Fragmentation Statistics of Food Diced and Crushed Using a Food Mixer

TL;DR

This study experimentally analyzes the size distribution of carrot fragments produced by a food mixer, revealing normal and power-law distributions that relate to fragmentation processes and comparing them to geomaterial fragmentation.

Contribution

It provides the first detailed analysis of food fragmentation statistics, linking experimental results to existing theories of sequential fragmentation and power-law distributions.

Findings

Raw carrot diced shows a normal distribution of fragment sizes.

Crushed carrot exhibits a power-law distribution with specific exponents.

Fragmentation behavior is influenced by the mixer blade size and a lower size limit.

Abstract

The fragment-size distributions of raw carrot diced or crushed using a food mixer are studied experimentally. For the 5-mm-square raw carrot, the normal distribution shows a characteristic feature of food fragmentation statistics. This simple result indicates that most random errors contribute to fragment-size fluctuation. On the other hand, for the crushed raw carrot, the cumulative fragment size distribution follows the power law where the exponent $\alpha \simeq 1.62 > 1$. Furthermore, considering the cumulative fragment-size distribution as a function of length for comparison with geomaterials, such as fault rocks, the exponent $D \simeq 3.64$. Previous studies have shown that the power-law distribution observed in sequential fragmentation tends to have a large exponent value. As our experiment is also based on sequential fragmentation, the obtained large values of exponents $\alpha$ and $D$ are consistent with those obtained in previous studies on sequential fragmentation. On the basis of previous studies and our observations, we discuss the effect of the preferential fragmentation of particles as large as the mixer blades. We also discuss the existence of a lower limit beyond which further fragmentation is difficult, resulting in a power-law distribution tendency for raw carrot crushed with a food mixer.