Volume Fraction Phi Research Articles

Magnetohydrodynamic double-diffusive peristaltic flow of radiating fourth-grade nanofluid through a porous medium with viscous dissipation and heat generation/absorption

This article focuses on determining how to double diffusion affects the non-Newtonian fourth-grade nanofluids peristaltic motion within a symmetrical vertical elastic channel supported by a suitable porous medium as well as, concentrating on the impact of a few significant actual peculiarities on the development of the peristaltic liquid, such as rotation, initial pressure, non-linear thermal radiation, heat generation/absorption in the presence of viscous dissipation and joule heating with noting that the fluid inside the channel is subject to an externally induced magnetic field, giving it electromagnetic properties. Moreover, the constraints of the long-wavelength approximation and neglecting the wave number along with the low Reynolds number have been used to transform the nonlinear partial differential equations in two dimensions into a system of nonlinear ordinary differential equations in one dimension, which serve as the basic governing equations for fluid motion. The suitable numerical method for solving the new system of ordinary differential equations is the Runge–Kutta fourth-order numerical method with the shooting technique using the code MATLAB program. Using this code, a 2D and 3D graphical analysis was done to show how each physical parameter affected the distributions of axial velocity, temperature, nanoparticle volume fraction, solutal concentration, pressure gradients, induced magnetic field, magnetic forces, and finally the trapping phenomenon. Under the influence of rotation Omega, heat Grashof number {Gr}_{t}, solutal Grashof number {Gr}_{t}, and initial stress {P}^{*}, the axial velocity distribution u changes from increasing to decreasing, according to some of the study’s findings. On the other hand, increasing values of nonlinear thermal radiation R and temperature ratio {theta }_{w} have a negative impact on the temperature distribution theta but a positive impact on the distributions of nanoparticle volume fraction Phi and solutal concentration gamma. Darcy number Da and mean fluid rate F also had a positive effect on the distribution of pressure gradients, making it an increasing function.

Heat transfer analysis of fractional model of couple stress Casson tri-hybrid nanofluid using dissimilar shape nanoparticles in blood with biomedical applications

During last decades the research of nanofluid is of great interest all over the World, particularly because of its thermal applications in engineering, and biological sciences. Although nanofluid performance is well appreciate and showed good results in the heat transport phenomena, to further improve conventional base fluids thermal performance an increasing number of researchers have started considering structured nanoparticles suspension in one base fluid. As to make an example, when considering the suspension of three different nanoparticles in a single base fluid we have the so called “ternary hybrid nanofluid”. In the present study three different shaped nanoparticles are uniformly dispersed in blood. In particular, the three different shaped nanoparticles are spherical shaped ferric oxide text{Fe}_{3} text{O}_{4}, platelet shaped zinc left( text{Zn} right), and cylindrical shaped gold left( text{Au} right), which are considered in blood base fluid because of related advance pharmaceutical applications. Accordingly, we focused our attention on the sharp evaluation of heat transfer for the unsteady couple stress Casson tri-hybrid nanofluid flow in channel. In particular, we formulated the problem via momentum and energy equations in terms of partial differential equations equipped with realistic physical initial and boundary conditions. Moreover, we transformed classical model into their fractional counterparts by applying the Atangana–Baleanu time-fractional operator. Solutions to velocity and temperature equations have been obtained by using both the Laplace and the Fourier transforms, while the effect of physical parameters on velocity and temperature profiles, have been graphically analyzed exploiting MATHCAD. In particular, latter study clearly shows that for higher values of volume fraction phi_{hnf} of the nanoparticles the fluid velocity declines, while the temperature rises for the higher values of volume fraction phi_{hnf} of the nanoparticles. Using blood-based ternary hybrid nanofluid enhances the rate of heat transfer up-to 8.05%, spherical shaped text{Fe}_{3} text{O}_{4} enhances up-to 4.63%, platelet shaped left( text{Zn} right) nanoparticles enhances up-to 8.984% and cylindrical shaped gold left( text{Au} right) nanoparticles enhances up-to 10.407%.

Experimental demonstration of negative refraction with 3D locally resonant acoustic metafluids

Negative refraction of acoustic waves is demonstrated through underwater experiments conducted at ultrasonic frequencies on a 3D locally resonant acoustic metafluid made of soft porous silicone-rubber micro-beads suspended in a yield-stress fluid. By measuring the refracted angle of the acoustic beam transmitted through this metafluid shaped as a prism, we determine the acoustic index to water according to Snell’s law. These experimental data are then compared with an excellent agreement to calculations performed in the framework of Multiple Scattering Theory showing that the emergence of negative refraction depends on the volume fraction Phi of the resonant micro-beads. For diluted metafluid (Phi =3%), only positive refraction occurs whereas negative refraction is demonstrated over a broad frequency band with concentrated metafluid (Phi =17%).

Consistent coarse-graining strategy for polymer solutions in the thermal crossover from good to θ solvent

We extend our previously developed coarse-graining strategy for linear polymers with a tunable number n of effective atoms (blobs) per chain [G. D'Adamo et al., J. Chem. Phys. 137, 024901 (2012)] to polymer systems in thermal crossover between the good-solvent and the θ regimes. We consider the thermal crossover in the region in which tricritical effects can be neglected, i.e., not too close to the θ point, for a wide range of chain volume fractions Φ = c∕c* (c* is the overlap concentration), up to Φ ≈ 30. Scaling crossover functions for global properties of the solution are obtained by Monte Carlo simulations of the Domb-Joyce model with suitably rescaled on-site repulsion. They provide the input data to develop a minimal coarse-grained model with four blobs per chain (tetramer model). As in the good-solvent case, the coarse-grained model potentials are derived at zero density, thus avoiding the inconsistencies related to the use of state-dependent potentials. We find that the coarse-grained model reproduces the properties of the underlying, full-monomer system up to some reduced density Φ which increases when lowering the temperature towards the θ state. Close to the lower-temperature crossover boundary, the tetramer model is accurate at least up to Φ ~/= 10, while near the good-solvent regime reasonably accurate results are obtained up to Φ ~/= 2. The density region in which the coarse-grained model is predictive can be enlarged by developing coarse-grained models with more blobs per chain. We extend the strategy used in the good-solvent case to the crossover regime. This requires a proper treatment of the length rescalings as before, but also a proper temperature redefinition as the number of blobs is increased. The case n = 10 is investigated in detail. We obtain the potentials for such finer-grained model starting from the tetramer ones. Comparison with full-monomer results shows that the density region in which accurate predictions can be obtained is significantly wider than that corresponding to the tetramer case.

High-frequency viscosity of concentrated porous particles suspensions

We determine the high-frequency limiting shear viscosity, eta(infinity), in colloidal suspensions of rigid, uniformly porous spheres of radius a as a function of volume fraction phi and (inverse) porosity parameter x. Our study covers the complete fluid-state regime. The flow inside the spheres is modeled by the Debye-Bueche-Brinkman equation using the boundary condition that fluid velocity and stress change continuously across the sphere surfaces. The many-sphere hydrodynamic interactions in concentrated systems are fully accounted for by a precise hydrodynamic multipole method encoded in our HYDROMULTIPOLE program extended to porous particles. A truncated virial expansion is used to derive an accurate and easy-to-use generalized Saito; formula for eta(infinity). The simulation data are used to test the performance of two simplifying effective particle models. The first model describes the effective particle as a nonporous sphere characterized by a single effective radius a(eff)(x)<a. In the more refined second model, the porous spheres are modeled as spherical annulus particles with an inner hydrodynamic radius a(eff)(x) defining the nonporous dry core and characterizing hydrodynamic interactions, and an outer excluded volume radius a characterizing the unchanged direct interactions. Only the second model is in a satisfactory agreement with the simulation data.

Geometric parameters of isotropic ensembles of right cylinders from the small-angle-scattering correlation function

The scattered intensity of ensembles of right homogeneous quasi-diluted cylinders with constant oval right section (RS) and volume fraction phi are analyzed using the small-angle-scattering (SAS) correlation function (CF) gamma(r) = gamma(r, phi) in the isotropic two-phase approximation. A relation between the CF of the cylinder RS, beta(0)(r), and the CF of the single cylinder of height H, gamma(0)(r, H), allows the calculation of the explicit cylinder parameters of height, surface area, RS surface area, RS perimeter and volume. This is accomplished by evaluating the first two derivatives of gamma(0)(r) at r = 0. Without the assumption of an oval RS, neither H nor the RS surface area can be uniquely determined.

Growth and Branching of Charged Wormlike Micelles as Revealed by Dilution Laws

The successive transitions of morphology in aqueous solutions of interacting micelles are directly evidenced by the position q* of the correlation peak of the small angle neutron scattering profiles. As the volume fraction Phi increases, q* successively fits to the dilution laws expected for spheres and cylinders, and eventually gets close to the one expected for sheets when the micelles get branched. Data in between the swelling laws are quantitatively analyzed in terms of aggregation number and junction density. Varying the temperature in the dilute regime yields the end-cap energy which varies with molecular structure and scales as Phi(-1/2). In the semidilute regime, the junction density scales as nu(j) approximately Phi(1.8), close but slightly faster than theoretically expected. The boosting effect of intermicellar repulsion on growth and branching is pointed out by the present results which directly show that both condensation processes keep the micelles further apart.

Experiments on the Random Packing of Tetrahedral Dice

Tetrahedra may be the ultimate frustrating, disordered glass forming units. Our experiments on tetrahedral dice indicate the densest (volume fraction phi=0.76+/-.02, compared with phi(sphere)=0.64), most disordered, experimental, random packing of any set of congruent convex objects to date. Analysis of MRI scans yield translational and orientational correlation functions which decay as soon as particles do not touch, much more rapidly than the approximately 6 diameters for sphere correlations to decay. Although there are only 6.3+/-.5 touching neighbors on average, face-face and edge-face contacts provide enough additional constraints, 12+/-1.6 total, to roughly bring the structure to the isostatic limit for frictionless particles. Randomly jammed tetrahedra form a dense rigid highly uncorrelated material.

Effective Properties of a Composite Half-Space: Exploring the Relationship Between Homogenization and Multiple-Scattering Theories

A classical problem in applied mathematics is the determination of the effective wavenumber of a composite material consisting of inclusions distributed throughout an otherwise homogeneous host phase. This problem is discussed here in the context of a composite half-space and a new integral equation method is developed. As a means of obtaining the effective material properties (density and elastic moduli) associated with the material, we consider low-frequency elastic waves incident from a homogeneous half-space onto the inhomogeneous material. We restrict attention to dilute dispersions of inclusions and therefore results are obtained under the assumption of small volume fractions phi. We consider how this theory relates to associated predictions derived from multiple-scattering theories (MSTs) in the low-frequency limit. In particular, we show that predictions of the effective elastic properties are exactly the same as those derived via either the non-isotropic Foldy or the Waterman-Truell MSTs.

Direct investigation of anisotropic suspension structure in pressure-driven flow

Evidence is presented to show the microstructural anisotropy responsible for normal stress in sheared suspensions. Particle velocimetry is combined with three-dimensional particle locations obtained via confocal microscopy at rest. A range of volume fractions phi and local shear rates gamma are investigated in a weakly Brownian pressure-driven suspension. At high gamma, the pairwise distribution shows a strong probability along the axis of compression similar to observations from Stokesian dynamics simulation at phi=0.32. At the channel center where gamma-->0, the concentrated suspension at phi=0.56 behaves as a confined isotropic fluid.

Glass transition of dense fluids of hard and compressible spheres

We use computer simulations to study the glass transition of dense fluids made of polydisperse repulsive spheres. For hard particles, we vary the volume fraction, phi , and use compressible particles to explore finite temperatures, T>0 . In the hard sphere limit, our dynamic data show evidence of an avoided mode-coupling singularity near phi(MCT) is approximately 0.592; they are consistent with a divergence of equilibrium relaxation times occurring at phi(0) is approximately 0.635, but they leave open the existence of a finite temperature singularity for compressible spheres at volume fraction phi>phi(0). Using direct measurements and a scaling procedure, we estimate the equilibrium equation of state for the hard sphere metastable fluid up to phi(0), where pressure remains finite, suggesting that phi(0) corresponds to an ideal glass transition. We use nonequilibrium protocols to explore glassy states above phi(0) and establish the existence of multiple equations of state for the unequilibrated glass of hard spheres, all diverging at different densities in the range phi in [0.642, 0.664]. Glassiness thus results in the existence of a continuum of densities where jamming transitions can occur.

Specific Surface Area and Volume Fraction of the Cherry-Pit Model with Packed Pits

This paper investigates volume fraction phi and specific surface area s for statistically homogeneous systems of partially penetrating spheres, i.e. so-called 'cherry-pit models'. In contrast to the version where the pits form an equilibrium system of hard spheres, here pits or hard spheres are considered which are packed, can be in direct contact, and form a nonequilibrium distribution. For this kind of system, new formulas for phi and s are given, which yield values in good agreement with the ones for large models constructed from hard sphere packings generated both experimentally and numerically. Surprisingly, the existing formulas for phi and s in the equilibrium cherry-pit model lead to values which deviate substantially from the values obtained here.

Dye-Adsorption-Induced Gelation of Suspensions of Spherical and Rodlike Zinc Oxide Nanoparticles in Organic Solvents

The adsorption of amphiphilic Ru(II) complex Z907 onto the surface of ZnO nanospheres and nanorods causes the gelation of organic solvents, such as THF and acetone. The gels are thermally stable at very low concentration (nanoparticle volume fraction phi = 0.009) but mechanically fragile, with the behavior being dependent on the nature of the solvent, nanoparticle concentration, and the Z907/ZnO mole/weight ratio. Rheological experiments confirmed that the solid component built up a network to give a viscoelastic gel-phase material with a weak value of storage modulus G'. However, TEM and SEM experiments did not give evidence that nanoparticle long-range ordering occurred under the experimental conditions investigated. Moreover, time-dependent SAXS measurements pointed to a decrease in the nanoparticle aggregate size upon gelation. All together, the data obtained might be rationalized in terms of the aggregate-to-aggregate transition in solution, with the primitive large aggregates giving rise to smaller ones upon reaction with Z907. The resulting smaller hybrid aggregates could be the active species that act as self-assembling components in the gelation process. Given the interesting electronic and photonic properties of zinc oxide nanoparticles, such hybrid organic-inorganic gels could open new directions in materials science, low-cost electronics, and photovoltaics.

Hydrodynamic Interactions in Colloidal Ferrofluids: A Lattice Boltzmann Study

We use lattice Boltzmann simulations, in conjunction with Ewald summation methods, to investigate the role of hydrodynamic interactions in colloidal suspensions of dipolar particles, such as ferrofluids. Our work addresses volume fractions phi of up to 0.20 and dimensionless dipolar interaction parameters lambda of up to 8. We compare quantitatively with Brownian dynamics simulations, in which many-body hydrodynamic interactions are absent. Monte Carlo data are also used to check the accuracy of static properties measured with the lattice Boltzmann technique. At equilibrium, hydrodynamic interactions slow down both the long-time and the short-time decays of the intermediate scattering function S(q, t), for wavevectors close to the peak of the static structure factor S(q), by a factor of roughly two. The long-time slowing is diminished at high interaction strengths, whereas the short-time slowing (quantified via the hydrodynamic factor H(q)) is less affected by the dipolar interactions, despite their strong effect on the pair distribution function arising from cluster formation. Cluster formation is also studied in transient data following a quench from lambda = 0; hydrodynamic interactions slow the formation rate, again by a factor of roughly two.

How does sensitivity to dynamical heterogeneity in supercooled colloidal liquids depend on tracer size?

Few experimental investigations have examined the dependence of probe length scale on the evolution of dynamical heterogeneity in supercooled liquids. In this study, we use fluorescent tracer probes, which are smaller than that of the constituent unlabeled particles in the matrix suspension, to investigate the tracer size sensitivity to the onset of dynamical heterogeneity in model hard-sphere colloidal suspensions close to the glass transition. The dynamics of poly(methyl methacrylate) (PMMA) tracer particles of radii a(S) = 137 nm embedded into constituent PMMA particles of a(L) = 212 and 637 nm with bulk volume fraction phi varied from 0.50 to 0.57 is examined using fluorescence correlation spectroscopy (FCS). Upon increasing phi for the largest tracer size ratio explored, f (= a(S)/a(L)) = 0.646, the onset of dynamic heterogeneity is observed from the broad distribution of characteristic decay times of the tracers, which is extracted from the measured FCS autocorrelation functions. The strong coupling between tracer size and its sensitivity to dynamical heterogeneity is reflected in the dynamic susceptibility, where dynamic correlation lengths are immeasurable for the smallest size ratio and show a marked increase to five tracer particle diameters for the largest size ratio.

Effects of Trimethylamine N-Oxide (TMAO) and Crowding Agents on the Stability of RNA Hairpins

We study the effect of the osmolyte, Trimethylamine N-Oxide (TMAO), which accumulates in cells in response to osmotic stress, on the stability of RNA hairpins. All atom molecular dynamics (MD) simulations of a nucleotide and the 22-nucleotide RNA hairpin P5GA in an aqueous TMAO solution show that TMAO preferentially interacts with the base through the formation of a single hydrogen bond. To circumvent the difficulties of adequately sampling the conformational space of polynucleotides, we used coarse-grained models (including one that is inspired by the results of all-atom MD simulations of a single nucleotide) to probe the effects of osmoyltes on the stability of P5GA. If, as revealed by our MD simulations, the cosolute specifically interacts with only one base at a time, then we find practically no change in hairpin stability as measured by Delta T m = T m(Phi) - T m, where T m(Phi) and T m are the melting temperatures at volume fraction Phi of the osmolyte and Phi = 0, respectively. This finding is in qualitative agreement with recent experiments. If the interactions between the RNA and osmolytes are repulsive, which is appropriate for mimicking the effects of crowding, Delta T m can vary from 5 to 15 K depending on the size of the osmolyte and the nature of RNA-osmolyte interactions. Cosolutes that interact favorably with multiple bases simultaneously can stabilize the hairpin more than a crowding agent of the same size. The implications of our predictions for experiments are briefly outlined.

Diffusing Wave Spectroscopy Study of the Colloidal Interactions Occurring between Casein Micelles and Emulsion Droplets: Comparison to Hard-Sphere Behavior

Understanding the underlying processes that govern interparticle interactions in colloidal systems is fundamental to predicting changes in their bulk properties. In this paper we discuss the colloidal behavior of casein micelles and protein-stabilized fat globules individually and in a mixture. The colloidal interactions were observed by transmission diffusing wave spectroscopy. The turbidity parameter, l*, and the diffusion coefficients of the samples studied were measured experimentally and compared to the theoretically calculated parameters for a hard-sphere system. The light scattering properties of casein micelles (volume fraction phi = 0.1-0.2) dispersed in milk permeate showed no deviation from the theoretically predicted model. Whey protein isolate (WPI)-stabilized emulsions (phi = 0.025-0.1) prepared either in milk permeate or in 5 mM imidazole buffer at pH 6.8 showed a behavior identical to that of the hard-sphere model. Similarly to the WPI-stabilized fat globules, the sodium caseinate (NaCas)-stabilized emulsions (phi = 0.025-0.1) prepared in milk permeate also showed resemblance to the theory. In contrast, NaCas-stabilized emulsions prepared in 5 mM imidazole buffer exhibited some discrepancy from the theoretically calculated parameters. The deviation from theory is attributed to the enhanced steric stabilization properties of these droplets in a low ionic strength environment. When recombined milks made from concentrated milk and WPI- and NaCas-stabilized droplets prepared in permeate (phi = 0.125-0.2) were studied, the experimental data showed a significant deviation from the theoretical behavior of a hard-sphere model due to mixing of two different species.

A comprehensive, time-resolved SANS investigation of temperature-change-induced sponge-to-lamellar and lamellar-to-sponge phase transformations in comparison with 2H -NMR results

Time-resolved small-angle neutron scattering (TR-SANS) was employed to observe temperature-induced phase transitions from the sponge (L (3) to the lamellar ( L (alpha) phase, and vice versa, in the water-oil (n -decane)-non-ionic surfactant ( C(12)E(5) system using both bulk and film contrast. Samples of different bilayer volume fractions phi and solvent viscosities eta were investigated applying various amplitudes of temperature jump DeltaT . The findings of a previous (2)H -NMR study could be confirmed, where the lamellar phase formation was determined to occur through a nucleation and growth process, while it was concluded that the L (3) -phase develops in a mechanistically different and more rapid manner involving uncorrelated passage formation. Likewise, the kinetic trends of the nucleation and growth transition (decreased transition time with increase of phi and DeltaT were witnessed once again. Additionally, NMR and SANS data that demonstrate a strong dependency of that process on solvent viscosity eta are presented. Contrariwise, it is made evident via both SANS and NMR results that the L (alpha) -to-L (3) transition time is independent (within experimental sensitivity) of the varied parameters (phi , DeltaT , eta . Unusual scattering evolution in one experiment, originating from a highly ordered lamellar phase, intriguingly hints that a major rate determining factor is the disruption of long-range order. Furthermore, the bulk contrast investigations give insight into structure peak shifts/development during the transitions, while the film contrast experiments prove the bilayer thickness to be constant throughout the phase transitions and show that there is no evidence for a change in the short-range order of the bilayer structure. The latter was considered possible, due to the different topology of the L (3) and L (alpha) phases. Lastly, an unexpected yet consistent appearance of anisotropic scattering is detected in the L (3) -to- L (alpha) transitions.

Primary Electroviscous Effect in a Moderately Concentrated Suspension of Charged Spherical Colloidal Particles

On the basis of the standard theory of the primary electroviscous effect in a moderately concentrated suspension of charged spherical particles in an electrolyte solution presented by Ruiz-Reina et al. (Ruiz-Reina, E.; Carrique, F.; Rubio-Hernández, F. J.; Gómez-Merino, A. I.; García-Sánchez, P. J. Phys. Chem. B 2003, 107, 9528), which is applicable for the case where overlapping of the electrical double layers of adjacent particles can be neglected, the general expression for the effective viscosity or the primary electroviscous coefficient p of the suspension is derived. This expression is applicable for a suspension of spherical particles of radius a carrying arbitrary zeta potentials zeta at the particle volume fraction phi < or = 0.3 for the case of nonoverlapping double layers, that is, at kappaalpha > 10 (where kappa is the Debye-Hückel parameter). A simple approximate analytic expression for p applicable for particles with large kappaalpha and arbitrary zeta is presented. The obtained viscosity expression is a good approximation for moderately concentrated suspensions of the particle volume fraction phi < or = 0.3, where the relative error is negligible for kappaalpha > or =100 and even at kappaalpha = 50 the maximum error is approximately 20%. It is shown that a maximum of p, which appears when plotted as a function of the particle zeta potential, is due to the relaxation effect as in the case of the electrophoresis problem.

Phase and Rheological Behavior of High‐Concentration Colloidal Hard‐Sphere and Protein Dispersions

Colloidal hard-sphere (HS) particles of narrow-size distribution exhibit crystalline and glassy states beginning at the particle volume fractions phi = 0.494 and phi(G) = 0.58, respectively. Dynamic rheological data on the dispersions were strongly modified to solid-like behavior as phi approached phi(G). In addition, cooperative motion in structural relaxation has been observed microscopically in the colloidal dispersions near the glassy state. Very high viscosities and glassy states were also found in high-concentration dispersions of sodium caseinate and the globular proteins: bovine serum albumin and beta-lactoglobulin. Viscosity models developed for HS dispersions predicted accurately the trends but not the absolute values of protein dispersions. Dispersions of food colloidal particles may be employed in studies, in which volume fraction is the thermodynamic variable, for understanding the relaxation and transport processes related to 1st-order and colloidal glass transitions.