Squeezing a viscoelastic fluid from a cone

The paper reports an exact kinematics for the squeezing flow from a cone of a general viscoelastic fluid. To obtain numerical values for the stresses, a network model that allows stress overshoot and shear-thinning in the start-up of a shear flow is adopted. Both these features are important in this flow. For the special case of an Oldroyd-B fluid it is shown that there is a limiting Weissenberg number above which at least one component of the stresses increases unboundedly with time.     

Preparative Synthesis of Vinyl Diamondoids

We describe a convenient four-step preparation of 1- vinyl adamantane, 1- vinyl diamantane, and 4,9-divinyl diamantane from the respective diamondoid acetic acids in 50–80% isolated yields involving esterification, reduction, and hydrobromination/dehydrobromination.

Supplemental materials are available for this article. Go to the publisher's online edition of Synthetic Communications® to view the free supplemental file.     

Boundary layer preconditioners for finite-element discretizations of singularly perturbed reaction-diffusion problems

We consider the iterative solution of linear systems of equations arising from the discretization of singularly perturbed reaction-diffusion differential equations by finite-element methods on boundary-fitted meshes. The equations feature a perturbation parameter, which may be arbitrarily small, and correspondingly, their solutions feature layers: regions where the solution changes rapidly. Therefore, numerical solutions are computed on specially designed, highly anisotropic layer-adapted meshes. Usually, the resulting linear systems are ill-conditioned, and so, careful design of suitable preconditioners is necessary in order to solve them in a way that is robust, with respect to the perturbation parameter, and efficient. We propose a boundary layer preconditioner, in the style of that introduced by MacLachlan and Madden for a finite-difference method (MacLachlan and Madden, SIAM J. Sci. Comput. 35(5), A2225–A2254 2013). We prove the optimality of this preconditioner and establish a suitable stopping criterion for one-dimensional problems. Numerical results are presented which demonstrate that the ideas extend to problems in two dimensions.     

A numerical method for stationary shock problems with monotonic solutions

Numerical methods are considered for singularly perturbed quasilinear problems having interior-shock solutions. It is shown that the direct discretization on a layer-adapted mesh is ineffective for these problems. A special method is proposed for the case when the solution is monotonic: the problem is transformed by interchanging the dependent and independent variables, and it is then discretized on a uniform mesh. The method is analyzed both theoretically and numerically. It is shown that it can be effective, but that it is not entirely without problems. An approach for improving the method is suggested.     

A hybrid stochastic optimization framework for composite nonconvex optimization

Mathematical Programming - We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea...     

A uniform bound of reducibility index of good parameter ideals for certain class of modules

Let $(R,\mathfrak{m})$ be a Noetherian local ring and M a finitely generated R-module. The invariants $\mathrm{p}(M)$ and $\mathrm{sp}(M)$ of M were introduced in [3] and [17] in order to measure the non-Cohen–Macaulayness and the non-sequential-Cohen–Macaulayness of M, respectively. Let $M=D_0?D_1?\dots ?D_k$ be the filtration of M such that $D_i$ is the largest submodule of M of dimension less than $\dim ?D_{i?1}$ for all $i\le k$ and $\mathrm{p}(D_k)\le 1$. In this paper we prove that if $\mathrm{sp}(M)\le 1$, then there exists a constant c such that ${\mathrm{ir}}_M(\mathfrak{q}M)\le c$ for all good parameter ideals $\mathfrak{q}$ of M with respect to this filtration. Here ${\mathrm{ir}}_M(\mathfrak{q}M)$ is the reducibility index of $\mathfrak{q}$ on M. This is an extension of the main results of [19], [20], [24].     

Effective moduli of particulate solids: Lubrication approximation method

To efficiently calculate the effective properties of a composite, which consists of rigid spherical inclusions not necessarily of the same sizes in a homogeneous isotropic elastic matrix, a method based on the lubrication forces between neighbouring particles has been developed. The method is used to evaluate the effective Lamé moduli and the Poisson's ratio of the composite, for the particles in random configurations and in cubic lattices. A good agreement with experimental results given by Smith (1975) for particles in random configurations is observed, and also the numerical results on the effective moduli agree well with the results given by Nunan & Keller (1984) for particles in cubic lattices.     

Viscosity of concentrated suspensions of spheres

Difficulties associated with the viscosity measurement of concentrated suspensions of particulate solids in a liquid solvent can effectively be overcome with the falling needle technique reported here. The comparison of the settling (terminal) velocity of a given needle in a Newtonian solvent, with its terminal velocity in a suspension, yields the suspension viscosity ratio directly. The van den Brule and Jongschaap constitutive model describes our high concentration data best. Falling sphere data (diameter of sphere/diameter of suspended particle 10) agree well with the falling needle data over the whole range (up to 40%) of solids concentrations used in our tests.In the opaque suspensions used, the passage of sedimenting needles and spheres was initially observed radiographically. Later tests used a more convenient technique using an inductance coil particle detector driven by a Colpitts oscillator.     

Oscillatory and simple shear flows of a flour-water dough: a constitutive model

We reported some dynamic and viscometric data on an Australia strong flour-water dough. In oscillatory shear flow experiments, we found the linear viscoelastic strain limit is extremely low, of O(10^–3), consistent with other published data on doughs. The relaxation spectrum derived from the dynamic data is broad, indicating the blend nature of dough. In the start-up of a simple shear flow, we found the shear stress increases nonlinearly with time to a peak value and then decreases rapidly, with no steady-state response. The concept of steady-state viscosity is not very meaningful here, unless the strain at which the measurements are taken is also specified. The stress peaks are strain-rate dependent; but they occur at a strain of O(10), for the strong flour/water dough used, over four decades of strain rates. The experimental data were used to construct a phenomenological model for dough, consisting of an hyperelastic term (representing the elastic gluten network of permanent cross-linked long chain polymers), and a viscoelastic contribution (representing the suspension of starch globules and other long-chain components in dough that are not parts of the permanent cross-linked gluten network). The model predictions compared favourably with experimental data in oscillatory and shear flows.     

Criteria of negative wake generation behind a cylinder

It was demonstrated by simulation in our previous study that both the normal stress and its gradient are responsible for the negative wake generation (overshoot in the axial velocity) and streamline shifting. Extensional properties of the fluids dominate the generation of the negative wake, while other factors strengthen or weaken the formation of velocity overshoot. In this study, the criteria for the negative wake generation are discussed in detail for various fluid models, including the PTT, the FENE-CR, the FENE-P, and the Giesekus models. With the FENE-CR fluid, it is easier to generate negative wake than with the FENE-P fluid. This confirms that the constant shear viscosity FENE-CR fluid enhances the velocity overshoot, and that the shear-thinning viscosity FENE-P fluid delays the negative wake generation. The Giesekus fluid has a similar behaviour to the PTT fluid with regarding to the critical conditions of negative wake generation when appropriate fluid parameters are selected. The mechanism of wall proximity in enhancing the negative wake generation is also demonstrated with the analysis for the first time.