Air Elimination in Milk

  • Michael Devereux
  • William Lee
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 17)


This paper presents the work done to model a novel design for accurate volume measurement of milk. The new design proposes the addition of an air elimination vessel to the current milk pumping systems. This is an extra tank between a farmer’s milk storage tank and the pumping storage system on a lorry designed to collect the milk from farms. The purpose of the air elimination vessel is to allow a pool of milk to accumulate so that air bubbles entrained with the milk can be removed and pumped out by a separate pump for air. The paper first discusses the flow of milk inside the air elimination vessel. This is modelled by a system of partial differential equations similar to the St Venant equations but modified for a cylindrical environment. The paper then discusses bubble formation and flow and predicts the level of milk required in the air elimination vessel for bubbles of air to rise and be pumped out. This is modelled by a single ordinary differential equation derived from momentum conservation.


Storage Tank Terminal Velocity Inside Wall Bubble Velocity Nonzero Initial Condition 
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    Clanet, C., Lasheras, J.: Depth of penetration of bubbles entrained by a plunging water jet. Phys. Fluid. 9(7), 1864–1866 (1997)Google Scholar
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    Toro, E.F.: Shock-Capturing Methods for Free-Surface Shallow Flows. Wiley, New York (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.MACSI, Department of Mathematics and StatisticsUniversity of LimerickLimerickIreland

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