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A. S. Lodge

Bio: A. S. Lodge is an academic researcher from University of Wisconsin-Madison. The author has contributed to research in topics: Shear rate & Shear stress. The author has an hindex of 13, co-authored 27 publications receiving 744 citations.

Papers
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Journal ArticleDOI
TL;DR: In this article, constitutive equations based on the network models of Yamamoto, Lodge, and Kaye are re-derived in a common notation involving the use of base vectors embedded in the deforming macroscopic continuum.
Abstract: In this mainly expository paper, constitutive equations based on the network models ofYamamoto,Lodge, andKaye are re-derived in a common notation involving the use of base vectors embedded in the deforming macroscopic continuum. The derivations are thereby simplified in some respects and the differences of detail between the models are clarified. InLodges theory, the sub-network superposition assumption is replaced by alternative assumptions concerning the creation and loss of network segments, and the theory is extended to non-Gaussian networks.Kayes theory is extended to allow for the presence of entanglement junctions of different complexities.

211 citations

Journal ArticleDOI
TL;DR: In this article, the theory of dilute polymer solutions based on the bead/spring model in the form given by Zimm is reformulated for arbitrary homogeneous flow histories, and it is shown that the center of resistance of a polymer molecule moves with the solvent.
Abstract: The theory of dilute polymer solutions based on the bead/spring model in the form given by Zimm is reformulated for arbitrary homogeneous flow histories. It is shown that the center of resistance of a polymer molecule moves with the solvent. By a preliminary transformation [3.4], the equations for the center-of- resistance motion are separated from those for the motion of the N spring vectors. The spring-vector equations involve a symmetric non-singular matrix B [3.14] whose characteristic values equal the non-zero characteristic values of Zimms singular matrix HA. A further transformation [4.2] which diagonalizes B yields separate differential eq. [5.4] for pq*, the polymer contribution to the stress tensor associated with the q normal mode. Transformation to an embedded basis enables one to integrate these equations so as to obtain pq* in terms of the flow history ([5.6], [5.9]), and summation over q then gives the required constitutive eq. [5.17] for the polymer solution. These are of the same form as the “rubber-like liquid” constitutive equations (with addition of a solvent-contribution term) derived from the network theory of Lodge, but the memory function is determined to within three constants (e. g. N, h*, τ1). Peterlina solution for the normal-coordinate distribution function in steady shear flow is generalized for an arbitrary homogeneous (time-dependent or steady) flow and expressed in terms of pq* which can be evaluated when the flow history is given.

98 citations

Journal ArticleDOI
TL;DR: The non-linear behavior observed by Meissner can be qualitatively described by the rubberlike liquid constitutive equations when the constants in the memory function are chosen to fit the data in the linear region at low elongation rates.
Abstract: The non-linear behavior observed byMeissner can be qualitatively described by the rubberlike-liquid constitutive equations when the constants in the memory function are chosen to fit the data in the linear region at low elongation rates.

69 citations

Journal ArticleDOI
TL;DR: In this article, a slit die rheometer was constructed to measure elastic and viscous properties of molten polymers at low shear rates, and the wall shear stress σ and the extrapolated exit pressurePx were determined by means of two pressure transducers mounted flush with a die wall.
Abstract: A new slit die rheometer has been constructed to measure elastic and viscous properties of molten polymers at low shear rates. The wall shear stress σ and the extrapolated exit pressurePx are determined by means of two pressure transducers mounted flush with a die wall. The hole pressureP* is obtained from one of the flush-mounted transducers and a third transducer mounted in a transverse slot opposite the flush-mounted transducer. The wall shear rate\(\dot s\) is obtained from a metering pump. Electrical heaters give melt temperatures that are uniform to within ±0.1 °C at 150°C. For two low-density polyethylene samples of Melt Index 2 and 50, at shear rates in the range 0.1 to 8 s−1, it is found that (a) viscosity values agree with those obtained using two Weissenberg Rheogoniometers (WRGs); (b) hole pressure data agree with the predictions of the “HPB” transverse-slot equationN1 = 2σdP*/dσ when WRG data are used for the first normal stress differenceN1; and (c) exit pressures are large and negative, in marked disagreement with certain published equations relatingPx,N1 andσ. An error analysis shows thatPx values can contain significant negative contributions arising from the pressure dependence of viscosity, even at low shear rates. As a means for in-line measurement of melt elasticity at low shear rates, the results favor the use of the hole pressure, but raise serious questions about the use of the exit pressure.

52 citations


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Journal ArticleDOI
TL;DR: In this paper, the authors studied possible motions for one polymer molecule P performing wormlike displacements inside a strongly cross-linked polymeric gel G. The topological requirement that P cannot intersect any of the chains of G is taken into account by a rigorous procedure: the only motions allowed for the chain are associated with the displacement of certain "defects" along the chain.
Abstract: We discuss possible motions for one polymer molecule P (of mass M) performing wormlike displacements inside a strongly cross‐linked polymeric gel G. The topological requirement that P cannot intersect any of the chains of G is taken into account by a rigorous procedure: The only motions allowed for the chain are associated with the displacement of certain “defects” along the chain. The main conclusions derived from this model are the following:(a) There are two characteristic times for the chain motion: One of them (Td) is the equilibration time for the defect concentration, and is proportional to M2. The other time (Tr) is the time required for complete renewal of the chain conformation, and is proportional to M3.(b) The over‐all mobility and diffusion coefficients of the chain P are proportional to M−2.(c) At times t < Tr the mean square displacement of one monomer of P increases only like 〈(rt − r0)2〉 = const t1/4.These results may also turn out to be useful for the (more difficult) problem of entangle...

3,467 citations

Journal ArticleDOI
TL;DR: In this paper, the authors analyzed and explained the reasons for the instability of a viscous jet of polymer solution at a pendent droplet, showing that the longitudinal stress caused by the external electric field acting on the charge carried by the jet stabilized the straight jet for some distance.
Abstract: Nanofibers of polymers were electrospun by creating an electrically charged jet of polymer solution at a pendent droplet. After the jet flowed away from the droplet in a nearly straight line, it bent into a complex path and other changes in shape occurred, during which electrical forces stretched and thinned it by very large ratios. After the solvent evaporated, birefringent nanofibers were left. In this article the reasons for the instability are analyzed and explained using a mathematical model. The rheological complexity of the polymer solution is included, which allows consideration of viscoelastic jets. It is shown that the longitudinal stress caused by the external electric field acting on the charge carried by the jet stabilized the straight jet for some distance. Then a lateral perturbation grew in response to the repulsive forces between adjacent elements of charge carried by the jet. The motion of segments of the jet grew rapidly into an electrically driven bending instability. The three-dimensional paths of continuous jets were calculated, both in the nearly straight region where the instability grew slowly and in the region where the bending dominated the path of the jet. The mathematical model provides a reasonable representation of the experimental data, particularly of the jet paths determined from high speed videographic observations.

2,324 citations

Book ChapterDOI
01 Jan 1974

1,090 citations

Journal ArticleDOI
TL;DR: In this paper, a constitutive equation is derived from a Lodge-Yamamoto type of network theory for polymeric fluids, where the network junctions are not assumed to move strictly as points of the continuum but allowed a certain "effective slip".
Abstract: A constitutive equation is derived from a Lodge—Yamamoto type of network theory for polymeric fluids. The network junctions are not assumed to move strictly as points of the continuum but allowed a certain “effective slip”. The rates of creation and destruction of junctions are assumed to depend on the instantaneous elastic energy of the network, or equivalently, the average extension of the network strand, in a simple manner. Agreement between model predictions and the I.U.P.A.C. data on L.D.P.E. is good.

1,066 citations

Journal ArticleDOI
Ronald G. Larson1
TL;DR: In this article, the authors present a review of the latest developments as well as earlier work in this area, organized into the following categories: Taylor-Couette flows, instabilities in cone and plate-and-plate flows, parallel shear flows, extrudate distortions and fracture, Instabilities in shear flow with interfaces, extensional flows, and thermohydrodynamic instabilities.
Abstract: Viscoelastic instabilities are of practical importance, and are the subject of growing interest. Reviewed here are the fresh developments as well as earlier work in this area, organized into the following categories: instabilities in Taylor-Couette flows, instabilities in cone-and-plate and plate-and-plate flows, instabilities in parallel shear flows, extrudate distortions and fracture, instabilities in shear flows with interfaces, instabilities in extensional flows, instabilities in multidimensional flows, and thermohydrodynamic instabilities. Emphasized in the review are comparisons between theory and experiment and suggested directions for future work.

883 citations