place to another to regain the equilibrium state.

The liquid in a tank with some temperature distribution is not in the equilibrium state. The heat energy is moving from the hotter regions to the colder ones until the temperature within the tank is levelled. The intensity of that movement is often described as: …………………………..

That expression is similar to the Ohm physics law. And in general is common for all transport processes. In the previous examplary case, the driving force was the temperature difference within the vessel.

Newtonian equation of viscosity Imagine the situation that we are stirring the liquid.

The liquid in a vessel is starting to move in that way that some parts are moving more quickly than the parts located near the vessel walls. When the stirring would be stopped the liquid gradually would quench its movement. That example indicates that there are some forces that act within the body of liquid that dissipated the motion energy. These forces within the liquid we call:

Viscosity

That parameter is common for liquids and gases. The viscosity is mathematically connected with shear stress and velocity gradient. Imagine a layer of liquid placed between two paralell plates (with area A). The upper plate is stable, while the lower one is moving in x direction. Let’s assume that there is no slip between plates and the liquid.

Therefore the fluid in the direct contact with the plate has the same velocity as the plate. Concequently, the fluid velocity is decreasing towards the upper plate, because of the internal friction within the layers fluid. The velocity gradient within the fluid is constant. In order to keep the gradient stable the shear force (F) appears between plates and fluid.

Fluid properties For the transport phenomena analysis the fluid properties at rest and in motion is very important. Such parameters are taken into consideration: – ………. – ………..

Fluid at rest

Consider a small fluid element that is a part of a large stationary body of fluid. For that element the condition of being stationary, all forces acting on it must be in balance.

Flow characteristics

Steady vs. unsteady flow

On the other hand we call a flow unsteady when conditions at any locations change in time. For example, when a valve in a pipeline is being opened, and the fluid velocity in the pipe is increasing, the flow is treated a unsteady. Once the valve is finally open and the fluid velocity reaches the constant value, the flow can be considered as steady.

One and multidimensional flow When we define the multidimensional flow, its velocity components and pressure gradients changes in all three dimensions (x,y,z).

There is a specific case when we consider a fricionless flow between paralell sheets of glass. Then velocity and pressure components has changes only in two dimensions (x,y). Such flow we called two – dimensional.

Streamlines Streamline –

Laminar flow Particles of fluid move in smooth paths in one direction along the direction of flow. The fluid layers do not mix together.

Turbulent flow In turbulent flow fluid particles in move irregulary in each direction. However, there can be determined an average, dominant fluid velocity direction. Turbulent flow is unsteady with local velocities fluctuates in time.

Reynolds number The characteristics of flow can be easy determined using the Reynolds number. That number was firstly „invented” by…

……………………………………………………………… The Reynolds number was named in honour of Osborne Reynolds who popularized that idea.

Reynolds number

To be continued… Thank you for today.