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Journal of Theoretical
and Applied Mechanics
8, 4, pp. 479-491, Warsaw 1970
and Applied Mechanics
8, 4, pp. 479-491, Warsaw 1970
O profilach prędkości przy laminarnych przepływach polimerów
Znajomość możliwie dokładnych profili prędkości dla roztworów i stopionych polimerów przepływających przez rury i kanały o przekroju prostokątnym posiada istotne znaczenie nie tylko dla analizy procesów technologicznych, lecz również dla badania i wyjaśnienia różnych „anomalii” towarzyszących przepływom. Metody doświadczalnego wyznaczania krzywych płynięcia (konsystencji) dla cieczy nienewtonowskich, za jakie uważa się większość roztworów i stopionych polimerów, znane są dobrze z literatury podstawowej. W niniejszych rozważaniach zwrócono uwagę na możliwość opisu przepływów stopionych polimerów przy małych szybkościach ścinania, za pomocą równań konstytutywnych nieściśliwej cieczy lepkosprężystej stopnia trzeciego. Odpowiednie analityczne profile prędkości porównano z doświadczalnymi wynikami pracy [12]. Właściwą część rozważań poprzedzono krótkim omówieniem innych równań o charakterze empirycznym, zwracając szczególną uwagę na wady i zalety różnych sposobów podejścia.
ON VELOCITY PROFILES IN LAMINAR FLOWS OF POLYMERS
A knowledge of possibly exact velocity profiles for polymer solutions and melts in pipe and channel flows is of great importance for technological processes as well as for more advanced analysis of flows (anomalous effects, instability etc.). There exist numerous methods of experimental determination of flow curves, on the basis of which analytical velocity profiles are obtained for various constitutive equations. One of the most widely used models is that of so-called power law fluid against which, however, many objections can be formulated (cf. [1]). More recently, attempts have been made to determine velocity profiles by means of direct measurements (cf. [9,11, 12]). In the present paper the constitutive equations of a visco-elastic fluid of third grade are proposed for description of slow laminar flows of molten polymers in slits and cylindrical capilaries. These equations are not only of more general nature (an approximation for simple fluids) but also the resultant relations can be easily modified for the case of effective slip at the walls. For further illustration, the velocity profiles resulting from our theoretical considerations have been compared with the slit flow experiments of other authors (cf. [12, 20]).
ON VELOCITY PROFILES IN LAMINAR FLOWS OF POLYMERS
A knowledge of possibly exact velocity profiles for polymer solutions and melts in pipe and channel flows is of great importance for technological processes as well as for more advanced analysis of flows (anomalous effects, instability etc.). There exist numerous methods of experimental determination of flow curves, on the basis of which analytical velocity profiles are obtained for various constitutive equations. One of the most widely used models is that of so-called power law fluid against which, however, many objections can be formulated (cf. [1]). More recently, attempts have been made to determine velocity profiles by means of direct measurements (cf. [9,11, 12]). In the present paper the constitutive equations of a visco-elastic fluid of third grade are proposed for description of slow laminar flows of molten polymers in slits and cylindrical capilaries. These equations are not only of more general nature (an approximation for simple fluids) but also the resultant relations can be easily modified for the case of effective slip at the walls. For further illustration, the velocity profiles resulting from our theoretical considerations have been compared with the slit flow experiments of other authors (cf. [12, 20]).