Dynamics of Polymeric Fluids：Part Ⅱ The Molecular Theory of Die Swell： Correlation of Ultimate Die Swelling Effect to the Molecular Parameters and the Operational Variables

A general expression for the correlation of the simple shear （tanφ） to the molecular parameters and the shear rate （·↑γ） was deduced. It shows that the simple shear （tanφ） may be resolved into free recoil （recoverable strain） and viscous heating （unrecoverable strain）. The magnitudes of the simple shears for recoil （tanφE） and （tanφv） for viscous heating not only depended on the molecular parameters and the operational variables, but also on the exponential fractions of the recoverable （1--↑W·↑γ） and unrecoverable （-↑W·↑γ） conformations for recoil and viscous heating. Therefore the magnitudes of the simple shears （tanφE） for recoil and （tanφv） for viscous heating are, respectively, expressed as the partition function to the （1--↑W·↑γ）th power and the partition function to the （-↑W·↑γ）th power. Thus correlations of the total recoil and the ultimately recoverable strains to the molecular parameters [n′, α, η0, GN^0 and （1--↑W·↑γ）] and the operational variables （·↑γ, （L/D） and tr） were deduced respectively, which show that at very different shear rates （0≤·↑γ≤∞） the polymeric liquids may exhibit a very different viscoelastic behaviors. After introducing the uniform two-dimensional extension, the definition of swelling ratio and the ratio of L to D [De=（L/D）], two expressions for the ultimate die swelling effect and the ultimate extrudate swelling ratio BEVT5 to the molecular parameters [n′, α, η0, GN^0 and （1--↑W·↑γ）] and the operational variables （·↑γ, （L/D） and tr） were obtained. The two correlation expressions were verified by the experimental data of high-density polyethylene （HDPE） which shows that the two correlation expressions can be used to predict the correlations of the ultimate extrudate swelling behaviors of polymeric liquids to the molecular parameters and the operational variables.

Dynamics of Polymeric Fluids 1. The Molecular Theory of Die Swell:A Set of Equation on Swelling Ratio in Extrudates

The structural model of the multiple-transient networks and the mechanism of the multiple-reptation entangled chains due to the dynamic reorganization in the entangled sites were extensively applied on the die swell of polymeric liquids in the steady simple shear flow. The total （recoverable and unrecoverable） viscoelastic free energy of deformation and flow, the constitutive equation and the expression of the simple shear （tanψ） were deduced from the conformational probability distribution function of the entangled polymer chains. It found that： （1） the magnitudes of simple shear （tanψ） depended not only on the free recoil （or recoverable strain） but also on the viscous heating （or unrecoverable strain）; （2） the total recoil may be resolved into the instantaneous and delayed recoil. Based on these facts, the functions of the partition and two experiential fractions of the recoverable （1-Wγ） and the unrecoverable （Wγ） conformations for the recoil and viscous heating of polymeric liquids were defined correspondingly. Then the correlation of the instantaneously and ultimately （or total） recoverable strains to the （N1/T12）w and the fraction of trans-form conformation was obtained. After introducing the condition of uniform two-dimensional extension （αx=αy=α, αz=α^-2） and the swell ratio （B=α）, two sets of equations on the instantaneous and ultimate swelling ratios （BE, BEVT） were obtained, and a method to determine the fraction of the recoverable transform conformation were proposed, The equations of BE and BE5 were verified by the experimental data of HDPE （high denisity polyethylene） at two different high temperatures. It shows that the molecular theory of die swell can be used to predict the correlation of the swelling to the （NI/TI2）w and the fraction of trans-form conformation.

Dynamic Theory of Die Swell for Entangled Polymeric Liquids in Tube Extrusion： Correlations of Total and Ultimate Extrudate Swell Effects to Growth Time, Shear Stress and Aspect Ratio Under the Free States

The dynamic theory of die swell deduced in a previous paper was extensively applied to study the extrudate swelling behaviors of two entangled polymeric liquids （HDPE and PBD） in a simple shear flow at steady shear stress. The mechanism and dynamics for the recoils and the recoveries of viscoelastic strains in the extrudate were investigated under the free recovery and dynamic states. It was found that in the course of recovery the free recoil and the growth of die swell in the extrudate may be divided into two recovery regions （instantaneous and delayed regions） and three growth stages （instantaneous, delayed, and ultimate extrudate swelling stages）. The free recoil and the extrudate swelling behaviors may be expressed as a function of shear stress. The correlations of instantaneous, delayed, total and ultimate extrudate swell effects to the molecular parameters and the operational variables in the simple shear flow at steady shear stress were derived from the dynamic theory of die swell. Also, two sets of new universal equations on the total extrudate swelling effect （TESE） and ultimate extrudate swelling effect （UESE） were deduced. The first is the universal equation of the logarithmic correlation between the TESE and the growth time under the free and dynamic states; the second is the universal equation of the logarithmic correlation between the UESE and the operational variables under the free and equilibrium states. The first equation was verified by experimental data of PBD with different molecular weights at different operational variables. The second equation was verified by experimental data of HDPE at two temperatures and different operational variables. An excellent agreement result was obtained. The excellent agreement shows that the two universal equations can be used directly to predict the correlations of the TESE and UESE to the growth time, the molecular parameters, and the operational variables under the dynamic and equilibrium states.

Hot melt extrusion:An industrially feasible approach for casting orodispersible film

Over the recent few decades,many groups of formulation scientists are concentrating on rapid release dosage forms in oral cavity.Among all fast release dosage forms,orodispersible films are successful to attract pharmaceutical industry due to ease of formulation and extension patent life.Films are popular in patients too because of quick onset and user friendliness of dosage form.From the beginning,solvent casting has been selected as method of choice for manufacturing of orodispersible films.Solvent casting has been proved as a benchmark technology because of ease in product development,process optimization,process validation and technology transfer to production scale despite of some drawbacks like more number of unit operations involved and consumption of large quantity of solvents with controlled limits of organic volatile impurities in final formulation.The application of hot-melt extrusion(HME)in the pharmaceutical industry is consecutively increasing due to its proven innumerable advantages like solvent free continuous process with fewer unit operations and better content uniformity.Very few development activities has been initiated in the field of hot melt extruded orodispersible films so far.This extensive review covers detailed discussion of heavy duty industrial extruders,selection of downstream equipments,selection of excipients,common problems found in formulations and their remedies.Successive part of review addresses identification of critical quality attributes,quality target profile of product,criticality in selection of process parameters and material for substantial simulation in laboratory scale and production for successful technology transfer.

A mixed finite element scheme for viscoelastic flows with XPP model

A mixed finite element formulation for viscoelastic flows is derived in this paper, in which the FIC （finite incremental calculus） pressure stabilization process and the DEVSS （discrete elastic viscous stress splitting） method using the Crank-Nicolson-based split are introduced within a general framework of the iterative version of the fractional step algorithm. The SU （streamline-upwind） method is particularly chosen to tackle the convective terms in constitutive equations of viscoelastic flows. Thanks to the proposed scheme the finite elements with equal low-order interpolation approximations for stress-velocity-pressure variables can be successfully used even for viscoelastic flows with high Weissenberg numbers. The XPP （extended Pom-Pom） constitutive model for describing viscoelastic behaviors is particularly integrated into the proposed scheme. The numerical results for the 4：1 sudden contraction flow problem demonstrate prominent stability, accuracy and convergence rate of the proposed scheme in both pressure and stress distributions over the flow domain within a wide range of the Weissenberg number, particularly the capability in reproducing the results, which can be used to explain the ＂die swell＂ phenomenon observed in the polymer injection molding process.

Coaxial liquid-liquid flows in tubes with limited length

Coaxial liquid-liquid flows were numerically studied in a nesting two-tube system. Calculations were carried out when various exit-lengths (meaning length differences between the two tubes) were used. Numerical results indicated that there exists a certain range of exit-length for the liquid-liquid flows to form stable and smooth interfaces, which requires that the exit-length should roughly be less than 5.6 times the outer tube diameter. In this range, interface instability is effectively restrained and the core fluid shows a phenomenon of die swell. When the exit-length is about 1.6 times the outer tube diameter, the core fluid has the greatest diameter size in the shell fluid. Velocity distributions at the outer tube exit favor formation of a continuous and stable core-shell structure.