Study Group report
This is the final report on the problem of modelling air bubbles in ice cream, brought to ESGI46 by Unilever.

Report authors
Peter Howell (University of Oxford)
Mark Muldoon (UMIST)

Introduction
A common manufacturing method of ice cream involves mixing the air, fat, ice crystals and water under high pressure (4–5 atmospheres) before discharging the product to atmospheric pressure for further processing. As the pressure is released, air may escape from the foam into the atmosphere, resulting in a lower air fraction in the final product than in the mixer. Such effects can also occur when ice cream is de-pressurised below atmospheric pressure and may cause degradation if the product is transported at high altitude. The aim of this study is to quantify this air loss and to predict how it might depend on, for example, the rheological properties of the foam mixture, the bubble size distribution and the rate at which the pressure is released.

This report adopts two alternative approaches to the problem. The first is to model the expansion of the foam as a two-phase flow, with air bubbles expanding in a deformable matrix. This allows the prediction of the pressure distribution inside the sample. The mismatch between the internal and external pressures drives a net flow of air out of the sample; this flow is localised in a boundary layer at the edge of the sample.

In the second approach, the report considers a random distribution of spherical bubbles of a given radius r. The aim here is to determine how many of the bubbles intersect and form “chains” that connect to the edge of the sample. This gives an estimate of the amount of air that is likely to escape from such chains as the sample expands and r increases.

Download 'IceCream.pdf' (155 Kb).