Effects of the Porous Microstructure on the Drag Coefficient in Flow of a Fluid with Pressure-Dependent Viscosity

Equations governing the flow of a fluid with pressure-dependent viscosity through an isotropic porous structure are derived using the method of intrinsic volume averaging. Viscosity of the fluid is assumed to be a variable function of pressure, and the effects of the porous microstructure are modelled and included in the pressure-dependent drag coefficient. Five friction factors relating to five different microstructures are used in this work

Two-Pressure Model of Particle-Fluid Mixture Flow with Pressure-Dependent Viscosity in a Porous Medium

Equations governing the flow of a fluid-particle mixture with variable viscosity through a porous structure are developed. Method of intrinsic volume averaging is used to average Saffman’s dusty gas equations. A modelling flexibility is offered in this work by introducing a dust-phase partial pressure in the governing equations, interpreted as the pressure necessary to maintain a uniform particle distribution in the flow field. Viscosity of the fluid-particle mixture is assumed to be variable, with variations in viscosity being due to fluid pressure. Particles are assumed spherical and Stokes’ coefficient of resistance is expressed in terms of the pressure-dependent fluid viscosity. Both Darcy resistance and the Forchheimer micro-inertial effects are accounted for in the developed model

Tropical Ehrhart theory and tropical volume

We introduce a novel intrinsic volume concept in tropical geometry. This is achieved by developing the foundations of a tropical analog of lattice point counting in polytopes. We exhibit the basic properties and compare it to existing measures. Our exposition is complemented by a brief study of arising complexity questions.

Construction of a Universal Gel Model with Volume Phase Transition

The physical principle underlying the familiar condensation transition from vapor to liquid is the competition between the energetic tendency to condense owing to attractive forces among molecules of the fluid and the entropic tendency to disperse toward the maximum volume available as limited only by the walls of the container. Van der Waals incorporated this principle into his equation of state and was thus able to explain the discontinuous nature of condensation as the result of instability of intermediate states. The volume phase transition of gels, also discontinuous in its sharpest manifestation, can be understood similarly, as a competition between net free energy attraction of polymer segments and purely entropic dissolution into a maximum allowed volume. Viewed in this way, the gel phase transition would require nothing more to describe it than van der Waals’ original equation of state (with osmotic pressure Π replacing pressure P). But the polymer segments in a gel are networked by cross-links, and a consequent restoring force prevents complete dissolution. Like a solid material, and unlike a van der Waals fluid, a fully swollen gel possesses an intrinsic volume of its own. Although all thermodynamic descriptions of gel behavior contain an elastic component, frequently in the form of Flory-style rubber theory, the resulting isotherms usually have the same general appearance as van der Waals isotherms for fluids, so it is not clear whether the solid-like aspect of gels, that is, their intrinsic volume and shape, adds any fundamental physics to the volume phase transition of gels beyond what van der Waals already knew. To address this question, we have constructed a universal chemical potential for gels that captures the volume transition while containing no quantities specific to any particular gel. In this sense, it is analogous to the van der Waals theory of fluids in its universal form, but although it incorporates the van der Waals universal equation of state, it also contains a network elasticity component, not based on Flory theory but instead on a nonlinear Langevin model, that restricts the radius of a fully swollen spherical gel to a solid-like finite universal value of unity, transitioning to a value less than unity when the gel collapses. A new family of isotherms arises, not present in a preponderately van der Waals analysis, namely, profiles of gel density as a function of location in the gel. There is an abrupt onset of large amplitude density fluctuations in the gel at a critical temperature. Then, at a second critical temperature, the entire swollen gel collapses to a high-density phase.

Density and Solvation Effects of Imidazolium Based Ionic Liquids in Propylene Carbonate

The results of densimetry investigation of the solutions of 1-butyl-3-methylimidazolium tetrafluoroborate (BMIMBF4), hexafluorophosphate (BMIMPF6) and bromide (BMIMBr) in propylene carbonate (PC) at 298.15, 318.15, 338.15 and 358.15 К are presented and discussed in terms of apparent partial molar volumes and solvation contribution. Density measurements were carried out using the vibrational tube densitometer Mettler Toledo DM 50 with accuracy ± 3∙10-5 g/cm3. The limiting partial molar volumes of investigated ionic liquids in PC were obtained from density experiment using Masson equation and divided into ionic contributions. Limiting partial molar volumes of BMIMBF4, BMIMPF6 and BMIMBr in PC slightly increase with the increase of temperature. The limiting partial molar volumes of BMIM+ cation obtained from three ionic liquids with different anions was found to have the same value, 115 cm3/mol at 298.15 K. The intrinsic volume of BMIM+ cation estimated from quantum chemical calculations at the M062X/6‑311++G(d,p) theory level exceeds one obtained from density experiment indicating that solvation of cation has a negative contribution to the volume of ion in propylene carbonate. In order to investigate the microscopic structure of the BMIM+ solvation shell in PC, molecular dynamics simulation of the infinitely dilute solution was carried out in the NVT ensemble at 298.15 K. The results of the simulation reveal that 5-6 PC molecules forming the first solvation shell penetrate into the inner space of the cation, which agrees with the results of a density experiment treatment. From the analysis of the cation-solvent site-site radial distribution functions and the running coordination numbers it was established that the most probable coordination center of PC molecule is carbonyl oxygen.

Negative linear compressibility

While all materials reduce their intrinsic volume under hydrostatic (uniform) compression, a select few actually expand along one or more directions during this process of densification.

TESTING HISTOLOGICAL IMAGES OF MAMMARY TISSUES ON COMPATIBILITY WITH THE BOOLEAN MODEL OF RANDOM SETS

Methods for testing the Boolean model assumption from binary images are briefly reviewed. Two hundred binary images of mammary cancer tissue and 200 images of mastopathic tissue were tested individually on the Boolean model assumption. In a previous paper, it had been found that a Monte Carlo method based on the approximation of the envelopes by a multi-normal distribution with the normalized intrinsic volume densities of parallel sets as a summary statistics had the highest power for this purpose. Hence, this method was used here as its first application to real biomedical data. It was found that mastopathic tissue deviates from the Boolean model significantly more strongly than mammary cancer tissue does.

Analysis of Strength Scaling Effect in Portuguese Limestone: Comparison between Three- and Four-Point Bending Tests

This paper presents a comparative study between 3- and 4-point bending tests applied to five Portuguese limestones. The study has been conducted on sawed limestone specimens, all showing the same surface finishing. The materials were compared for two distinct situations: i) using a 3-point flexure loading configuration in batches of materials with larger cross sectional specimen dimension (50 × 30 mm2); and ii) using a 4-point flexure loading configuration in the same batch of materials but with smaller cross sectional dimensions (30 × 25 mm2). In all situations, the materials have broken due to intrinsic volume defects. Formulae for the effective volumes and effective surfaces for rectangular beam specimens loaded in flexure were reviewed in order to analyse the strength scaling effect. The results show the applicability of the Weibull statistics to explain the differences in the results of the 3-point and 4-point bending tests, even when different cross sectional sizes are employed. Among other important remarks, in all the different limestone specimens used it was possible to confirm that the strength values determined experimentally via 3-point bending are of the same order as those estimated for the same loading configuration but via experimental data of 4-point bending tests using the Weibull strength scaling approach, even if employing a different cross-sectional dimension.

Microfluidic single-cell analysis of intracellular compounds

Biological analyses traditionally probe cell ensembles in the range of 10 3 –10 6 cells, thereby completely averaging over relevant individual cell responses, such as differences in cell proliferation, responses to external stimuli or disease onset. In past years, this fact has been realized and increasing interest has evolved for single-cell analytical methods, which could give exciting new insights into genomics, proteomics, transcriptomics and systems biology. Microfluidic or lab-on-a-chip devices are the method of choice for single-cell analytical tools as they allow the integration of a variety of necessary process steps involved in single-cell analysis, such as selection, navigation, positioning or lysis of single cells as well as separation and detection of cellular analytes. Along with this advantageous integration, microfluidic devices confine single cells in compartments near their intrinsic volume, thus minimizing dilution effects and increasing detection sensitivity. This review overviews the developments and achievements of microfluidic single-cell analysis of intracellular compounds in the past few years, from proof-of-principle devices to applications demonstrating a high biological relevance.