Physics Report: Measuring the Half-Life of Beer Froth Decay

This report details a physics experiment investigating the decay of beer froth. The experiment aims to determine the half-life of beer foam as a function of time and temperature, and to demonstrate the exponential decay law. Using a measuring cylinder, stopwatch, and non-alcoholic beer, the experiment measures the liquid level over time, allowing for the analysis of foam decay. The methodology involves marking liquid levels at intervals and calculating the foam volume based on the difference between the maximum liquid height and the current liquid height. The analysis assumes constant beer mass and explores the relationship between foam, liquid, and height. The results indicate an exponential decay of foam, with the half-life calculated using the decay constant. The report also discusses the influence of factors like temperature and glass size on the decay rate, referencing previous studies on foam properties and bubble arrangements. The conclusion confirms the observed exponential decay and highlights the significance of these factors in the decay process.

Beer Frothing Decay

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Abstract
This report describes a reliable method to measure the half-life of beer foam. Several
techniques have been used to investigate the half-life of beer foam. This experiment presents one
such technique that assesses the beer froth decay as a function of beer type and temperature.
Factors such as glass surface area are not mentioned extensively in this report, although the
surface area plays a role in determining the bubble structure. Using a measuring cylinder, a
stopwatch, and non-alcoholic beer, this experiment will demonstrate how to determine the
exponential decay and half-life of beer foam.

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Aims and Objectives
1. To determine the half-life of beer froth as a function of time
2. To determine the half-life of beer froth as a function of temperature
3. To investigate the effect of time on the volume of beer froth
4. To demonstrate the exponential decay law using beer froth
Background
This report describes a method that was used to measure the half-life of beer froth. The
formation and subsequent stability of froth has been studied extensively and applied in many
industrial settings. Beer foam is a fascinating concept to scientists and connoisseurs alike. The
decay of bear froth is particularly of interest to scientists as evidenced by the several studies that
have been done on the phenomenon. One study found that the volume of beer froth decays
exponentially with time. The surface of the beer glass strongly influences the properties of the
foam [1]. This property has made it challenging to determine inner the function of inner bubble
size distribution during the decay of the froth just by observation from outside the glass.
However, the temporal development of the foam can help to illustrate how the outer and inner
structures of the setup of bubbles correlate [2]. Different beers have different fluidic properties
such as the density, gas content, carbonation, viscosity, and surface tension among other factors
[1]. More procedures have been proposed concerning the measurement of the decay phenomenon
of beer by several researchers. This report presents findings from one such method that was used
to determine the half-life of beer froth.
Methodology for Measuring the Decay

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The apparatus used in the experiment were a measuring cylinder, a stopwatch, centimeter
ruler, masking tape, and a bottle of beer. A strip of masking tape was put along the vertical scale
of the measuring cylinder and the beer was poured into the measuring cylinder. The liquid level
was marked on the tape at equal time intervals after obtaining the initial height of the beer in the
measuring cylinder. The beer was poured into the measuring cylinder until the foam nearly
reached the top. The liquid beer level was marked on the tape and the stopwatch was started. The
beer level was marked every 5 seconds for two minutes and the results recorded. When no
noticeable changes were observed on the beer liquid level, the set up was left to stand for an
additional two minutes to allow as much foam to turn into liquid as possible. The maximum beer
liquid height was then marked on the tape. The markings represented the beer liquid height as a
function of time, and the maximum beer liquid height.
Analysis and Discussion
Assuming that no amount of beer was spilled or drank the beer’s total mass remained
constant. Consequently, the sum of all the changes in total mass of beer (decreasing foam and
increasing liquid) amounts to zero. As the mass of the froth decreases, the liquid beer’s mass was
increasing in a principle called the Conservation of libation [1]. If we assume that the mass of the
beer foam has a direct proportionality to the volume of the beer foam, then the mass of the beer
liquid is also directly proportional to the volume of the beer liquid. Due to the uniformity
provided by the measuring cylinder, the heights of the froth and of the liquid are also directly
proportional to their respective volumes [1]. Since the heights are proportional to the volume,
which is proportional to the mass, then the height is directly proportional to the mass. Thus, at
any given point the foam is equal to the difference between the maximum beer liquid height and
the beer liquid height. This relationship is illustrated in the formula below

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Foam = hliquid max – hliquid
Assuming uniform foam density then the mass of the beer foam is equal to the amount of
beer foam. A graph of beer level against time thus yields an increasing trend with a gradient that
decreases as a function of time since less foam is converting into liquid beer. The decrease in
gradient implies an exponential decay of foam because less foam remains meaning less beer
mass per unit time converting into liquid from foam [2]. Thus, a graph of the effective amount of
froth against time will yield a decreasing amount of foam and a negative gradient that resembles
an exponential decay. On the other hand, a graph of the natural logs of the beer level against time
will produce a decay constant λ = -0.0122s-1 as shown below
Thus, the beer foam half-life is given by the following formula
t1/2 = ln 2/λ ≈ 57 s.

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For the case of beer foam, the surface of the beer glass considerably influences the
foam’s properties. Thus, depending on the inner bubble distribution relationship to observe
changes from outside the glass makes it difficult to determine any changes within a brief period
[3]. Foam forms when the beer is poured out from the bottle. Temperature is crucial in the
formation of foam since in low temperatures a smaller amount of initial foam will form [3]. The
opposite is also true. The size of the glass also affects the decay of the beer foam. A wider glass
implies more beer being used in the inspection of the decay, with more beer being foamed up.
Thus, the drainage and rearrangement back to liquid beer will be much slower.
Conclusion
The experiment set out to determine the decay of beer foam. An exponential rate of decay
was observed for this experiment. The decay of beer foam has been characterized by several
other different methods such as measuring the temporal behavior of the volume of foam, bubble
arrangements, estimating liquid content in the foam phase, and bubble distribution. The
temperature and the size of the glass, which in the experiment was represented by the measuring
cylinder have also been determined to influence the decay rate of the foam.

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References
1. Fisher, N. (2005). The physics of your pint: Head of beer exhibits exponential decay. Physics
Education, 39, 34-35.
2. Leike, A. (2002). Demonstration of the exponential decay law using beer froth. European
Journal of Physics, 23, 21-26.
3. Sauerbrei, S., Haß, E., & PLATH, P. (2005). The Apollonian decay of beer foam bubble size
distribution and the lattices of young diagrams and their correlated mixing functions.
Dsicrete Dynamics in Nature and Society, 2006(79717), 1-35.