Fluid motion along a smooth, solid surface is examined when the free surface forms a final visible angle with the solid boundary. The dependence of this angle on the velocity with allowance for capillary forces is determined. The Reynolds number is small. The problem of the motion of the phase interface in a capillary and the spreading of viscous fluid drops on solid surfaces are solved. Experimental results are explained. Up to now, not only were analytical results lacking in this field, but also there was not even a precise formulation of the problem (see the review in [1]).

Hydrodynamics of wetting

The viscosity of polymers and their concentrated solutions

The dynamics of concentration fluctuations in binary polymer mixtures AB, A and B being long and flexible chains, is studied near the critical point of unmixing. A ‘‘hydrodynamic’’ theory in close analogy to the treatments of Cahn–Hilliard and Cook for the dynamics of unmixing alloys is developed, and its validity is carefully analyzed. It is shown that homogeneous nucleation for long chains is negligible except in a narrow region of volume fraction φ0 near the spinodal curve φs0 of width (φs0−φ0)/φ0∝N−1, where N is the number of subunits of the chains. For N→∞ the spinodal curve hence is well defined, in contrast to mixtures with short‐range forces, and also the linearized theory of spinodal decomposition is predicted to have wider validity. The collective relaxation in the one‐phase region is described by a characteristic time involving the collective diffusion constant Dcoll τq=(Dcoll q2)−1, if the wave vector q is smaller than the inverse correlation length ξ−1coll, while in the range ξ−1coll≪q≪R−1 (R...

Collective diffusion, nucleation, and spinodal decomposition in polymer mixtures

The shear-thinning behaviour of a liquid is represented in terms of a relaxation timeλ, defined by the ratioη
0/G0 of initial viscous and elastic constants. The relationship provides a very simple basis for the evaluation ofλ andG
0 from viscosity/shear data. Results are compared with relaxation times and moduli from primary normal-stress measurement, from stress relaxation and from direct measurement of recoverable shear strain. Good agreement is found but there is experimental evidence the recoverable shear strainγ
e is related to normal stressN
1 and shear stressσ byγ
e = N1/3σ, which does not agree with the theoretical prediction of eitherWeissenberg orLodge.

Relation between viscoelasticity and shear-thinning behaviour in liquids

Using a realistic united-atom force field, molecular dynamics simulations were performed to study homogeneous nucleation of the crystal phase at about 30% supercooling from the melts of n-pentacontahectane (C150) and a linear polyethylene (C1000), both of which are long enough to exhibit the chain folding that is characteristic of polymer crystallization. The nucleation rate was calculated and the critical nuclei were identified using a mean first-passage time analysis. The nucleation rate was found to be insensitive to the chain length in this range of molecular weight. The critical nucleus contains about 150 carbons on average and is significantly smaller than the radius of gyration of the chains, at this supercooling. A cylinder model was used to characterize the shape of the crystal nuclei and to calculate the interfacial free energies. A chain segment analysis was performed to characterize the topology of the crystal surface in terms of loops (including folds) and tails. The length distribution of lo...

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Molecular Dynamics Simulation of Homogeneous Crystal Nucleation in Polyethylene

Viscosity–molecular weight relationship for polydimethylsiloxane

Experiments in which an oscillatory shear flow is superimposed on a steady state shear flow were performed on polyethylene melts by the use of a cone and plate type rheogoniometer. The phase difference between oscillatory shear stress and shear strain increases in all cases and for all frequencies with the increase of the superimposed shear rate. Between ω0, the frequency at which the phase difference is π/2 and the steady shear rate , as found by Booij for polymer solution, the relation ω0 = 1/2 . holds also for polyethylene melts. The significance of this relation is discussed briefly from the viewpoint that the entanglement density decreases with the increase of the imposed shear rate.

Influence of superimposed steady shear flow on the dynamic properties of polyethylene melts

Zero shear viscosities of two-component blends of polydimethylsiloxane with different molecular weights were measured over the whole range of composition. Results are analyzed on the basis of the conventional treatments for the viscosity of polymer blends and some comments are made on such treatments of data. After that, an empirical equation is derived: 



where η is the viscosity, v the volume fraction, subscripts 1, 2, and bl denote the lower and higher molecular weight component and the blend, respectively, and a is a constant independent of composition. The equation is not only applicable to all series of blends of polydimethylsiloxane but also to other polymers.

Viscosity of polydimethylsiloxane blends

Viscosities of polydimethylsiloxane–pentamer systems were measured over the whole range of concentration Twelve samples having molecular weights from about 1000 to 5 × 105 were studied The empirical reduction scheme, plots of log η versus log cM068, suggested by Ferry and co-workers is applicable to samples of Mv ≥ 22,000 over the entire concentration Such satisfying superposition of data may be attributed to the systems being the homologous mixtures in which glass temperatures of polymers are very low On the basis of the treatment of Fox and Allen, the effects of the number and weight-average molecular weight on viscosity were examined, and the friction coefficient ζ per chain atom at constant Mn was calculated over a wide range of Mn The value ζ is almost constant (ζ = 74 × 10−9 dyne-sec/cm) in the region of Mn ≥ Mc, and where otherwise it decreases rapidly with decreasing Mn The length of the chainend segment was tentatively calculated

Viscosity of polydimethylsiloxane–pentamer systems

Flow properties for low-density and high-density polyethylene over a broad range of shear stress are described. Flow equations presented in literatures are tested from the point of view of the extrapolating method for evaluating the zero shear viscosity. It is shown that the method based on the equation of Cross gives relatively good results. The recoverable shear strain calculated from the capillary end correction is practically equal to that determined from the creep experiment at the same shear stress. The effect of shear stress on the elastic property is examined.

Shigeyuki Ueda

Papers

Viscosity–molecular weight relationship for polydimethylsiloxane

Influence of superimposed steady shear flow on the dynamic properties of polyethylene melts

Viscosity of polydimethylsiloxane blends

Viscosity of polydimethylsiloxane–pentamer systems

Flow properties of polyethylene melt