Lubricated squeezing flow of thin slabs of wheat flour dough: comparison of results at constant plate speed and constant extension rates

Abstract

Lubricated squeezing flow experiments on wheat flour dough have, until now, mostly been performed in constant plate speed mode (CPS), i.e. at a permanently increasing extension rate. We have compared the results obtained under the CPS and constant extension rate (CER) modes using one of the very few commercial rheometers that allow operation in the CER mode. In both cases, and at any constant biaxial strain, a power law could be fitted to the stress versus extension rate data, the “consistency index” (K) increasing continuously with the strain and the “flow behaviour index” (n) being constant only up to a low strain value (≈0.25) and then decreasing. When compared to the CER mode, the CPS mode produced higher K and n values. For wheat flour doughs, an increase in K with extension may be associated to a strain-hardening phenomenon but the roles of viscoelasticity and lubricant thinning are discussed.

Appendix: calculation of t 1 (CER), t 2 (CPS) and t 2/t 1

$$ t_1 =\frac{\varepsilon _{\rm b} }{{\mathop \varepsilon\limits^\cdot} _{\rm b} }=\frac{2L}{v}\varepsilon _{\rm b} $$

$$ t_1 =\frac{2L\varepsilon _{\rm b} }{v} $$

$$ {\mathop \varepsilon \limits^\cdot} _{\rm b} =\frac{1}{2}\frac{{\rm d}L}{L{\rm d}t}=\frac{1}{2}\frac{v}{L} $$

$$ \left( {v \textgreater 0} \right)\,\,\,\,L=L_{\rm 0} -vt $$

$$\begin{array}{lll} \varepsilon _{\rm b}&=&\frac{v}{2}\int {\frac{{\rm d}t}{L_0-vt}}=-\frac{1}{2}\big[ {Ln\big( {L_0-vt} \big)} \big]_0^{t_2 }\\[6pt] &=&-\frac{1}{2}\,Ln\frac{L_0 -vt_2 }{L_0 }=-\frac{1}{2}\;L\left( {1-\frac{vt_2 }{L_0 }} \right) \end{array}$$

$$ 1-\frac{vt_2 }{L_0 }=\exp \big( {-2\;\varepsilon _{\rm b} } \big) $$

$$ t_2 =\frac{L_0 }{v}\big[ {1-\exp \big( {-2\varepsilon _{\rm b} } \big)} \big] $$

$$ \frac{t_2 }{t_1 }=\frac{L_0 }{2L\varepsilon _{\rm b} }\big[ {1-\exp \big( {-2\varepsilon _{\rm b} } \big)} \big] $$

$$ \varepsilon _{\rm b} =-\frac{1}{2}Ln\frac{L}{L_0 } $$

$$ \frac{L_0 }{L}=\frac{1}{\exp \big( {-2\varepsilon _{\rm b} } \big)}=\exp \big( {2\varepsilon _{\rm b} } \big) $$

$$ \frac{t_2 }{t_1 }=\frac{1}{2\varepsilon _{\rm b} }\left[ {\exp \big( {2\varepsilon _{\rm b} } \big)-1} \right] $$