Foam 

High Frequency Fill Level inspection

    

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Knowingly, soft-drinks obtained by adding CO2 to sweetened water are markedly foaming.   

But, what is foam ?  

An extremely complex system of polydisperse gas bubbles, separated by draining films.  The total amount of liquid lies in two separate forms: liquid and draining films like in the figure below, at left side.  Until very recently, the main studies of foam were empiric and based on the studies of the physicist Joseph Plateau.   Bubbles, something we all played with when children, in the reality are one of the most difficult object of Mathematical Physics.  

Foam dynamics, however visible at naked eye, is a process involving simultaneously the modification occurring in a multitude of objects.   Each object with a size different than others.   It is a (useful) banalization the mathematical model where they all have identical diameter and volume.   And it is because of this intrinsic complexity that foam had, until recently, mainly been studied by the mere observation of its effects, say in an empiric way. 





Bubbles’ equilibrium is based on the minimization of surface area of liquid films:

  • three lamellae of foam meet at an edge, implying three coplanar angles of 120°;
  • four edges meet at a point, determining angles ~109°.

where the foam bubbles’ shapes are a consequence of the fact that bubbles’ own dynamics follows these Laws.  The special case of a foam composed of same volume bubbles, is  what we observe after each one of them has assumed the geometric shape of a regular pentagonal dodecahedron.  

  When all bubbles in a foam have same volume, they all assume the geometrical shape of the regular pentagonal dodecahedron (image credit User VG-3, available under CC 3.0)



Surfaces in a bubble intersection are spherical sectors                Surfaces 3-by-3 in 120º angles                            Borders intersect 3-by-3 in tetrahedral angles 

       Click-to-enlarge.  Plateau Laws’ domain of application is wider than the Beverages’ foam (credit stratocaster 47, 2014)



Nanometric details of the Plateau Border visible in a picture obtained by a Cryo-Scanning Electron Microscope (image credit N. Duerr-Auster, ETH, 2008)

In the foam bed, thin liquid films separate the pentagonal dodecahedral bubbles from each other. Each bubble has twelve liquid films that it shares with twelve surrounding bubbles.  The edge at which these films meet is called a "Plateau border".   Each bubble has thirty Plateau Borders as its edges; three bubbles share each Plateau border.  

Mind the familiar beer aspect when it’s in a glass.  They are the Plateau Borders those responsible for the visible thinning of foam films and foam drainage.  Bottling Companies and Filling specialists know how relevant is to prevent the oxidation resulting after a direct contact between the beverage and the oxygen in the air.  


  Nanometric details of the Plateau Border visible in a picture obtained by a Cryo-Scanning Electron Microscope (image credit N. Duerr-Auster, ETH, 2008)




Foam shape

Prevention made necessary because of the joint effect of gravity force and Plateu physical laws, starting the:

  • thinning process;
  • drainage process.     

A deep exam of these processes is out of the scopes of these pages. However, the Law of capillarity of Laplace’s implies a pressure gradient.  Pressure gradient directed from the center of the liquid film, towards the center of the Plateau border.   As an example, originating the familiar drainage of beer from films into Plateau Borders, we all have seen.  In other terms, are the Plateau Borders whom, following the local geodesics, provide the path for the liquid drainage. 

  Ongoing thinning and drainage in a foam



    Laplace’s Law of capillarity implies a pressure gradient. Pressure gradient directed from the center of the liquid film, toward the center of the Plateau border. As an example, originating the familiar drainage of beer from films into Plateau Borders. The Plateau Borders whom, following the local geodesics, provide the path for the liquid drainage


Electronic inspection and foam

We have examined here the simplest case, no foam at all: we’ll see in the following how-to treat the case with foam.  The figure at right side shows an example of foam curve, programmed along an inspector commissioning phase, to reach minimum false rejects and maximum fill level inspection performances, when checking for under and over filled bottles.   Underfilling boundary appears light-blue colour and over filling boundary depicted with blue colour.  


   Foam + liquid phases, after a sample of one thousand accumulated measurements. Each  white colour dot represents a the couple of measurements: (Foam; Liquid) referred to different statuses of the water. Graphics uses the term “fill” to mean “liquid”




Each white colour dot in between light and dark blue splines represents, for each one bottle, the couple of independent measurements (X, Y) where: 

                             (X, Y)   =   (Foam,  Liquid) 

In the example considered, in adimensional units: 

  • 13, is the measured foam value (abscissa axe);
  • 123, the measurement referred to the liquid phase. 


   The necks full of foam in a European famous Brewery, 10 metres after the starwheel release point of a Filler Machine.  Beer remains densely foamy along ~ 8 to 15 m after bottles’ are released by the Filler.  Where to inspect the fill level ?  An empirical rule of design prescribes at least 1 meter of distance by the release (tangent) point per each 10000 containers-per-hour of production speed.  To have the Full Bottle Inspector closer inhibits its basic Quality Control function



beer-immediately-after med


Graphics has been rendered monometric to easy its comprehension. Foam compensation module implies two separate hardware channels along which two distinct informations are separately processed.  

For liquids like still and carbonated water it is unnencessary, but vital for carbonated soft-drinks with added sugar.




 The presence of a foamy neck of the bottle implies the necessity for a special version of the HF fill level inspection, thinked on the base of a foam compensation module.  Two separate hardware channels along which two distinct informations have to be separately processed.  What for liquids like still and carbonated water is unnencessary, results vital for carbonated soft-drinks with added sugar








Case Study  

The Brewery which considered the Technical Guarantees 

part of a Contract to be respected

























To the date, we living 20 years of real cases.   Between the many, we also remember how, who, where and when a truly great Brewery, today core of the greatest Group of Breweries of the World: 

  1. signed a Contract, buying by mean of an OEM, some HF fill level inspectors built by a known Vendor, 
  2. let them be installed at the outfeed of what were in that moment the fastest existing GRB Filler Machines of the entire Planet,
  3. reality get out very soonillusory Technical Guarantees, requesting the Brewery to decide what, one way or another, was an auto-goal: 
    • downgrading its own Quality Control Policies and Standards under the Legal saleability levels, reducing the sensitivity in the Inspectors so to let bottles underfilled 1.5 % pass to the Market,
    • or, cut the entire beer Bottling Line Production efficiency with the micro-stops deriving by the fallen bottles and jams implicit in extremely high levels of false rejects, plus the losses due to the false rejects themselves.
  4. imposed to the OEM (and the Inspectors’ Vendor) to respect the Contract.    In no Contract is written that “a Bottler shall have Quality or Production”, rather than that Quality and those Production losses (mechanical efficiency + false rejects) shall be simultaneously given;
  5. Vendor had to keep on-site nearly 6 months one of its Service Technicians, trying to demonstrate True what, in the reality was perfectly (and, obviously, secretly) knowing be False.   A logic, a behaviour seemingly inconsistent.   One which has on the opposite its coherence when thinking that these Companies are organized as “Cost Centres” with antagonist duties and interests.  [A way to increase the net income cutting the losses and…, sadly, the Quality too].    Meaning that that Service Technician was there because the Centre of Cost with the “economic responsibility for the lies written in the Contract”, imposed that to another Centre of Cost in the same Company,
  6. several months after the telenovela started to be expensively staged, the Electronic Inspectors were thrown out.    The OEM compelled to replace them with inspection equipments by its and Vendor's main Competitor,
  7. Competitor’s equipments were nothing better than the others, same intrinsically low Quality High Frequency fill level inspections.   But, with a full knowledge of what happened after the contractual lies of the other Vendor, the Competitor cared to sign only goals they really could fulfill. 



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This website has no affiliation with, endorsement, sponsorship, or support of Heuft Systemtechnik GmbH, MingJia Packaging Inspection Tech Co., Pressco Technology Inc., miho Inspektionsysteme GmbH, Krones AG, KHS GmbH, Bbull Technology, Industrial Dynamics Co., FT System srl, Cognex Co., ICS Inex Inspection Systems, Mettler-Toledo Inc., Logics & Controls srl, Symplex Vision Systems GmbH, Teledyne Dalsa Inc., Microscan Systems Inc., Andor Technology plc, Newton Research Labs Inc., Basler AG, Datalogic SpA, Sidel AG, Matrox Electronics Systems Ltd.  

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