Nothing is more pleasing to a brewer than pouring a beer with a beautiful, foamy head and lofting it skyward to observe the transparent, bright, clarity of a well made beer! With the notable exception of beers that are supposed to be cloudy (e.g. wheat beers), clear beer is beautiful beer.
Clarification is an important part of the brewing process. Haze or cloudiness in beer is caused by the presence of suspended solids within the beer. These suspended solids may be yeast cells, protein solids from cold or hot break, or possibly may be the result of the formation of an insoluble colloid-complex from soluble proteins and tannins (polyphenols) during the fermentation process. These kinds of colloidal-complexes (haze) are often relatively soluble at room temperature, but much less soluble at the cooler temperatures at which beer is typically served. Hazes like this are called "chill haze".
Curing cloudy beer
There are several ways to cure cloudy beer. One way is to filter the beer. Filtering beer is a good option for some styles of beer, but there are numerous reasons why this may not be the best choice. Filtering removes flavor and color-producing compounds from the beer, and is also likely to increase the rate of oxidation of the beer by exposing it to more air than an equivalent unfiltered beer. Another widely used method for clarifying beer is to allow the suspended solids to settle from the beer by simply allowing the force of gravity to act on the suspended particles for a sufficient amount of time.
A discrete particle settling in water (or beer) accelerates until the drag force reaches equilibrium with the driving force1. Once this happens, the settling velocity becomes constant; this equilibrium velocity is referred to as the "terminal velocity". At terminal velocity the settling velocity of a discrete particle is given by the equation:
v = settling velocity (m/s)
g = acceleration due to gravity
ρs = density of the particle (kg/m3)
ρ = density of the liquid (kg/m3)
V = volume of the particle (m3)
A = projected area in the direction of
CD = drag coefficient
If we take the liberty and assume that the solid particle that is settling out of the fermented beer is spherical, then the above equation simplifies to:
d = settling particle diameter (m)
If we take one additional liberty and assume that the settling velocity is such that the fluid flow around the particle is laminar (not turbulent), then we can substitute:
CD = 24/Re
into the above equation (Where Re = Reynolds number for this specific settling situation) to get an actual, useful equation:
μ = dynamic viscosity of the liquid
With this equation we can finally predict the settling time required to remove the particulate from our fermentation vessel. All we need to know is the density of the settling particle, the density of the liquid, the diameter of the settling particle and the viscosity of the liquid.
As an example: Assume the density of the settling particle = 1984 kg/m3, the density of the fermented beer = 1012 kg/m3, the diameter of the settling particle = 3 microns (3 x 10-6 m) and the viscosity of the fermented beer is 1.5 centipoise (1.51 x10-3 kg/m-sec)];Then we get:
v = [(9.8 m/s2)(1984 kg/m3 – 1012kg/m3)(3 x 10-6 m)2]/[18(1.51x10-3 kg/m-sec)] = 3.15x10-6 m/s
This means that it will take a 3 micron diameter, spherical particle approximately 317,000 seconds (88 hrs or 3.67 days) to settle one meter. Table 1 illustrates the typical diameters of substances of interest to homebrewers.
Figure 1 illustrates the settling velocity of various sized spherical particles in beer.
Figure 1: Settling Time for Particles in Beer
As you can see in Table 1 and Figure 1, colloidal matter will take a very long time to settle out on its own. Fortunately there are ways that the rate of settling of the particulate matter can be increased. The equation for terminal setting velocity provides the guidance.
Speeding up the clarification process Increasing particle diameter, d
Settling rate is proportional to the square of the diameter
of the particle. Doubling the particle diameter will result in a factor of four increase in the settling rate. The rate of settling can therefore be increased if the particle diameter is increased. This principle is exploited particularly by natural clumping of particles that occur by protein coagulation during and after wort boiling and by yeast clumping together during flocculation. The process of clumping is also enhanced by using fining agents and clarification aids, which cause the individual particles to stick together. This increases the effective diameter of the particles and accelerates the settling process.
Increasing density difference, (ρs – ρ)
The rate of sedimentation is proportional to the difference in density between the suspended particle and the liquid. This is indicated by the (ρs – ρ) term in the settling velocity equation. Unfortunately there is very little that a brewer can do to alter the difference in density between the wort/beer and the suspended particles. One interesting point to note is that the density of the solids will remain relatively constant while the density of the liquid usually decreases with increases in temperature. Hotter liquid is less dense, so warming of the system should theoretically result in a slightly faster settling velocity. In practical terms, however, the density variation of the liquid with temperature is very small, so this method of increasing settling velocity is of no value to the brewer.
The settling velocity equation indicates that decreasing viscosity, μ, of the liquid should proportionally reduce the settling time for the suspended particles. Liquid viscosity usually decreases with increase in temperature, so increasing the temperature of the system should, theoretically, result in a more rapid settling rate. Unfortunately, adjustment of viscosity is not really a viable option for the brewer. The viscosity of the beer or wort is dependent upon many factors including the protein and dextrin content of the liquid, and the total amount of dissolved solids and residual sugars within the liquid. These things are also responsible for sensory attributes in the beer including body and mouthfeel. Because of this, it is really not possible to adapt the viscosity in order to cause the particles to settle faster.
Increasing the settling force (gravity), g
The "g" term in the equation refers to the acceleration due to gravity on the Earth. The acceleration due to gravity on earth is 9.81m/s2. There is nothing that anyone can do to change this. It is possible, however, to increase the force that is driving the sedimentation process by replacing the gravitational force of the earth with a much stronger "g-force" that is produced by some mechanical means.
A much stronger force can be induced mechanically
by causing the liquid/particle system to experience angular acceleration. This can be done by pumping the liquid into a tangential entry vessel as is done with cyclones or whirl-pools. It can also be done by rotating the liquid/particle system very rapidly in a machine such as a centrifuge. Centrifuges are capable of generating forces that are many thousands of "g's". Since the settling rate is proportional to the settling "g" force, this can greatly increase the rate of removal of the suspended solids from the liquid.
Prevention of haze in beer
Prevention is always better than cure when it comes to haze. Hazes, particularly chill-hazes, in beer are often caused by formation of colloidal protein-tannin species within the beer. To prevent the formation of this colloidal haze, the brewer needs to remove enough of either the complex-forming proteins or tannins to prevent the formation of the insoluble colloidal-complex. Throughout the history of brewing, many different fining agents and clarification substances have been used to assist in this effort. A table of these substances with the mechanism of removal is given on the BYO website at http://byo.com/story2838 as Table 2.
Those clarification agents all (except for the first two, Papian and tannic acid) generally "adsorb something" as the method of preventing chill haze and improving the clarification of beer. This adsorption is the result of surfaces charges on the molecules that comprise the clarification aid attracting opposite surface charges on the protein or tannin molecules. Opposite charges attract, and the protein or tannin becomes physio-chemically bound to the surface of the clarification agent.
After this initial adsorption step, the whole "clump" of protein-or-tannin-covered-clarification-aid settles out of suspension or "flocculates." The clarification aids cause the suspended matter to form larger particles. Because particles settle out of suspension at a rate that is proportional to the square of the diameter of the particles:
larger particles result in a much more rapid clarification of the beer.
Conclusions and Practical Takeaway
Clarification of beer by allowing the particulate matter to settle under the influence of gravity is a tried-and-true approach to producing clear beer. Although it is theoretically possible to increase the rate of settling of the suspended particles by manipulating physical characteristics of the system (e.g. temperature), the best approach for the home brewer is to use clarification aids to cause the particulate matter to form larger "clumps" which will settle out more rapidly due to the increased effective diameter of the particulate matter.
Clarification aids can also help prevent cloudiness in beer by preventing "chill haze". Prevention is better than cure, so use appropriate fining and clarification agents to prevent chill-haze. Select the type and amount of clarification agent best suited for the particular style of beer that you are brewing.
1) Viessman, W. and Hammer, M., Water Supply and Pollution Control, 4th ed,1985
2) "Sedimentation – Liquid/Solid Separation in the Brewing Process", The Brewer International Technical Summary, May 2002
3) The Practical Brewer, MBAA, 1977