The Janssen effect and the Chini ordinary differential equation

Adam Rogers, George Dyck, Jitendra Paliwal, Kurt Hildebrand, Michael D. Montross, Aaron P. Turner

Research output: Contribution to journalArticlepeer-review


The Janssen effect describes the increase in pressure with depth in granular materials. However, the original Janssen formulation treats the density as constant. In this work, we examine parametric density models that depend on both pressure and moisture content and allow for temperature dependence to be easily included. We focus on physically-motivated empirical models that are built on power-law terms. These power-law terms correspond to thermodynamic equations of state, such as the ideal gas law, and polytropic processes. When coupled with the Janssen ordinary differential equation (ODE), these power-law models have the form of a Chini ODE. We study the properties of the Chini ODE for both constant and variable coefficients. We review Chini's method for transforming these equations into separable forms and the conditions under which this approach fails. We derive a variety of novel expressions, including a critical value for the vertical-to-horizontal stress ratio which varies with depth.

Original languageEnglish
Article number119493
JournalPowder Technology
StatePublished - Mar 1 2024

Bibliographical note

Publisher Copyright:
© 2024 The Authors


  • Bulk solids
  • Compression
  • Grain bin
  • Janssen effect
  • Mathematical Modeling
  • Pressure

ASJC Scopus subject areas

  • General Chemical Engineering


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