Steady shear measurement of thixotropic fluid properties
Summary Measurements of the viscometric properties of a thixotropic fuel oil at constant shear rate have shown a reduction of viscosity that has the characteristics of combined long term and short term exponential decay processes. It is possible to evaluate parameters from experimental data for deca...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Godfrey, J. C. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1973 |
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| Schlagwörter: |
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| Anmerkung: |
© Dr. Dietrich Steinkopff Verlag 1973 |
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| Übergeordnetes Werk: |
Enthalten in: Rheologica acta - Steinkopff-Verlag, 1961, 12(1973), 4 vom: Dez., Seite 540-545 |
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| Übergeordnetes Werk: |
volume:12 ; year:1973 ; number:4 ; month:12 ; pages:540-545 |
| Links: |
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| DOI / URN: |
10.1007/BF01525594 |
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| Katalog-ID: |
OLC2055983563 |
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| 245 | 1 | 0 | |a Steady shear measurement of thixotropic fluid properties |
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| 520 | |a Summary Measurements of the viscometric properties of a thixotropic fuel oil at constant shear rate have shown a reduction of viscosity that has the characteristics of combined long term and short term exponential decay processes. It is possible to evaluate parameters from experimental data for decay processes which combine to represent the observed time dependence of viscosity. At a particular shear rate the time dependence can be represented as:$$\begin{gathered} \mu (t) = \mu _0 - \Delta \mu _1 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ \end{gathered} $$. When measurements are made for a range of shear rates it is found that the time constants,λ1 andλ2, are relatively unchanged while the viscosity deficits,Δµ1 andΔµ2, and the initial viscosity are shear rate dependent. For a limited shear rate range the nature of this dependency can be expressed as:$$\begin{gathered} \Delta \mu (\dot \gamma ) = \Delta \mu ^1 \dot \gamma ^n \hfill \\ \mu _0 (\dot \gamma ) = \mu _0^1 \dot \gamma ^{n_0 } \hfill \\ \end{gathered} $$ whereΔμ1 andµ01 are evaluated at$$\dot \gamma = 1$$ and the various indices all lie between 0 and −1. The time dependence of viscosity measured at constant shear rate can then be represented as:$$\begin{gathered} \mu (t) = \mu _0^1 \dot \gamma ^{n_0 } - \Delta \mu _1^1 \dot \gamma ^{n_1 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2^1 \dot \gamma ^{n_2 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _2 }}} \right. \kern-\nulldelimiterspace} {\lambda _2 }}} ). \hfill \\ \end{gathered} $$ With this characterization method long term, short term, time independent and shear rate dependent characteristics of a material can be individually identified. | ||
| 650 | 4 | |a Viscosity | |
| 650 | 4 | |a Shear Rate | |
| 650 | 4 | |a Time Dependence | |
| 650 | 4 | |a Decay Process | |
| 650 | 4 | |a Steady Shear | |
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10.1007/BF01525594 doi (DE-627)OLC2055983563 (DE-He213)BF01525594-p DE-627 ger DE-627 rakwb eng 540 660 VZ 530 VZ Godfrey, J. C. verfasserin aut Steady shear measurement of thixotropic fluid properties 1973 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Dr. Dietrich Steinkopff Verlag 1973 Summary Measurements of the viscometric properties of a thixotropic fuel oil at constant shear rate have shown a reduction of viscosity that has the characteristics of combined long term and short term exponential decay processes. It is possible to evaluate parameters from experimental data for decay processes which combine to represent the observed time dependence of viscosity. At a particular shear rate the time dependence can be represented as:$$\begin{gathered} \mu (t) = \mu _0 - \Delta \mu _1 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ \end{gathered} $$. When measurements are made for a range of shear rates it is found that the time constants,λ1 andλ2, are relatively unchanged while the viscosity deficits,Δµ1 andΔµ2, and the initial viscosity are shear rate dependent. For a limited shear rate range the nature of this dependency can be expressed as:$$\begin{gathered} \Delta \mu (\dot \gamma ) = \Delta \mu ^1 \dot \gamma ^n \hfill \\ \mu _0 (\dot \gamma ) = \mu _0^1 \dot \gamma ^{n_0 } \hfill \\ \end{gathered} $$ whereΔμ1 andµ01 are evaluated at$$\dot \gamma = 1$$ and the various indices all lie between 0 and −1. The time dependence of viscosity measured at constant shear rate can then be represented as:$$\begin{gathered} \mu (t) = \mu _0^1 \dot \gamma ^{n_0 } - \Delta \mu _1^1 \dot \gamma ^{n_1 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2^1 \dot \gamma ^{n_2 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _2 }}} \right. \kern-\nulldelimiterspace} {\lambda _2 }}} ). \hfill \\ \end{gathered} $$ With this characterization method long term, short term, time independent and shear rate dependent characteristics of a material can be individually identified. Viscosity Shear Rate Time Dependence Decay Process Steady Shear Enthalten in Rheologica acta Steinkopff-Verlag, 1961 12(1973), 4 vom: Dez., Seite 540-545 (DE-627)129512052 (DE-600)210407-6 (DE-576)014919613 0035-4511 nnns volume:12 year:1973 number:4 month:12 pages:540-545 https://doi.org/10.1007/BF01525594 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OPC-GEO SSG-OPC-GGO GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_24 GBV_ILN_30 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_95 GBV_ILN_170 GBV_ILN_252 GBV_ILN_285 GBV_ILN_2006 GBV_ILN_2016 GBV_ILN_2020 GBV_ILN_2245 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4307 GBV_ILN_4319 GBV_ILN_4323 AR 12 1973 4 12 540-545 |
| spelling |
10.1007/BF01525594 doi (DE-627)OLC2055983563 (DE-He213)BF01525594-p DE-627 ger DE-627 rakwb eng 540 660 VZ 530 VZ Godfrey, J. C. verfasserin aut Steady shear measurement of thixotropic fluid properties 1973 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Dr. Dietrich Steinkopff Verlag 1973 Summary Measurements of the viscometric properties of a thixotropic fuel oil at constant shear rate have shown a reduction of viscosity that has the characteristics of combined long term and short term exponential decay processes. It is possible to evaluate parameters from experimental data for decay processes which combine to represent the observed time dependence of viscosity. At a particular shear rate the time dependence can be represented as:$$\begin{gathered} \mu (t) = \mu _0 - \Delta \mu _1 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ \end{gathered} $$. When measurements are made for a range of shear rates it is found that the time constants,λ1 andλ2, are relatively unchanged while the viscosity deficits,Δµ1 andΔµ2, and the initial viscosity are shear rate dependent. For a limited shear rate range the nature of this dependency can be expressed as:$$\begin{gathered} \Delta \mu (\dot \gamma ) = \Delta \mu ^1 \dot \gamma ^n \hfill \\ \mu _0 (\dot \gamma ) = \mu _0^1 \dot \gamma ^{n_0 } \hfill \\ \end{gathered} $$ whereΔμ1 andµ01 are evaluated at$$\dot \gamma = 1$$ and the various indices all lie between 0 and −1. The time dependence of viscosity measured at constant shear rate can then be represented as:$$\begin{gathered} \mu (t) = \mu _0^1 \dot \gamma ^{n_0 } - \Delta \mu _1^1 \dot \gamma ^{n_1 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2^1 \dot \gamma ^{n_2 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _2 }}} \right. \kern-\nulldelimiterspace} {\lambda _2 }}} ). \hfill \\ \end{gathered} $$ With this characterization method long term, short term, time independent and shear rate dependent characteristics of a material can be individually identified. Viscosity Shear Rate Time Dependence Decay Process Steady Shear Enthalten in Rheologica acta Steinkopff-Verlag, 1961 12(1973), 4 vom: Dez., Seite 540-545 (DE-627)129512052 (DE-600)210407-6 (DE-576)014919613 0035-4511 nnns volume:12 year:1973 number:4 month:12 pages:540-545 https://doi.org/10.1007/BF01525594 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OPC-GEO SSG-OPC-GGO GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_24 GBV_ILN_30 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_95 GBV_ILN_170 GBV_ILN_252 GBV_ILN_285 GBV_ILN_2006 GBV_ILN_2016 GBV_ILN_2020 GBV_ILN_2245 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4307 GBV_ILN_4319 GBV_ILN_4323 AR 12 1973 4 12 540-545 |
| allfields_unstemmed |
10.1007/BF01525594 doi (DE-627)OLC2055983563 (DE-He213)BF01525594-p DE-627 ger DE-627 rakwb eng 540 660 VZ 530 VZ Godfrey, J. C. verfasserin aut Steady shear measurement of thixotropic fluid properties 1973 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Dr. Dietrich Steinkopff Verlag 1973 Summary Measurements of the viscometric properties of a thixotropic fuel oil at constant shear rate have shown a reduction of viscosity that has the characteristics of combined long term and short term exponential decay processes. It is possible to evaluate parameters from experimental data for decay processes which combine to represent the observed time dependence of viscosity. At a particular shear rate the time dependence can be represented as:$$\begin{gathered} \mu (t) = \mu _0 - \Delta \mu _1 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ \end{gathered} $$. When measurements are made for a range of shear rates it is found that the time constants,λ1 andλ2, are relatively unchanged while the viscosity deficits,Δµ1 andΔµ2, and the initial viscosity are shear rate dependent. For a limited shear rate range the nature of this dependency can be expressed as:$$\begin{gathered} \Delta \mu (\dot \gamma ) = \Delta \mu ^1 \dot \gamma ^n \hfill \\ \mu _0 (\dot \gamma ) = \mu _0^1 \dot \gamma ^{n_0 } \hfill \\ \end{gathered} $$ whereΔμ1 andµ01 are evaluated at$$\dot \gamma = 1$$ and the various indices all lie between 0 and −1. The time dependence of viscosity measured at constant shear rate can then be represented as:$$\begin{gathered} \mu (t) = \mu _0^1 \dot \gamma ^{n_0 } - \Delta \mu _1^1 \dot \gamma ^{n_1 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2^1 \dot \gamma ^{n_2 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _2 }}} \right. \kern-\nulldelimiterspace} {\lambda _2 }}} ). \hfill \\ \end{gathered} $$ With this characterization method long term, short term, time independent and shear rate dependent characteristics of a material can be individually identified. Viscosity Shear Rate Time Dependence Decay Process Steady Shear Enthalten in Rheologica acta Steinkopff-Verlag, 1961 12(1973), 4 vom: Dez., Seite 540-545 (DE-627)129512052 (DE-600)210407-6 (DE-576)014919613 0035-4511 nnns volume:12 year:1973 number:4 month:12 pages:540-545 https://doi.org/10.1007/BF01525594 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OPC-GEO SSG-OPC-GGO GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_24 GBV_ILN_30 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_95 GBV_ILN_170 GBV_ILN_252 GBV_ILN_285 GBV_ILN_2006 GBV_ILN_2016 GBV_ILN_2020 GBV_ILN_2245 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4307 GBV_ILN_4319 GBV_ILN_4323 AR 12 1973 4 12 540-545 |
| allfieldsGer |
10.1007/BF01525594 doi (DE-627)OLC2055983563 (DE-He213)BF01525594-p DE-627 ger DE-627 rakwb eng 540 660 VZ 530 VZ Godfrey, J. C. verfasserin aut Steady shear measurement of thixotropic fluid properties 1973 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Dr. Dietrich Steinkopff Verlag 1973 Summary Measurements of the viscometric properties of a thixotropic fuel oil at constant shear rate have shown a reduction of viscosity that has the characteristics of combined long term and short term exponential decay processes. It is possible to evaluate parameters from experimental data for decay processes which combine to represent the observed time dependence of viscosity. At a particular shear rate the time dependence can be represented as:$$\begin{gathered} \mu (t) = \mu _0 - \Delta \mu _1 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ \end{gathered} $$. When measurements are made for a range of shear rates it is found that the time constants,λ1 andλ2, are relatively unchanged while the viscosity deficits,Δµ1 andΔµ2, and the initial viscosity are shear rate dependent. For a limited shear rate range the nature of this dependency can be expressed as:$$\begin{gathered} \Delta \mu (\dot \gamma ) = \Delta \mu ^1 \dot \gamma ^n \hfill \\ \mu _0 (\dot \gamma ) = \mu _0^1 \dot \gamma ^{n_0 } \hfill \\ \end{gathered} $$ whereΔμ1 andµ01 are evaluated at$$\dot \gamma = 1$$ and the various indices all lie between 0 and −1. The time dependence of viscosity measured at constant shear rate can then be represented as:$$\begin{gathered} \mu (t) = \mu _0^1 \dot \gamma ^{n_0 } - \Delta \mu _1^1 \dot \gamma ^{n_1 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2^1 \dot \gamma ^{n_2 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _2 }}} \right. \kern-\nulldelimiterspace} {\lambda _2 }}} ). \hfill \\ \end{gathered} $$ With this characterization method long term, short term, time independent and shear rate dependent characteristics of a material can be individually identified. Viscosity Shear Rate Time Dependence Decay Process Steady Shear Enthalten in Rheologica acta Steinkopff-Verlag, 1961 12(1973), 4 vom: Dez., Seite 540-545 (DE-627)129512052 (DE-600)210407-6 (DE-576)014919613 0035-4511 nnns volume:12 year:1973 number:4 month:12 pages:540-545 https://doi.org/10.1007/BF01525594 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OPC-GEO SSG-OPC-GGO GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_24 GBV_ILN_30 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_95 GBV_ILN_170 GBV_ILN_252 GBV_ILN_285 GBV_ILN_2006 GBV_ILN_2016 GBV_ILN_2020 GBV_ILN_2245 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4307 GBV_ILN_4319 GBV_ILN_4323 AR 12 1973 4 12 540-545 |
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10.1007/BF01525594 doi (DE-627)OLC2055983563 (DE-He213)BF01525594-p DE-627 ger DE-627 rakwb eng 540 660 VZ 530 VZ Godfrey, J. C. verfasserin aut Steady shear measurement of thixotropic fluid properties 1973 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Dr. Dietrich Steinkopff Verlag 1973 Summary Measurements of the viscometric properties of a thixotropic fuel oil at constant shear rate have shown a reduction of viscosity that has the characteristics of combined long term and short term exponential decay processes. It is possible to evaluate parameters from experimental data for decay processes which combine to represent the observed time dependence of viscosity. At a particular shear rate the time dependence can be represented as:$$\begin{gathered} \mu (t) = \mu _0 - \Delta \mu _1 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ \end{gathered} $$. When measurements are made for a range of shear rates it is found that the time constants,λ1 andλ2, are relatively unchanged while the viscosity deficits,Δµ1 andΔµ2, and the initial viscosity are shear rate dependent. For a limited shear rate range the nature of this dependency can be expressed as:$$\begin{gathered} \Delta \mu (\dot \gamma ) = \Delta \mu ^1 \dot \gamma ^n \hfill \\ \mu _0 (\dot \gamma ) = \mu _0^1 \dot \gamma ^{n_0 } \hfill \\ \end{gathered} $$ whereΔμ1 andµ01 are evaluated at$$\dot \gamma = 1$$ and the various indices all lie between 0 and −1. The time dependence of viscosity measured at constant shear rate can then be represented as:$$\begin{gathered} \mu (t) = \mu _0^1 \dot \gamma ^{n_0 } - \Delta \mu _1^1 \dot \gamma ^{n_1 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2^1 \dot \gamma ^{n_2 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _2 }}} \right. \kern-\nulldelimiterspace} {\lambda _2 }}} ). \hfill \\ \end{gathered} $$ With this characterization method long term, short term, time independent and shear rate dependent characteristics of a material can be individually identified. Viscosity Shear Rate Time Dependence Decay Process Steady Shear Enthalten in Rheologica acta Steinkopff-Verlag, 1961 12(1973), 4 vom: Dez., Seite 540-545 (DE-627)129512052 (DE-600)210407-6 (DE-576)014919613 0035-4511 nnns volume:12 year:1973 number:4 month:12 pages:540-545 https://doi.org/10.1007/BF01525594 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OPC-GEO SSG-OPC-GGO GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_24 GBV_ILN_30 GBV_ILN_32 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_95 GBV_ILN_170 GBV_ILN_252 GBV_ILN_285 GBV_ILN_2006 GBV_ILN_2016 GBV_ILN_2020 GBV_ILN_2245 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4307 GBV_ILN_4319 GBV_ILN_4323 AR 12 1973 4 12 540-545 |
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For a limited shear rate range the nature of this dependency can be expressed as:$$\begin{gathered} \Delta \mu (\dot \gamma ) = \Delta \mu ^1 \dot \gamma ^n \hfill \\ \mu _0 (\dot \gamma ) = \mu _0^1 \dot \gamma ^{n_0 } \hfill \\ \end{gathered} $$ whereΔμ1 andµ01 are evaluated at$$\dot \gamma = 1$$ and the various indices all lie between 0 and −1. 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Godfrey, J. C. |
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steady shear measurement of thixotropic fluid properties |
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Steady shear measurement of thixotropic fluid properties |
| abstract |
Summary Measurements of the viscometric properties of a thixotropic fuel oil at constant shear rate have shown a reduction of viscosity that has the characteristics of combined long term and short term exponential decay processes. It is possible to evaluate parameters from experimental data for decay processes which combine to represent the observed time dependence of viscosity. At a particular shear rate the time dependence can be represented as:$$\begin{gathered} \mu (t) = \mu _0 - \Delta \mu _1 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ \end{gathered} $$. When measurements are made for a range of shear rates it is found that the time constants,λ1 andλ2, are relatively unchanged while the viscosity deficits,Δµ1 andΔµ2, and the initial viscosity are shear rate dependent. For a limited shear rate range the nature of this dependency can be expressed as:$$\begin{gathered} \Delta \mu (\dot \gamma ) = \Delta \mu ^1 \dot \gamma ^n \hfill \\ \mu _0 (\dot \gamma ) = \mu _0^1 \dot \gamma ^{n_0 } \hfill \\ \end{gathered} $$ whereΔμ1 andµ01 are evaluated at$$\dot \gamma = 1$$ and the various indices all lie between 0 and −1. The time dependence of viscosity measured at constant shear rate can then be represented as:$$\begin{gathered} \mu (t) = \mu _0^1 \dot \gamma ^{n_0 } - \Delta \mu _1^1 \dot \gamma ^{n_1 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2^1 \dot \gamma ^{n_2 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _2 }}} \right. \kern-\nulldelimiterspace} {\lambda _2 }}} ). \hfill \\ \end{gathered} $$ With this characterization method long term, short term, time independent and shear rate dependent characteristics of a material can be individually identified. © Dr. Dietrich Steinkopff Verlag 1973 |
| abstractGer |
Summary Measurements of the viscometric properties of a thixotropic fuel oil at constant shear rate have shown a reduction of viscosity that has the characteristics of combined long term and short term exponential decay processes. It is possible to evaluate parameters from experimental data for decay processes which combine to represent the observed time dependence of viscosity. At a particular shear rate the time dependence can be represented as:$$\begin{gathered} \mu (t) = \mu _0 - \Delta \mu _1 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ \end{gathered} $$. When measurements are made for a range of shear rates it is found that the time constants,λ1 andλ2, are relatively unchanged while the viscosity deficits,Δµ1 andΔµ2, and the initial viscosity are shear rate dependent. For a limited shear rate range the nature of this dependency can be expressed as:$$\begin{gathered} \Delta \mu (\dot \gamma ) = \Delta \mu ^1 \dot \gamma ^n \hfill \\ \mu _0 (\dot \gamma ) = \mu _0^1 \dot \gamma ^{n_0 } \hfill \\ \end{gathered} $$ whereΔμ1 andµ01 are evaluated at$$\dot \gamma = 1$$ and the various indices all lie between 0 and −1. The time dependence of viscosity measured at constant shear rate can then be represented as:$$\begin{gathered} \mu (t) = \mu _0^1 \dot \gamma ^{n_0 } - \Delta \mu _1^1 \dot \gamma ^{n_1 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2^1 \dot \gamma ^{n_2 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _2 }}} \right. \kern-\nulldelimiterspace} {\lambda _2 }}} ). \hfill \\ \end{gathered} $$ With this characterization method long term, short term, time independent and shear rate dependent characteristics of a material can be individually identified. © Dr. Dietrich Steinkopff Verlag 1973 |
| abstract_unstemmed |
Summary Measurements of the viscometric properties of a thixotropic fuel oil at constant shear rate have shown a reduction of viscosity that has the characteristics of combined long term and short term exponential decay processes. It is possible to evaluate parameters from experimental data for decay processes which combine to represent the observed time dependence of viscosity. At a particular shear rate the time dependence can be represented as:$$\begin{gathered} \mu (t) = \mu _0 - \Delta \mu _1 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2 (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ \end{gathered} $$. When measurements are made for a range of shear rates it is found that the time constants,λ1 andλ2, are relatively unchanged while the viscosity deficits,Δµ1 andΔµ2, and the initial viscosity are shear rate dependent. For a limited shear rate range the nature of this dependency can be expressed as:$$\begin{gathered} \Delta \mu (\dot \gamma ) = \Delta \mu ^1 \dot \gamma ^n \hfill \\ \mu _0 (\dot \gamma ) = \mu _0^1 \dot \gamma ^{n_0 } \hfill \\ \end{gathered} $$ whereΔμ1 andµ01 are evaluated at$$\dot \gamma = 1$$ and the various indices all lie between 0 and −1. The time dependence of viscosity measured at constant shear rate can then be represented as:$$\begin{gathered} \mu (t) = \mu _0^1 \dot \gamma ^{n_0 } - \Delta \mu _1^1 \dot \gamma ^{n_1 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2^1 \dot \gamma ^{n_2 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _2 }}} \right. \kern-\nulldelimiterspace} {\lambda _2 }}} ). \hfill \\ \end{gathered} $$ With this characterization method long term, short term, time independent and shear rate dependent characteristics of a material can be individually identified. © Dr. Dietrich Steinkopff Verlag 1973 |
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For a limited shear rate range the nature of this dependency can be expressed as:$$\begin{gathered} \Delta \mu (\dot \gamma ) = \Delta \mu ^1 \dot \gamma ^n \hfill \\ \mu _0 (\dot \gamma ) = \mu _0^1 \dot \gamma ^{n_0 } \hfill \\ \end{gathered} $$ whereΔμ1 andµ01 are evaluated at$$\dot \gamma = 1$$ and the various indices all lie between 0 and −1. The time dependence of viscosity measured at constant shear rate can then be represented as:$$\begin{gathered} \mu (t) = \mu _0^1 \dot \gamma ^{n_0 } - \Delta \mu _1^1 \dot \gamma ^{n_1 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _1 }}} \right. \kern-\nulldelimiterspace} {\lambda _1 }}} ) \hfill \\ - \Delta \mu _2^1 \dot \gamma ^{n_2 } (1 - e^{{{ - t} \mathord{\left/ {\vphantom {{ - t} {\lambda _2 }}} \right. \kern-\nulldelimiterspace} {\lambda _2 }}} ). \hfill \\ \end{gathered} $$ With this characterization method long term, short term, time independent and shear rate dependent characteristics of a material can be individually identified.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Viscosity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Shear Rate</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Time Dependence</subfield></datafield><datafield tag="650" ind1=" " 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