Introduction
Stokes law is fundemental to understanding many wastewater processes. The law describes a small spherical particle moving through a viscous fluid - in our case water - with a small reynolds number. For our purposes the most useful form of the law is the following:
In this form the terminal velocity of the particle can be found. The terminal velocity determines how long it will take a particle to separate from the fluid in which it is suspended. For the purposes of this article we will not be calculating the terminal velocity of any particles but rather looking at the variables that go into the equation. By examining these variables we can gain insight into a great deal of the basic concepts of wastewater process design. Before we look at these variables however, it is important to understand some of the requirements laid out in stokes law.
Calm Down
Stokes law is only applicable when the Reynolds number - an indication of turbulence - of the water is small. In our case we want a glassy lake at sunset rather than some class four rapids. This intuitively makes sense, particles suspended in the water are unlikely to settle in a predictable manner if it is turbulent.
In wastewater equipment design a great deal of effort is made to ensure that turbulence is minimized. Clarifiers have energy dissipating inlets, density current baffles and feedwells; High rate DAFs and inclined plate clarifiers are designed to keep turbulence to a minimum between plates; and centrifuges operate with a low differential speed between the bowl and scroll.
Something to Settle
Before separation can occur in a predictable manner a particle must be formed in the wastewater. Most industrial wastewater streams contain emulsified fats, oils and grease (FOG); collidal solids and/or dissolved solids. These mixtures do not obey stokes law and must be modified in order to form particles.
A great deal of work goes into design chemical treatment schemes. In very basic terms - read gross oversimplification - the goal is to form particles and/or to neutralize the negative charges surrounding those particles that allow them to stay in suspension. These charges that keep the particles in suspension are very much like the way your hair on a dry winter day stands on end and defies gravity after removing your hat these particles will never settle. Once the charge has been neutralized the FOG and/or other solids will start to coagulate and form small particulate that will follow stokes law.
A great deal of work goes into design chemical treatment schemes. In very basic terms - read gross oversimplification - the goal is to form particles and/or to neutralize the negative charges surrounding those particles that allow them to stay in suspension. These charges that keep the particles in suspension are very much like the way your hair on a dry winter day stands on end and defies gravity after removing your hat these particles will never settle. Once the charge has been neutralized the FOG and/or other solids will start to coagulate and form small particulate that will follow stokes law.
Supersize Me
The particles that are formed during coagulation and precipitation are small and typically called microflocs. While these particles will obey stokes law, they have a very low terminal velocity would require enormous wastewater process equipment to achieve the desired clarification.
In order to keep process equipment costs and foot print requirements under control long chain polymers are added to the wastewater. These polymers typically have a many positively or negatively charged sites that can attach to the small particles formed through coagulation. As more and more particles attach themselves to the polymer large macroflocs are formed through bridging.
These macro flocs have a radius that is orders of magnitudes larger than what was initially generated during the coagulation process. A quick inspection of stokes law reveals that this increase in raidus will drastically increase the settling velocity of the particle which will ultimately result in a faster separation and more reasonably sized process equipment.
In order to keep process equipment costs and foot print requirements under control long chain polymers are added to the wastewater. These polymers typically have a many positively or negatively charged sites that can attach to the small particles formed through coagulation. As more and more particles attach themselves to the polymer large macroflocs are formed through bridging.
These macro flocs have a radius that is orders of magnitudes larger than what was initially generated during the coagulation process. A quick inspection of stokes law reveals that this increase in raidus will drastically increase the settling velocity of the particle which will ultimately result in a faster separation and more reasonably sized process equipment.
Will it Float?
Despite our best efforts in selecting the right chemicals for coaulation and flocculation, not all particles readily sink. Wastewater that is high in FOG - commonly found in the food and beverage industry - is one of the worst offenders because it will form macroflocs that have a density that is very similar to the density of water. When this happens the terminal velocity as indicated by stokes law is very small again making the process equipment requirements un-economical.
|
High FOG wastewater created such an issue for industrial facilities that over the years clever designers found that adding dissolved air to the wastewater solved the problem and the dissolved air flotation unit (DAF) was born. In this processes the macroflocs are formed normally and then mixed with a stream of pressureized air saturated water. The macroflocs serve as nucleation sites for the dissolved air to come out of solution once the pressure is released - like an imperfection on your glass of soda - and adhere to the particle, drastically reducing their density. Stokes law is still valid despite the particle haveing a lower density than the fluid so we end up with a negative terminal velocity, meaning it floats to the top now! In most cases the flotation velocity achieved in a DAF unit are very high allowing for a cost effective and compact wastewater solution.
|
|
In some cases there is also a desire to increase the density of the particles so that they settle faster. In most situations settling rates should be increased by improved coagulation or flocculation, there are some cases where that just isn't enough. In these instances weighting agents can be added to increase the particle density. The weighting agents come in many forms and names but typically they are composed of sand or iron that have a much higher density than water. As the macroflocs are formed in the wastewater process these agents can be added greatly increasing the density of the macrofloc and thus increasing the settling rate. This elevated settling rate allows for the equipment sizing to be far more aggressive resulting in a smaller footrpint or increased capacity.
Use the Force
You are probably thinking to yourself, there is no way to increase the gravitational acceleration constant without moving to another planet, and you would be correct; but sometimes desparate times call for desparate measures. In order to take advantage of this aspect of stokes law equipment is desinged to exert centrifugal forces that are far greater than what is experienced by gravity alone. Sometimes the forces are many thousand times stronger than the force of gravity.
To this exert additional force on the wastewater particles are usually spun at very high speeds using centrifuges or hydrocyclones. With both systems the heavier wastewater particles are forced to the outside of the rotating liquid and the clarified liquid accumulates towards the center. These high forces greatly increase the speed of liquid solid separation allowing the equipment to have incredibly small footprints. Unfortunately the energy requirements of centrifuges and hydrocyclones can be much higher than gravity based separation systems.
*it should be noted that the validity of stokes law in these systems can be questioned but it still serves as a good guide for why these systems have been developed.*
*it should be noted that the validity of stokes law in these systems can be questioned but it still serves as a good guide for why these systems have been developed.*
Work Smarter, Not Harder
It is pretty obvious that reducing the distance a particle at terminal velocity needs to settle or float will decrease the amount of time it will take to reach the solid surface. Unfortunately making the tank for the DAF or clarifier shorter doesn't work all that well becuase solids would quickly build up and causing a great deal of carryover in the clarified liquid and the solids will not have time to dewater and thicken leaving the operators with an large volume of sludge to handle.
|
To combat this some types wastewater treatment equipment are designed with inclined plate stacks or tubes. Between each plate or tube there is approximately one to three inches of open area for the wastewater to flow through. As the wastewater flows through, the particles only need to travel a few inches before they reach a solid surface. Once the particles reach the plate they aggregate with other particles and rapidly slide down (or up) to the sludge accumulation zone. Decreasing the settling time by such a significant amount allows the wastewater equipment to handle much higher flow rates for a given footprint.
This strategy is applied in a wide variety of wastewater processes including DAFs, Clarifiers/Thickeners, and Centrifuges. |
|