The Three Directional Components of Mixing:

SWIRL VS. VERTICAL & RADIAL MIXING

There are three directional components to mixing in a vertical cylindrical tank.  The same is true for a plug flow device, such as a static mixer, it is just the orientation that changes (generally static mixers are viewed using a sideward flow).  

The vertical component is motion from the tank bottom to the liquid surface and from the liquid surface to the tank bottom (the later is referred to as recirculation).  The radial component is motion from the tank centerline to the tank wall and the tank wall to the tank centerline.  The angular component is commonly referred to as swirl or vortexing, which is defined as angular mixing.  Once again, the same is true for a plug flow design, except the view of the vertical cylinder would be turned on its side. 

By far, the worst or least desired component of mixing is angular or swirl.  Generally speaking, the objective of mixing is to have component "A" to interact with component "B" to form product "C" or the desired end result.  Angular mixing or swirl is analogous to, or can be compared to, two (2) horses on a merry-go-round.  They never meet and as such demonstrate poor mixing.  Swirl is actually a bit more dynamic but you get the general idea as to why it's not the preferred method of mixing, especially when you factor in other mechanical design consideration that further penalize a mixing design.   

So at this point, you might be asking yourself why is angular mixing considered poor mixing.  The answer may not be quite so obvious, but when swirl is present, it becomes the dominant flow pattern.  Imagine a bunch of kids in a 24' diameter pool all walking, or rather jump-walking, in the same "angular-direction" thereby creating a massive angular flow pattern (whirlpool).  Now try to stop and imagine those fluid forces on your body. Those forces are significant and must be accounted for.   Now look where all the pool solids accumulated (at the bottom in the very center of the pool).  Alas, the very principles of a cyclone separator system.  The vertical and radial components of mixing do exist but are negligible compared to swirl or radial mixing.  The solids do not suspend because the vertical component of mixing is non-existent.  Now imagine trying to suspend solids or to add a reactant at the liquid surface ... there are no compelling vertical forces to either incorporate or suspend the material.  You could argue that the sucking action of a vortex will incorporate solids, but on it's own, will that same vortex suspend the solids or better yet, disperse them.  To redirect the the angular flow pattern either an angular offset mounting arrangement could be used or anti-swirl baffles must be incorporated to redirect the flow pattern.       

So why is this mixing discussion not just a simple matter of common sense.  Mixing applications are typically viewed from the liquids surface or from above a vertical cylindrical tank.  A common example of this view is someone stirring a cup of coffee using a spoon to angularly rotate the contents of the mug.   From this view, the surface motion generated by a swirl pattern indicates good mixing.  If we were to observe that same application from the side of the tank, it would indicate something very different.  Solids added, such as sugar, would initially be caught in the swirl pattern, they would eventually fall vertically downward, where the heavier solids drop due to the effects of gravity.  This flow pattern is actually the design concept of the operation of a cyclone separator (heavy components fall due to the effects of gravity).  Since the mixing is predominantly dominated by the angular component of mixing (swirl), there is virtually no vertical component to suspend the solids off the tank bottom.  The same could be said of coffee creamer, which just clumps and lies on the surface.  Again, there is no vertical component of mixing to incorporate the solids using just a dominant angular flow pattern.  As such, the solids will accumulate and may even form a quasi-boundary layer on the tank bottom if the solids are sticky or if they tend to pack.  Most mixing application, such as blending, suffer from the same flow scheme.  Imagine if you will, stratified vertical layers of either varying viscosities and/or densities.  So what is not clear common knowledge, and is not commonly understood and perceived, is that although there is some (actually very little) vertical and radial mixing, once swirl is present, it dominates the flow scheme.  In other words, the horses of the merry-go-round no only don't get the chance to meet radially, they don't get to interact vertically either, which are the prime objectives of mixing.  

There are two (2) primary methods of overcoming the angular component of mixing in a vertical cylindrical tank.  In the case where the mixer is mounted vertically on the tanks centerline, multiple anti-swirl baffle plates {typically running the full straight side of the tank) are vertically mounted to the tanks walls.  When the angular motion encounters the baffle, it has no choice but to be redirected either upward or downward.  Since the liquid level is somewhat constant, the flow directed up the baffle will then re-circulate back toward the centerline of the tank.  Thereby achieving good top to bottom motion or the preferred vertical and radial components of mixing.  The second method is to use an angular offset mounting arrangement.  In this case the impeller rotates clockwise in the liquid which sets up a clockwise motion.  The shaft & impeller are oriented in such a way to provide a downward discharge that is directed counter clockwise.  These two motions counter each other in such a way as to eliminate angular motion to achieve the preferred vertical and radial components of mixing.

Static or plug flow mixers operate using internal baffles.  Some of these internal are designed to create swirl or angular mixing.  Others create a combination of effects but in all cases, the residence time distribution, or the actual time within the mixed zone, is very small (just a few seconds or less) where downstream mixing, or entrained residual flow patterns are relied upon to complete the mixing.  Static mixing is exceptional for instantaneous reactions but suffers greatly when the reactions are either are time dependent or are somewhat time dependent.  Mixing problems arise when the assumption that the reaction is instantaneous, such as for water treatment flocculation, where further downstream processing and upset conditions are apparent, which affects both chemical usage and water quality. 

 09.21.23