Stress–dielectric relationships in Nutella Yiyan Peng a , Thomas Ellingham a , Ni Jin b , Hongyue Yuan c , Xinchao Wang c , Haimei Li c , Lih-Sheng Turng a,d,⇑ a Wisconsin Institute for Discovery, University of Wisconsin–Madison, Madison, WI 53705, United States b Department of Food Science, University of Wisconsin–Madison, Madison, WI 53705, United States c School of Material Science and Engineering, Zhengzhou University, Henan 450002, China d Department of Mechanical Engineering, University of Wisconsin–Madison, Madison, WI 53706, United States article info Article history: Received 19 August 2014 Received in revised form 13 November 2014 Accepted 26 December 2014 Available online 3 January 2015 Keywords: Dielectrostriction Stress–dielectric relationship Rheodielectric effect Food rheology Process control abstract Dielectrostriction is a rheodielectric phenomenon that describes the variation of dielectric properties of a material with deformation and is a fundamental property of any dielectric material. During the study of the dielectrostriction phenomenon in polymers, it was found that under small deformations a linear relationship exists between the change in dielectric constant and the stress. Like polymers, most foods are dielectric materials; hence, a change in their dielectric properties with deformation can be expected as well. In this study, the dielectrostriction effect was investigated in food for the first time. Nutella was chosen for this study. It has been found that a linear stress–dielectric relationship exists in Nutella during shear flow. The potential applications of the stress–dielectric relationship in food rheology and process- ing control are discussed. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction Dielectrostriction describes the variation of dielectric properties of a material with deformation (Landau et al., 1984; Peng et al., 2005; Shkel and Klingenberg, 1998; Stratton, 1941). It is a fundamental property of any dielectric material. The dielectric properties of a deformed isotropic material can be described by a second order dielectric constant tensor, e ij , which can be approximated as a linear function of the strain tensor, u ij , (Landau et al., 1984; Stratton, 1941), De ij ¼ðe ij  ed ij Þ¼ a 1 u ij þ a 2 u ll d ij : ð1Þ Here, e is the dielectric constant of the initially isotropic mate- rial, d ij is the Kronecker delta tensor, and a 1 and a 2 are the strain–dielectric coefficients, which are material parameters. To justify the assumption of linearity in Eq. (1), small variations of dielectric properties with deformation are required, namely: ka 1 u ij k e and ja 2 u ll j e: ð2Þ The single and double line brackets indicate the magnitude of the scalar and the components in the tensor, respectively. During the study of the dielectrostriction phenomenon in polymers subjected to small deformations, it was found that a linear relationship existed between the change in dielectric constant and the stress (Peng et al., 2005). This stress–dielectric relationship, named the stress–dielectric rule, can be expressed as, De ij ð¼ e ij  ed ij Þ¼ k 1 r ij þ k 2 r ll d ij ; ð3Þ where k 1 and k 2 are stress–dielectric coefficients and r ij is a compo- nent of the stress tensor. Like polymers, most foods are dielectric materials; hence, a change in their dielectric properties with deformation can be expected. This study aims to explore the relationship between the dielectric response and the stress, and measure the first stress–dielectric coefficient, k 1 , in Nutella. Nutella has a particu- late-matrix composition, which makes it an ideal model for food rheological studies as many foods are mixtures of this type. 2. Materials and methods 2.1. Planar capacitive sensor A planar capacitive sensor has been developed for this dielectrostriction study. It consists of inter-digitated electrodes deposited on a non-conductive substrate (Fig. 1). When the elec- trodes are placed adjacent to a dielectric material, a change in the dielectric constant of the material caused by deformation can http://dx.doi.org/10.1016/j.jfoodeng.2014.12.021 0260-8774/Ó 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author at: Wisconsin Institute for Discovery, and Deparment of Mechanical Engineering, University of Wisconsin–Madison, Madison, WI 53705, United States. E-mail address: turng@engr.wisc.edu (L.-S. Turng). Journal of Food Engineering 154 (2015) 25–29 Contents lists available at ScienceDirect Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng