Describing the firmness, springiness and rubberiness of food gels using fractional calculus: Part I: Theoretical framework

T.J. Faber, A. Jaishankar, G.H. McKinley

Research output: Contribution to journalArticleAcademicpeer-review

37 Citations (Scopus)


Constitutive models for soft solids that quantitatively relate the state of the stress in the material to the deformation history have the potential to be used in a structure-texture engineering context, but successful examples are scarce. In the present work we define equations for the firmness F, springiness S, and rubberiness R, of semi-soft food gels such as cheeses that exhibit broad power-law stress relaxation over a wide range of timescales. The equations contain only two material properties, which have their origin in the food microstructure: a fractional exponent, which quantifies the frequency and temporal response and secondly a scale factor or “quasi-property”, which sets the magnitude of the stress in the material. Together they form a constitutive element, known as the ‘springpot’ or Scott Blair element which can accurately capture the viscoelastic properties of food gels such as semi-hard cheeses. Using this model it becomes possible to provide clear and unambiguous definitions of textural parameters such as firmness, springiness and rubberiness, and to quantify their time-dependence and interrelationship. The magnitude of the firmness and springiness are inversely related through the fractional constitutive model. Our FSR-equations can be used in a texture engineering context to guide effective product reformulation of soft-solid, hydrocolloidal gels.

Original languageEnglish
Pages (from-to)311-324
Number of pages14
JournalFood Hydrocolloids
Issue numberJanuary 2017
Publication statusPublished - 1 Jan 2017


  • Constitutive model
  • Food gels
  • Fractional calculus
  • Rational reformulation
  • Scott Blair
  • Structure-texture engineering


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