The Janssen effect and the Chini ordinary differential equation

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...
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Autor*in:	Rogers, Adam [verfasserIn] Dyck, George [verfasserIn] Paliwal, Jitendra [verfasserIn] Hildebrand, Kurt [verfasserIn] Montross, Michael D. [verfasserIn] Turner, Aaron P. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2024

Schlagwörter:	Janssen effect Compression Pressure Mathematical Modeling Bulk solids Grain bin

Übergeordnetes Werk:	Enthalten in: Powder technology - Amsterdam [u.a.] : Elsevier Science, 1967, 436
Übergeordnetes Werk:	volume:436

DOI / URN:	10.1016/j.powtec.2024.119493

Katalog-ID:	ELV06720385X

Internformat


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520			\|a 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.
650		4	\|a Janssen effect
650		4	\|a Compression
650		4	\|a Pressure
650		4	\|a Mathematical Modeling
650		4	\|a Bulk solids
650		4	\|a Grain bin
700	1		\|a Dyck, George \|e verfasserin \|0 (orcid)0000-0002-5920-1240 \|4 aut
700	1		\|a Paliwal, Jitendra \|e verfasserin \|0 (orcid)0000-0002-1665-3626 \|4 aut
700	1		\|a Hildebrand, Kurt \|e verfasserin \|0 (orcid)0000-0002-7655-3547 \|4 aut
700	1		\|a Montross, Michael D. \|e verfasserin \|4 aut
700	1		\|a Turner, Aaron P. \|e verfasserin \|4 aut
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allfields	10.1016/j.powtec.2024.119493 doi (DE-627)ELV06720385X (ELSEVIER)S0032-5910(24)00135-9 DE-627 ger DE-627 rda eng 660 VZ 58.10 bkl 52.77 bkl Rogers, Adam verfasserin (orcid)0000-0003-2953-2054 aut The Janssen effect and the Chini ordinary differential equation 2024 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. Janssen effect Compression Pressure Mathematical Modeling Bulk solids Grain bin Dyck, George verfasserin (orcid)0000-0002-5920-1240 aut Paliwal, Jitendra verfasserin (orcid)0000-0002-1665-3626 aut Hildebrand, Kurt verfasserin (orcid)0000-0002-7655-3547 aut Montross, Michael D. verfasserin aut Turner, Aaron P. verfasserin aut Enthalten in Powder technology Amsterdam [u.a.] : Elsevier Science, 1967 436 Online-Ressource (DE-627)320599019 (DE-600)2019938-7 (DE-576)098474278 0032-5910 nnns volume:436 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 58.10 Verfahrenstechnik: Allgemeines VZ 52.77 Urformen VZ AR 436
spelling	10.1016/j.powtec.2024.119493 doi (DE-627)ELV06720385X (ELSEVIER)S0032-5910(24)00135-9 DE-627 ger DE-627 rda eng 660 VZ 58.10 bkl 52.77 bkl Rogers, Adam verfasserin (orcid)0000-0003-2953-2054 aut The Janssen effect and the Chini ordinary differential equation 2024 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. Janssen effect Compression Pressure Mathematical Modeling Bulk solids Grain bin Dyck, George verfasserin (orcid)0000-0002-5920-1240 aut Paliwal, Jitendra verfasserin (orcid)0000-0002-1665-3626 aut Hildebrand, Kurt verfasserin (orcid)0000-0002-7655-3547 aut Montross, Michael D. verfasserin aut Turner, Aaron P. verfasserin aut Enthalten in Powder technology Amsterdam [u.a.] : Elsevier Science, 1967 436 Online-Ressource (DE-627)320599019 (DE-600)2019938-7 (DE-576)098474278 0032-5910 nnns volume:436 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 58.10 Verfahrenstechnik: Allgemeines VZ 52.77 Urformen VZ AR 436
allfields_unstemmed	10.1016/j.powtec.2024.119493 doi (DE-627)ELV06720385X (ELSEVIER)S0032-5910(24)00135-9 DE-627 ger DE-627 rda eng 660 VZ 58.10 bkl 52.77 bkl Rogers, Adam verfasserin (orcid)0000-0003-2953-2054 aut The Janssen effect and the Chini ordinary differential equation 2024 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. Janssen effect Compression Pressure Mathematical Modeling Bulk solids Grain bin Dyck, George verfasserin (orcid)0000-0002-5920-1240 aut Paliwal, Jitendra verfasserin (orcid)0000-0002-1665-3626 aut Hildebrand, Kurt verfasserin (orcid)0000-0002-7655-3547 aut Montross, Michael D. verfasserin aut Turner, Aaron P. verfasserin aut Enthalten in Powder technology Amsterdam [u.a.] : Elsevier Science, 1967 436 Online-Ressource (DE-627)320599019 (DE-600)2019938-7 (DE-576)098474278 0032-5910 nnns volume:436 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 58.10 Verfahrenstechnik: Allgemeines VZ 52.77 Urformen VZ AR 436
allfieldsGer	10.1016/j.powtec.2024.119493 doi (DE-627)ELV06720385X (ELSEVIER)S0032-5910(24)00135-9 DE-627 ger DE-627 rda eng 660 VZ 58.10 bkl 52.77 bkl Rogers, Adam verfasserin (orcid)0000-0003-2953-2054 aut The Janssen effect and the Chini ordinary differential equation 2024 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. Janssen effect Compression Pressure Mathematical Modeling Bulk solids Grain bin Dyck, George verfasserin (orcid)0000-0002-5920-1240 aut Paliwal, Jitendra verfasserin (orcid)0000-0002-1665-3626 aut Hildebrand, Kurt verfasserin (orcid)0000-0002-7655-3547 aut Montross, Michael D. verfasserin aut Turner, Aaron P. verfasserin aut Enthalten in Powder technology Amsterdam [u.a.] : Elsevier Science, 1967 436 Online-Ressource (DE-627)320599019 (DE-600)2019938-7 (DE-576)098474278 0032-5910 nnns volume:436 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 58.10 Verfahrenstechnik: Allgemeines VZ 52.77 Urformen VZ AR 436
allfieldsSound	10.1016/j.powtec.2024.119493 doi (DE-627)ELV06720385X (ELSEVIER)S0032-5910(24)00135-9 DE-627 ger DE-627 rda eng 660 VZ 58.10 bkl 52.77 bkl Rogers, Adam verfasserin (orcid)0000-0003-2953-2054 aut The Janssen effect and the Chini ordinary differential equation 2024 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. Janssen effect Compression Pressure Mathematical Modeling Bulk solids Grain bin Dyck, George verfasserin (orcid)0000-0002-5920-1240 aut Paliwal, Jitendra verfasserin (orcid)0000-0002-1665-3626 aut Hildebrand, Kurt verfasserin (orcid)0000-0002-7655-3547 aut Montross, Michael D. verfasserin aut Turner, Aaron P. verfasserin aut Enthalten in Powder technology Amsterdam [u.a.] : Elsevier Science, 1967 436 Online-Ressource (DE-627)320599019 (DE-600)2019938-7 (DE-576)098474278 0032-5910 nnns volume:436 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 58.10 Verfahrenstechnik: Allgemeines VZ 52.77 Urformen VZ AR 436
language	English
source	Enthalten in Powder technology 436 volume:436
sourceStr	Enthalten in Powder technology 436 volume:436
format_phy_str_mv	Article
bklname	Verfahrenstechnik: Allgemeines Urformen
institution	findex.gbv.de
topic_facet	Janssen effect Compression Pressure Mathematical Modeling Bulk solids Grain bin
dewey-raw	660
isfreeaccess_bool	false
container_title	Powder technology
authorswithroles_txt_mv	Rogers, Adam @@aut@@ Dyck, George @@aut@@ Paliwal, Jitendra @@aut@@ Hildebrand, Kurt @@aut@@ Montross, Michael D. @@aut@@ Turner, Aaron P. @@aut@@
publishDateDaySort_date	2024-01-01T00:00:00Z
hierarchy_top_id	320599019
dewey-sort	3660
id	ELV06720385X
language_de	englisch
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author	Rogers, Adam
spellingShingle	Rogers, Adam ddc 660 bkl 58.10 bkl 52.77 misc Janssen effect misc Compression misc Pressure misc Mathematical Modeling misc Bulk solids misc Grain bin The Janssen effect and the Chini ordinary differential equation
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title	The Janssen effect and the Chini ordinary differential equation
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title_sort	the janssen effect and the chini ordinary differential equation
title_auth	The Janssen effect and the Chini ordinary differential equation
abstract	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.
abstractGer	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.
abstract_unstemmed	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.
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title_short	The Janssen effect and the Chini ordinary differential equation
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author2	Dyck, George Paliwal, Jitendra Hildebrand, Kurt Montross, Michael D. Turner, Aaron P.
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doi_str	10.1016/j.powtec.2024.119493
up_date	2024-07-06T20:27:41.279Z
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The Janssen effect and the Chini ordinary differential equation

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