Jens Feder

Random sequential adsorption

Abstract By placing at random disks onto a surface, but adsorbing only those that do not overlap previously adsorbed disks, one will finally reach the jamming limit beyond which no more disks can be adsorbed. We find, using computer simulations, that the coverage at the jamming limit is θ = 0·547 ± 0·002 for disks and θ = 0·562 ± 0·002 for aligned squares. For the jammed state we have evaluated the pair correlation function for the disks and the size distribution for non-overlapping holes. The coverage saturates asymptotically as τ −1 2 , where τ is the number of attempts to place a new disk. From electron microscopic examination of uranyl acetate stained ferritin, we conclude that this iron storage protein adsorbs on carbon in a way consistent with our results for random sequential adsorption.

Geometry of random sequential adsorption

By sequentially adding line segments to a line or disks to a surface at random positions without overlaps, we obtain configurations of the one- and two-dimensional random sequential adsorption (RSA) problem. We have simulated the one- and two-dimensional problem with periodic boundary condition. The one-dimensional simulations are compared with the exact analytical solutions to give an estimate of the accuracy of the simulation. In two dimensions the geometrical properties of the RSA configuration are discussed and in addition known results of the RSA process are reproduced. Various statistical distributions of the Voronoi-Dirichlet (VD) network corresponding to the RSA disk configuration are analyzed. In order to characterize pores in the RSA configuration, we introduce circular holes. There is a direct correspondence between vertices of the VD network and these holes, and also between direct/indirect geometrical neighbors and these holes. The hole size distribution is found to be a parabola. We also find general relations that connect the asymptotic behavior of the surface coverage, the correlation function, and the hole size distribution.

Adsorption of ferritin

Abstract The adsorption of ferritin molecules onto both Lexan polycarbonate and carbon surfaces has been studied with the help of an electron microscope. The amount of ferritin adsorbed is a sensitive function of both the pH and the salinity of the ferritin solution. Complete coverage of a surface could be obtained only under very special conditions. Complete coverage is defined by a model calculation that places disks onto a surface at random and only those disks that do not overlap previous disks are adsorbed.

The fractal nature of geochemical landscapes

Abstract Fractals are shapes that look basically the same on all scales of magnification — they are self-like. Numerous natural phenomena have this property, and fractal geometry has contributed significantly to their analysis. Geochemical maps and other geochemical data from the literature indicate that geochemical dispersion patterns (geochemical landscapes) may have fractal dimensions because they appear similar at all scales of magnitude from microscopic to continental, in agreement with diverse geological processes of varying rapidity and spatial extent ranging from chemical reactions to continental movements. Analysis of variogrammes and other tests carried out on geochemical dispersion patterns (contents of 21 acid soluble elements in 6000 samples of stream sediment) with a 250,000 km2 survey area in northern Fennoscandia indicates a fractal dimension of between 2.1 and 2.9 for 10 elements (Al, Ba, Ca, Fe, Li, Mg, Sc, Sr, V and Zn), while the remaining 11 (Ag, Ce, Co, Cr, Cu, La, Mn, Mo, Ni, P and Zr) give inconclusive results presumably due, mainly, to inadequate precision of the chemical analyses. These fractal dimensions were found to exist between distances of 5 and 150 km, which are the linear limits set by the sample spacing and the size of the survey area respectively. It is proposed that various sets of geochemical, geophysical and other types of data from around the world be analyzed for their fractal properties, collecting evidence as to whether fractal dimensions are a general quality of geochemical dispersion patterns. If it can be shown that geochemical landscapes are usually true fractals analogoues to topographic landscapes, the impact on applied geochemistry may be profound. One practical consequence in mineral exploration could be the possible existence of numerous economically interesting regional to continental geochemical provinces on earth. Such provinces could be detected at relatively low cost through analysis of wide-spread samples. Consecutive denser sampling within the disclosed provinces would reveal subprovinces, which again could be investigated further by successively more intensive sampling. This type of systematic survey employing the principles of fractal geometry for stepwise selection and progressively more thorough examination of subareas of decreasing size, would apply to any survey area of interest and could improve cost-efficiency in mineral exploration.

Enhanced pressure solution creep rates induced by clay particles: Experimental evidence in salt aggregates

Pressure solution is responsible for mechano-chemical compaction of sediments in the upper crust (2–10 km). This process also controls porosity variations in a fault gouge after an earthquake. We present experimental results from chemical compaction of aggregates of halite mixed with clays. It is shown that clay particles (1–5 microns) greatly enhance the deformation by pressure solution in salt aggregates (100–200 micron), the strain rates being 50% to 200% faster in samples containing 10% clays than for clay-free samples. Even the presence of 1% clay increases the strain rate significantly. We propose that clay particles enhance pressure solution creep because these microscopic minerals are trapped within the salt particle contacts where they allow faster diffusion of solutes from the particle contacts to the pore space and inhibit grain boundary formation.

Photon correlation spectroscopy of human IgG.

The translational diffusion coefficient D20,w0, of monomeric human immunoglobulin G (IgG) has been studied by photon-correlation spectroscopy as a function of pH and protein concentration. At pH 7.6, we find D20,w0=3.89×10−7±0.02 cm2/sec, in good agreement with the value determined by classic mehods. This value corresponds to an effective hydrodynamic radius R, of 55.1±0.3 Å. As pH is increased to 8.9; with the same ionic strength, the molecule appears to expand slightly (3.5% increase in hydrodynamic radius). The concentration dependence of the IgG diffusion constant is interpreted in terms of solution electrostatic effects and shows that long-range repulsive interactions are negligible in the buffer used. The diffusion coefficient for dimeric IgG has also been determined to be D20,w=2.81×10−7±0.04 cm2/sec at 1.6 mg/ml, which corresponds to a hydrodynamic radius of 75 Å. For light-scattering studies of protein molecules in the dimension range of 5–10 nm (Mr=105−107) we find monomeric horse spleen ferritin well suited as a reference standard. Ferritin is a spherical molecule with a hydrodynamic radius R of 6.9±0.1 nm and is stable for years in our standard Tris-HCl-NaCl buffer even at room temperature.

TRACER DISPERSION IN A SELF-ORGANIZED CRITICAL SYSTEM

We have studied experimentally transport properties in a slowly driven granular system which recently was shown to display self-organized criticality [Frette et al., Nature (London) 379, 49 (1996)]. Tracer particles were added to a pile and their transit times measured. The distribution of transit times is a constant with a crossover to a decaying power law. The average transport velocity decreases with system size. This is due to an increase in the active zone depth with system size. The relaxation processes generate coherently moving regions of grains mixed with convection. This picture is supported by considering transport in a 1D cellular automaton modeling the experiment.

Slow two-phase flow in artificial fractures: Experiments and simulations

The slow displacement of a wetting fluid by a nonwetting fluid in models of a single fracture was studied experimentally and by computer simulations on identical geometries. The fracture was modeled by the gap between a rough plate and a smooth transparent plate, both oriented horizontally. Two different rough plates were used, a textured glass plate and a polymethyl methacrylate plate with a computer-generated pattern. A nonwetting fluid (air) was injected slowly through an inlet into the model and displaced a wetting fluid (water) initially filling the model. The aperture fields of the artifical fractures were measured using a light absorption technique. The experiments were simulated using modified invasion percolation models, making use of the measured aperture fields. The simulation models captured invasion bursts and fragmentation and redistribution of the invading air. Experiments and simulations were compared step by step, and good qualitative and quantitative agreement was found.

Invasion percolation and secondary migration: experiments and simulations

Abstract Experiments have been carried out to study the displacement of wetting fluids by immiscible non-wetting fluids in quasi-two-dimensional and three-dimensional granular porous media. These experiments included a systematic investigation of the effects of gravity acting on the density difference between the two fluids. The simple invasion percolation model provides a surprisingly realistic simulation of the slow fluid–fluid displacement process in the absence of gravity, and a simple extension of the model can be used to simulate the most important features of gravity stabilized and destabilized fluid–fluid displacement processes. The dimensionless Bond number Bo (the ratio between buoyancy forces and capillary forces on the pore scale) can be used to compare experiments and simulations carried out using different (geometrically similar) porous media, different fluid–fluid interfacial tensions and different fluid densities. The complex patterns generated by gravity stabilized and gravity destabilized fluid–fluid displacement processes can be described in terms of a pattern of blobs of size ξ that have a fractal structure on length scales l in the range ϵ≤l≤ξ, where ϵ is the characteristic porous medium grain size. The blob size ξ is related to the Bond number by the simple scaling relationship ξ∼Bo−ν/(1+ν), which was first derived by Wilkinson, 1984 , Wilkinson, 1996 ) for gravity-stabilized displacement. Here, ν is the percolation theory correlation length exponent (ν=4/3 in two-dimensional systems and ν≈0.88 in three-dimensional systems). The experiments and simulations have been extended to include fluid–fluid displacement in fracture apertures and the effects of flow of the wetting fluid under the influence of a hydraulic potential gradient. These experimental and simulation results have important implications for our understanding of secondary migration. They indicate that the residual hydrocarbon saturation in the enormous volume of porous sedimentary rock (carrier rocks) between the hydrocarbon source and the reservoir can be very low, thus allowing significant quantities of oil and gas to reach the reservoir. Simulations have been carried out to explore the effects of heterogeneities on gravity destabilized fluid–fluid displacement processes and fluid–fluid displacement in fracture apertures. However, the structure of the carrier rocks is highly dynamic on the time scales over which secondary migration takes place (of the order of 108 years, in many cases). A better understanding of the pore structure of the carrier rocks and its dynamics on long time scales is needed to more accurately model secondary migration.

Thermal properties of human IgG

Dynamic light scattering experiments have been performed to study the aggregation kinetics of human immunoglobulin G (IgG). Aggregation and irreversible cluster growth results when IgG solutions (2-15 mg/ml) are heated above 50 degrees C. The measured scattering intensity I and effective hydrodynamic radius (R) can be described consistently by a Smoluchowski aggregation process. The number of clusters ni(t) containing i monomers at time t are computed. The radius of an i cluster is assumed to be Ri = R0 i beta, where beta is the cluster exponent. This kinetic process results in the following characteristic power law behavior: (R)/R0 = (1 + gamma R (T, C, c)t) alpha R and (I)/I0 = (1 + gamma 1 (T, C, c)t) alpha I. Here R0 = 5.51 nm, is the monomer hydrodynamic radius, and I0 the scattered intensity from the monomer solution at temperature T and concn C. A fraction, c approximately 0.48 of the IgG monomers are heat stable up to 63 degrees C and do not participate in the aggregation process. The power-law behavior of mean value of R/R0 and mean value of I/I0 indicates scaling, and indeed a very satisfactory data collapse results from our data. The best non-linear fit of the power-law forms gives alpha R = 0.48 +/- 0.05, alpha I = 1.00 +/- 0.01 and beta = 0.39 +/- 0.04. We also find that the heat aggregation of IgG is an activated process. Fits of the experimental data Gibbs free energy for the activated complex delta G* = 13.8 +/- 0.1 kcal/mole at 56 degrees C. The temp dependence of the growth rates exhibits an Arrhenius behavior with an enthalpy of activation delta H* = 120 +/- 5 kcal/mole.