Resistance to flow of molten polymers through granular beds

Summary The resistance to flow of molten polymers (exhibiting memory effects) through granular beds was investigated. The data were correlated using simple methods of rheological characteristics of polymer melts.

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Zusammenfassung Es wird der Strömungswiderstand von Polymerschmelzen (welche Gedächtnis-Effekte zeigen) in Kornschüttungen untersucht. Bei der Korrelation der Meßwerte werden einfache Methoden zur rheologischen Charakterisierung der Schmelzen verwendet.

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Notation a^* regression coefficient - b constant in eq. [22] - b^* regression coefficient - B swell ratio, defined by eq. [2] - B₁ swell ratio, defined by eq. [17a] - B₂ swell ratio, defined by eq. [18a] - B₃ swell ratio, defined by eq. [19a] - B₀ swell ratio during the extrusion of a Newtonian fluid from the capillary - B_exp swell ratio determined according to the method described byCogswell (22) - B_exp swell ratio determined according to the method described byMendelson andFinger (23) - C constant in eq. [22] - d_p particle diameter, m - D extrudate diameter, m - D₀ capillary diameter, m - f_CM friction factor, defined by eq. [12] - F() function occurring in eq. [15] - k fluid consistency factor, Nsⁿ/m² - l bed height, m - L₁,L₂ length scales, m - n flow behaviour index - p pressure, N/m² - p₁₁ –p₂₂ first normal-stress difference, N/m² - r correlation coefficient - S recoverable shear strain, defined by eq. [3] - S average value of recoverable shear strain - S_w recoverable shear strain at the wall - s bed permeability, defined by eq. [8], m² - v₀ mean linear velocity of fluid, related to an empty cross-section of the column, m/s - w₀ mass flow rate, kg/m² s - level of probability of the correlation - shear rate, s^–1 - shear rate in a porous bed, defined by eq. [14], s^–1 - porosity - coefficient of dynamic fluid viscosity, Ns/m² - relaxation time, defined by eq. [1], s - friction factor, defined by eq. [5] - density of molten polymer, kg/m³ - ₀ density of polymer at room temperature, kg/m³ - ₁₂ shear stress, N/m² - parameter, defined by eq. [7], Nsⁿ/m¹⁺ⁿ - function occurring in eq. [4] - De Deborah number, defined by eq. [16] - Re_BK Reynolds number, defined by eq. [25] - Re_BK generalized Reynolds number, defined by eq. [6] - Re_CM generalized Reynolds number, defined by eq. [13]With 10 figures and 3 tables