TY - JOUR
T1 - The Janssen effect and the Chini ordinary differential equation
AU - Rogers, Adam
AU - Dyck, George
AU - Paliwal, Jitendra
AU - Hildebrand, Kurt
AU - Montross, Michael D.
AU - Turner, Aaron P.
N1 - Publisher Copyright:
© 2024 The Authors
PY - 2024/3/1
Y1 - 2024/3/1
N2 - 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.
AB - 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.
KW - Bulk solids
KW - Compression
KW - Grain bin
KW - Janssen effect
KW - Mathematical Modeling
KW - Pressure
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U2 - 10.1016/j.powtec.2024.119493
DO - 10.1016/j.powtec.2024.119493
M3 - Article
AN - SCOPUS:85184816408
SN - 0032-5910
VL - 436
JO - Powder Technology
JF - Powder Technology
M1 - 119493
ER -