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A generalized rheological model of thixotropic materials

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Summary

A generalization of the rheological model of thixotropic materials, presented previously, was carried out. In the generalized rheological equation of state the yield stress depending on the structural parameter was introduced. In the generalized rate equation the difference in the destruction and recovery rates of the material structure was taken into account. A procedure leading to the determination of nine rheological parameters of the generalized model was worked out. The model was checked experimentally for a thixotropic paint.

Zusammenfassung

Eine früher dargestellte Theorie thixotroper Stoffe wird verallgemeinert, wobei eine von dem Strukturparameter abhängige Fließspannung eingeführt wird. Weiterhin wird der Unterschied zwischen der Zerstörungs-und der Wiederaufbaugeschwindigkeit der Stoffstruktur berücksichtigt. Eine Methode zur Bestimmung der neun benötigten Stoffparameter wird ausgearbeitet. Das Modell wird am Beispiel einer thixotropen Farbe experimentell geprüft.

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Abbreviations

a :

rheological parameter in eq. [26], s−1

A :

rheological parameter in eq. [16]

b :

rheological parameter in eq. [26]

c :

function in eq. [21]

\(\bar c\) :

averaged value of functionc in eq. [28]

c Λ :

function in the rate equation [23], defined by eq. [21]

G :

function [1] defining material of the rate type

h :

function [2] determining the state of thixotropic fluid

k :

rheological parameter in the Herschel-Bulkley equation [17] or, in special case, in eq. [8], Nsn/m2

K :

function in eq. [18], Nsm/m2

m :

rheological parameter in eq. [18] or, in special case, in eq. [10]

n :

rheological parameter in the Herschel-Bulkley model [17] or, in special case, in eq. [8]

s :

rheological parameter in eq. [16]

t :

time, s

x :

arbitrary real variable

α :

rheological parameter in eq. [9], s

\(\dot \gamma \) :

shear rate, s−1

κ :

structural parameter, defined by eq. [2]

\(\dot k\) :

substantial derivative of structural parameter, s−1

κ e :

function [6] describing the equilibrium curve in the coordinate system (\(\left( {\dot \gamma , k} \right)\))

κ 0 :

initial value of structural parameter (att = 0)

Λ :

natural time function of the thixotropic material, defined by eq. [22]

τ :

shear stress, N/m2

\(\dot \tau \) :

substantial derivative of shear stress, N/m2 s

τ e :

function describing equilibrium flow curve in the coordinate system (\(\left( {\dot \gamma , \tau } \right)\))

τ 0 :

equilibrium yield stress, defined by eq. [12], N/m2

τ y :

function of structural parameterκ describing the yield stress

ψ :

function in eq. [11]

i,j,k :

integer

k e (i) :

ordinal number of the experimental point at which the line ofκ i = const intersects the equilibrium flow curve

l i :

number of the experiments of the type “stepchange of the shear rate”

l j :

number of experimental points in one experiment of the type “step-change of the shear rate”

n e :

number of experimental points on the equilibrium flow curve

n k :

number of experimental points on the line of constantκ

n y :

number of lines of constantκ

t(j) :

measured time interval (from the moment of the step-change of shear rate)

\(\dot \gamma \left( {i, k} \right)\) :

abscissa of the experimental point of ordinal numberk on the line ofκ i = const, in the coordinate system (\(\left( {\dot \gamma , \tau } \right)\))

\(\dot \gamma _e (i)\) :

abscissa of the experimental point of ordinal numberi on the equilibrium flow curve, in the coordinate system (\(\left( {\dot \gamma , \tau } \right)\))

\(\dot \gamma _s (i)\) :

shear rate at which the experiment of the type “step-change of shear rate” was carried out

τ e (i) :

ordinate of the experimental point of ordinal numberi on the equilibrium flow curve, in the coordinate system (\(\left( {\dot \gamma , \tau } \right)\))

τ y (i) :

value of yield stress atκ = κ i

τ s (i,j) :

experimental value of shear stress at constant value of shear rate\(\bar \rho \)(2i) for time intervalt(j)

τ κ (i,k) :

ordinate of the experimental point of ordinal numberk on the line ofκ i = const, in the coordinate system (\(\left( {\dot \gamma , \tau } \right)\))

Δτ 0 :

the admissible value of the difference between the experimental and theoretical value of shear stress

References

  1. Kembłowski, Z., J. Petera Rheol. Acta18, 702 (1979).

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  2. Cheng, D. C. H., F. Evans Brit. J. Appl. Phys.16, 1599 (1965).

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  3. Gillespie, T. J. Coll. Sci.15, 219 (1960).

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  4. Mewis, J. J. Non-Newtonian Fluid Mech.6, 1 (1979).

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Authors and Affiliations

  1. Institute of Chemical Engineering, Łódź Technical University, ul. Wólczańska 175, PL-90-924, Łódź, Poland

    Z. Kembłowski & J. Petera

Authors
  1. Z. Kembłowski
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  2. J. Petera
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With 4 figures and 1 table

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Kembłowski, Z., Petera, J. A generalized rheological model of thixotropic materials. Rheol Acta 19, 529–538 (1980). https://doi.org/10.1007/BF01517508

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  • DOI: https://doi.org/10.1007/BF01517508

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