Capillary hyperdisperson of wetting liquids in fractal porous media

Recent displacement experiments show anomalously rapid spreading of water during imbibition into a prewet porous medium. We explain this phenomenon, calledhyperdispersion, as viscous flow along fractal pore walls in thin films of thicknessh governed by disjoining forces and capillarity. At high capillary pressure, total wetting phase saturation is the sum of thin-film and pendular stucture inventories:S _w =S _tf +S _ps . In many cases, disjoining pressure is inversely proportional to a powerm of film thicknessh, i.e. h _–m , so thatS _tf P _c ^–1/m. The contribution of fractal pendular structures to wetting phase saturation often obeys a power lawS _ps P _c ^(3–D), whereD is the Hausdorff or fractal dimension of pore wall roughness. Hence, if wetting phase inventory is primarily pendular structures, and if thin films control the hydraulic resistance of wetting phase, the capillary dispersion coefficient obeysD _c S _w ^v , where v=[3–m(4–D) ]/m(3–D). The spreading ishyperdispersive, i.e.D _c (S _w ) rises as wetting phase saturation approaches zero, ifm>3/(4–D),hypodispersive, i.e.D _c (S ₂) falls as wetting phase saturation tends to zero, ifm<3>D), anddiffusion-like ifm=3/(4–D). Asymptotic analysis of the capillary diffusion equation is presented.     

The fractal statistics of liquid slug lengths

A rescaled range (R/S) analysis is presented of gas-liquid and gas-liquid-liquid slug length data from two extremely different pipeline systems with i.d. = 32 and 189 mm and length-to-diameter ratios of about 800 and 2000, respectively. The results indicate that slug lengths in horizontal pipe flow obey fractal statistics. The R/S analysis of 30–250 slugs for each experiment shows that the length spectrum satisfies Hurst's law with a Hurst exponent in the range 0.53–0.76, linearly dependent on the total superficial velocity. Conversely, if the Hurst exponent and average slug length with standard deviation are given, slug length spectra may be obtained in good agreement with experimental data.     

Dimension in a Radiative Stellar Atmosphere

Dimensional scales are examined in an extended 3 + 1 Vaidya atmosphere surrounding a Schwarzschild source. At one scale, the Vaidya null fluid vanishes and the spacetime contains only a single spherical 2-surface. Both of these behaviors can be addressed by including higher dimensions in the spacetime metric.     

The Use of Fractal Geostatistics and Artificial Neural Networks for Carbonate Reservoir Characterization

In this study, a carbonate oil reservoir located in the southeast part of Turkey was characterized by the use of kriging and the fractal geometry. The three-dimensional porosity and permeability distributions were generated by both aforementioned methods by using the wireline porosity logs and core plug permeability measurements taken from six wells of the field. Since classical regression (lognormal or polynomial) and geostatistical techniques (cross variograms) fail to estimate permeability from wireline log-porosity data, the use of artificial neural networks (ANNs) is proposed in this study to generate permeability data at uncored intervals of porosity logs. For both of the methods, kriging and fractal techniques, the validation of the estimated/simulated data with known wellbore data resulted with acceptable agreements, especially for porosity. Also the comparison of both methods at unsampled locations show better agreements for porosity than permeability.     

Mapping physical problems on fractals onto boundary value problems within continuum framework

In this Letter, we emphasize that methods of fractal homogenization should take into account a loop structure of the fractal, as well as its connectivity and geodesic metric. The fractal attributes can be quantified by a set of dimension numbers. Accordingly, physical problems on fractals can be mapped onto the boundary values problems in the fractional-dimensional space with metric induced by the fractal topology. The solutions of these problems represent analytical envelopes of non-analytical functions defined on the fractal. Some examples are briefly discussed. The interplay between effects of fractal connectivity, loop structure, and mass distributions on electromagnetic fields in fractal media is highlighted. The effects of fractal connectivity, geodesic metric, and loop structure are outlined.     

The theory of fractal interpolated surface and its applications

I.IntroductionFI.actillilltcrpolationwastlrstpEltforwardbyunA]ncrica1llathematician,M.F.Barllsley.in1986.ItgivesanewInethodologytardataf'ittillg,whichnotonlyopedsupanewresearch11eldfol'tilnctiollappl'oachingtheory,butalsoprovidespowerfultoolsforcolnptltcrgraphicsThistool'sapplicabilityisnowfilllyappreciated.Theuseoflinearfunctions,polynomialfunctionsandSurtllcespringfunctionstoestablishvariousmeterialobjectmodelsinreallifefi-omtraditionalEuclideangeometryisnowcommonpractice.Theavailabilit…     

Enhanced Catalytic Aryl Alkene Oxidation by Constructing Hierarchical Polyoxometalate-Based Metal-Organic Framework

Achieving highly selective oxidation of aryl alkenes to aldehydes is of great significance in chemical industry. Herein, the performance of catalytic aryl alkene oxidation is enhanced via constructing a hierarchical fractal polyoxometalate-based metal–organic framework (POM@MOF) containing hierarchical pores and layered surface structure, which improve the mass transfer efficiency of substrates and increase the accessibility to active POMs clusters. Accordingly, the activity of fractal POM@MOF is increased by 4.8 times compared with microporous counterpart in 4-tert-butylstyrene oxidation to aldehyde product. This work paves a way for designing efficient catalysts for selective oxidation of aryl alkenes via increasing the accessibility of active sites and broadening the diffusion channels by hierarchical construction.