Shortcomings of discontinuous-pressure finite element methods on a class of transient problems

Past studies that have compared LBB stable discontinuous- and continuous-pressure finite element formulations on a variety of problems have concluded that both methods yield Solutions of comparable accuracy, and that the choice of interpolation is dictated by which of the two is more efficient. In this work, we show that using discontinuous-pressure interpolations can yield inaccurate solutions at large times on a class of transient problems, while the continuous-pressure formulation yields solutions that are in good agreement with the analytical Solution.

Correlation between conductivity or diffusivity and activation energy in amorphous solids

There exist many investigations of ionic transport in a variety of glasses. These studies exhibit strong correlation between ionic conductivity and activation energy: Typically, it is found that higher conductivity is associated with lower activation energies and vice versa. Although there are explanations for this at a phenomenological level, there is no consistent physical picture to explain the correlation between conductivity and activation energy. We have carried out molecular dynamics simulation as a function of the size of the impurity atom or diffusant (both neutral and charged) in a host amorphous matrix. We find that there is a maximum in self-diffusivity as a function of the size of the impurity atom suggesting that there is an appropriate size for which the diffusivity is maximum. The activation energy is found to be the lowest for this size of the impurity. A similar maximum has been previously found in other condensed phases, such as confined fluids and dense liquids, and has its origin in the levitation effect. The implications of this result for understanding ionic conductivity in glasses are discussed. Our results suggest that there is a relation between microscopic structure of the amorphous solid, diffusivity or conductivity, and activation energy. The nature of this relationship is discussed in terms of the levitation parameter showing that diffusivity is maximum when the size of the neck or doorway radius is comparable with the size of the diffusant. Our computational results here are in excellent agreement with independent experimental results of Nascimento et al. [Braz. J. Phys. 35, 626 (2005)] that structural features of the glass are important in determining the ionic conductivity.

Dispersibility of Barium Titanate Suspension in the Presence of Polyelectrolytes: A Review

Dispersibility of colloidal barium titanate suspensions is reviewed with an emphasis on the use of various polyelectrolytes as dispersants. The fundamentals of colloidal stability are discussed followed by the colloidal properties of barium titanate powder. Dispersion behavior of BaTiO3 in both nonaqueous and aqueous media has been reviewed. Several studies on the stabilization of micron and nano-sized barium titanate using various polymeric dispersants and a rhamnolipid biosurfactant are presented and discussed. The article attempts to provide a comprehensive review of the current state-of-the-art in the area of colloidal processing of barium titanate.

Effect of the headgroup variation on the gene transfer properties of cholesterol based cationic lipids possessing ether linkage

Eight cholesterol based cationic lipids differing in the headgroup have been synthesized based on the ether linkage between the cationic headgroup and the cholesterol backbone. All the lipids formed stable suspensions in water. Transfection efficacies were examined in the absence and presence of serum using their optimized liposomal (lipid:DOPE) formulations. Our results showed that the transfection activities depend on the nature of the headgroup. Lipid bearing 4-N,N′-dimethylaminopyridine (DMAP) as headgroup showed the maximum transfection efficacy in the presence of serum. Importantly, the optimized formulation for this cationic lipid does not require DOPE, which is being used by most commercially available formulations. Cytotoxicity studies showed that the introduction of the positive charge decreases the cell viability of the cationic lipid formulations. Gel electrophoresis and Ethidium bromide exclusion assay revealed the different DNA binding abilities of formulations depending upon the headgroup of the cholesteryl lipid.

Polymer melt dynamics: Microscopic roots of fractional viscoelasticity

The rheological properties of polymer melts and other complex macromolecular fluids are often successfully modeled by phenomenological constitutive equations containing fractional differential operators. We suggest a molecular basis for such fractional equations in terms of the generalized Langevin equation (GLE) that underlies the renormalized Rouse model developed by Schweizer [J. Chem. Phys. 91, 5802 (1989)]. The GLE describes the dynamics of the segments of a tagged chain under the action of random forces originating in the fast fluctuations of the surrounding polymer matrix. By representing these random forces as fractional Gaussian noise, and transforming the GLE into an equivalent diffusion equation for the density of the tagged chain segments, we obtain an analytical expression for the dynamic shear relaxation modulus G(t), which we then show decays as a power law in time. This power-law relaxation is the root of fractional viscoelastic behavior.

Gene Transfection Efficacies of Novel Cationic Gemini Lipids Possessing Aromatic Backbone and Oxyethylene Spacers

Six novel gemini cationic lipids based on aromatic backbone, bearing n-C14H29 or n-C16H33 hydrocarbon chains, differing in the length of oxyethylene type spacers −CH2-(CH2-O-CH2)m-CH2− between each ammonium headgroups have been synthesized, where m varies from 1 to 3. Each of these lipids formed stable suspensions in aqueous media. Cationic liposomes were prepared from each of these lipids individually and as mixtures of each cationic lipid and DOPE. These were used as nonviral gene delivery agents. Transfection studies showed that among lipids bearing n-C14H29 chains, the transfection efficacies decreased with the increase in the length of the spacer, whereas in case of lipids bearing n-C16H33 chains, the transfection efficacies increased with the increase in the length of the spacer. Lipid bearing n-C16H33 hydrocarbon chains with a [−(CH2-CH2-O-CH2-CH2-O-CH2-CH2-O-CH2-CH2)−] spacer was found to be a potent gene transfer agent and its transfection was highly serum compatible even in the presence of 50% serum conditions.

Modelling of solute transport in a mild heterogeneous porous medium using stochastic finite element method: Effects of random source conditions

Randomness in the source condition other than the heterogeneity in the system parameters can also be a major source of uncertainty in the concentration field. Hence, a more general form of the problem formulation is necessary to consider randomness in both source condition and system parameters. When the source varies with time, the unsteady problem, can be solved using the unit response function. In the case of random system parameters, the response function becomes a random function and depends on the randomness in the system parameters. In the present study, the source is modelled as a random discrete process with either a fixed interval or a random interval (the Poisson process). In this study, an attempt is made to assess the relative effects of various types of source uncertainties on the probabilistic behaviour of the concentration in a porous medium while the system parameters are also modelled as random fields. Analytical expressions of mean and covariance of concentration due to random discrete source are derived in terms of mean and covariance of unit response function. The probabilistic behaviour of the random response function is obtained by using a perturbation-based stochastic finite element method (SFEM), which performs well for mild heterogeneity. The proposed method is applied for analysing both the 1-D as well as the 3-D solute transport problems. The results obtained with SFEM are compared with the Monte Carlo simulation for 1-D problems.

Evolution of isolated streamwise vortices in the late stages of boundary layer transition

Experiments were conducted with two, smooth hills, lying well within the boundary layer over a flat plate mounted in a wind tunnel. One hill was shallow, with peak height 1.5 mm and width 50 mm; the other, steep, 3 mm high and 30 mm wide. Since the hills occupied one-half of the tunnel span, streamwise vorticity formed near the hills' edge. At a freestream speed of 3.5 m/s, streaks formed with inflectional wall-normal and spanwise velocity profiles but without effecting transition. Transition, observed at 7.5 m/s, took different routes with the two hills. With the steep hill, streamwise velocity signals exhibited the passage of a wave packet which intensified before breakdown to turbulence. With the shallow hill there was a broad range of frequencies present immediately downstream of the hill. These fluctuations grew continuously and transition occurred within a shorter distance. Since the size of the streamwise vorticity generated at the hill edge is of the order of the hill height, the shallow hill generates vorticity closer to the wall and supports an earlier transition, whereas the steep hill creates a thicker vortex and associated streaks which exhibit oscillations due to their own instability as an additional precursor stage before transition.

Rheology of dense sheared granular flows

Rapid granular flows are defined as flows in which the time scales for the particle interactions are small compared to the inverse of the strain rate, so that the particle interactions can be treated as instantaneous collisions. We first show, using Discrete Element simulations, that even very dense flows of sand or glass beads with volume fraction between 0.5 and 0.6 are rapid granular flows. Since collisions are instantaneous, a kinetic theory approach for the constitutive relations is most appropriate, and we present kinetic theory results for different microscopic models for particle interaction. The significant difference between granular flows and normal fluids is that energy is not conserved in a granular flow. The differences in the hydrodynamic modes caused by the non-conserved nature of energy are discussed. Going beyond the Boltzmann equation, the effect of correlations is studied using the ring kinetic approximation, and it is shown that the divergences in the viscometric coefficients, which are present for elastic fluids, are not present for granular flows because energy is not conserved. The hydrodynamic model is applied to the flow down an inclined plane. Since energy is not a conserved variable, the hydrodynamic fields in the bulk of a granular flow are obtained from the mass and momentum conservation equations alone. Energy becomes a relevant variable only in thin 'boundary layers' at the boundaries of the flow where there is a balance between the rates of conduction and dissipation. We show that such a hydrodynamic model can predict the salient features of a chute flow, including the flow initiation when the angle of inclination is increased above the 'friction angle', the striking lack of observable variation of the volume fraction with height, the observation of a steady flow only for certain restitution coefficients, and the density variations in the boundary layers.

Thermotropic and hydration studies of membranes formed from gemini pseudoglyceryl lipids possessing polymethylene spacers

Membrane formation from gemini pseudoglyceryl lipids bearing n-C14H29 and n-C16H33 chains has been reported. These lipid aggregates have been characterized using transmission electron microscopy (TEM), dynamic light scattering (DLS), high sensitivity differential scanning calorimetry (DSC), and Paldan fluorescence studies. The length of the spacer between the cationic ammonium headgroups has been varied from -(CH2)(3)- (propandiyl) to -(CH2)(12)- (dodecandiyl) in these lipids. All gemini lipids were found to generate stable suspensions in aqueous media. Electron microscopic studies revealed the smaller size of the gemini lipid aggregates as compared to their monomeric lipid counterparts. DLS measurements showed that the gemini lipid suspensions with a -(CH2)(8)- spacer length were bigger in size than that of other analogues. DSC studies suggest the unusual behavior of the gemini lipids bearing -(CH2)3- propanediyl spacer based lipids. These observations were consistent irrespective of the hydrocarbon chain lengths of the lipids. Paldan fluorescence based hydration studies showed that the hexadecyl chain based gemini lipid aggregates bearing a -(CH2)(12)- spacer were the most hydrated in their gel states among all the gemini lipid series investigated herein.

New empirical expressions to correlate solubilities of solids in supercritical carbon dioxide

Supercritical processes are gaining importance in the last few years in the food, environmental and pharmaceutical product processing. The design of any supercritical process needs accurate experimental data on solubilities of solids in the supercritical fluids (SCFs). The empirical equations are quite successful in correlating the solubilities of solid compounds in SCF both in the presence and absence of cosolvents. In this work, existing solvate complex models are discussed and a new set of empirical equations is proposed. These equations correlate the solubilities of solids in supercritical carbon dioxide (both in the presence and absence of cosolvents) as a function of temperature, density of supercritical carbon dioxide and the mole fraction of cosolvent. The accuracy of the proposed models was evaluated by correlating 15 binary and 18 ternary systems. The proposed models provided the best overall correlations. (C) 2009 Elsevier BA/. All rights reserved.

Heat transfer in plane Couette flow of a rarefied gas using Bhatnagar-Gross-Krook model

Using the linearized BGK model and the method of moments of half-range distribution functions the temperature jumps at two plates are determined, and it is found that the results are in fair agreement with those of Gross and Ziering, and Ziering.

Electron temperature distribution across a shock wave in a partially ionized gas

The electron temperature structure in a weakly ionized plasma is studied allowing the degree of ionization to vary across the shock wave. The values of the electron temperature and the downstream equilibrium temperature obtained with variable ionization are less than those for frozen ionization. The electron temperature rises sharply behind the shock for variable ionization while a gradual increase is predicted by frozen ionization.

Moment methods and "restricted variation" in kinetic theory

It is shown that there is a strict one-to-one correspondence between results obtained by the use of "restricted" variational principles and those obtained by a moment method of the Mott-Smith type for shock structure.

Steady flow of a maxwell fluid in a porous cylindrical annulus with circular cross-section

When a fluid with memory is injected into any flow region some assumptions regarding the initial state of stress have to be made in order to determine the state of stress at any subsequent instant. For a Maxwell fluid, it is assumed that the fluid near the surface of injection is suddenly stressed and responds by starting flow in accordance with the mechanical model chosen. The flow of a Maxwell fluid with a single relaxation time has been determined under the above assumption in the following two cases: (i) annulus between two porous concentric circular cylinders, and (ii) space between two porous and infinitely extending parallel plates. The nature of flow in the present case is similar to that of the Reiner-Rivlin fluids obtained by Narasimhan2).