Fragmentation Statistics of Food Diced and Crushed Using a Food Mixer

• Published in: arXiv.org 2021-10
• Main Authors: Kobayashi, Naoki, Shibayama, Hitoshi
• Format: Article
• Language: English
• Subjects: Crushing; Food; Fragmentation; Geomaterials; Normal distribution; Particle size distribution; Power law; Random errors
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2110.10988

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.