Dynamics of particle chopping in blenders and food processors

Mathematical models are developed to explain the size distribution of particles in blenders to give insight into the behaviour of possible blender designs. The initial models consider idealized simplified situations, first with the chopping of long thin particles and then of spheres. The models are first presented using the idea of chopping at discrete places but then extended to account for chopping at any point via a continuous model. Some of the simple models can be solved analytically while others require numerical calculations. Comparisons of the predictions from the various models with experimental data at a fixed time are presented and show that the models account for much of the behaviour. The initial models do not however predict the large amount of extremely small particles (debris) that are observed at the end of the blending process. The models are thus modified using simple extensions to account for additional effects and numerical solutions of these models are compared with the observed data. The theory should provide a useful tool that eliminates the need to perform costly and time-consuming experiments when understanding how a particular food will be blended.