Superfast non-linear diffusion: capillary transport in particulate porous media

The migration of liquids in porous media, such as sand, has been commonly considered at high saturation levels with liquid pathways at pore dimensions. In this letter we reveal a low saturation regime observed in our experiments with droplets of extremely low volatility liquids deposited on sand. In this regime the liquid is mostly found within the grain surface roughness and in the capillary bridges formed at the contacts between the grains. The bridges act as variable-volume reservoirs and the flow is driven by the capillary pressure arising at the wetting front according to the roughness length scales. We propose that this migration (spreading) is the result of interplay between the bridge volume adjustment to this pressure distribution and viscous losses of a creeping flow within the roughness. The net macroscopic result is a special case of non-linear diffusion described by a superfast diffusion equation (SFDE) for saturation with distinctive mathematical character. We obtain solutions to a moving boundary problem defined by SFDE that robustly convey a time power law of spreading as seen in our experiments.

(Non-)ergodicity of a degenerate diffusion modeling the fiber lay down process

We analyze the large time behavior of a stochastic model for the lay down of fibers on a moving conveyor belt in the production process of nonwovens. It is shown that under weak conditions this degenerate diffusion process has a unique invariant distribution and is even geometrically ergodic. This generalizes results from previous works [M. Grothaus and A. Klar, SIAM J. Math. Anal., 40 (2008), pp. 968–983; J. Dolbeault et al., arXiv:1201.2156] concerning the case of a stationary conveyor belt, in which the situation of a moving conveyor belt has been left open.

Determination of the gas diffusion coefficient of a peat grassland soil

Peatland habitats are important carbon stocks that also have the potential to be significant sources of greenhouse gases, particularly when subject to changes such as artificial drainage and application of fertilizer. Models aiming to estimate greenhouse gas release from peatlands require an accurate estimate of the diffusion coefficient of gas transport through soil (Ds). The availability of specific measurements for peatland soils is currently limited. This study measured Ds for a peat soil with an overlying clay horizon and compared values with those from widely available models. The Ds value of a sandy loam reference soil was measured for comparison. Using the Currie (1960) method, Ds was measured between an air-filled porosity (ϵ) range of 0 and 0.5 cm3 cm−3. Values of Ds for the peat cores ranged between 3.2 × 10−4 and 4.4 × 10−3 m2 hour−1, for loamy clay cores between 0 and 4.7 × 10−3 m2 hour−1 and for the sandy reference soil they were between 5.4 × 10−4 and 3.4 × 10−3 m2 hour−1. The agreement of measured and modelled values of relative diffusivity (Ds/D0, with D0 the diffusion coefficient through free air) varied with soil type; however, the Campbell (1985) model provided the best replication of measured values for all soils. This research therefore suggests that the use of the Campbell model in the absence of accurately measured Ds and porosity values for a study soil would be appropriate. Future research into methods to reduce shrinkage of peat during measurement and therefore allow measurement of Ds for a greater range of ϵ would be beneficial.

Analysis of diffusion tensor magnetic resonance imaging data using principal component analysis

An analysis method for diffusion tensor (DT) magnetic resonance imaging data is described, which, contrary to the standard method (multivariate fitting), does not require a specific functional model for diffusion-weighted (DW) signals. The method uses principal component analysis (PCA) under the assumption of a single fibre per pixel. PCA and the standard method were compared using simulations and human brain data. The two methods were equivalent in determining fibre orientation. PCA-derived fractional anisotropy and DT relative anisotropy had similar signal-to-noise ratio (SNR) and dependence on fibre shape. PCA-derived mean diffusivity had similar SNR to the respective DT scalar, and it depended on fibre anisotropy. Appropriate scaling of the PCA measures resulted in very good agreement between PCA and DT maps. In conclusion, the assumption of a specific functional model for DW signals is not necessary for characterization of anisotropic diffusion in a single fibre.

Influence of mass diffusion in sea ice dynamical models

The mixing of floes of different thickness caused by repeated deformation of the ice cover is modeled as diffusion, and the mass balance equation for sea ice accounting for mass diffusion is developed. The effect of deformational diffusion on the ice thickness balance is shown to reach 1% of the divergence effect, which describes ridging and lead formation. This means that with the same accuracy the mass balance equation can be written in terms of mean velocity rather than mean mass-weighted velocity, which one should correctly use for a multicomponent fluid such as sea ice with components identified by floe thickness. Mixing (diffusion) of sea ice also occurs because of turbulent variations in wind and ocean drags that are unresolved in models. Estimates of the importance of turbulent mass diffusion on the dynamic redistribution of ice thickness are determined using empirical data for the turbulent diffusivity. For long-time-scale prediction (≫5 days), where unresolved atmospheric motion may have a length scale on the order of the Arctic basin and the time scale is larger than the synoptic time scale of atmospheric events, turbulent mass diffusion can exceed 10% of the divergence effect. However, for short-time-scale prediction, for example, 5 days, the unresolved scales are on the order of 100 km, and turbulent diffusion is about 0.1% of the divergence effect. Because inertial effects are small in the dynamics of the sea ice pack, diffusive momentum transfer can be disregarded.

On the role of specific interactions in the diffusion of nanoparticles in aqueous polymer solutions

Understanding nanoparticle diffusion within non-Newtonian biological and synthetic fluids is essential in designing novel formulations (e.g., nanomedicines for drug delivery, shampoos, lotions, coatings, paints, etc.), but is presently poorly defined. This study reports the diffusion of thiolated and PEGylated silica nanoparticles, characterized by small-angle neutron scattering, in solutions of various water-soluble polymers such as poly(acrylic acid) (PAA), poly(Nvinylpyrrolidone) (PVP), poly(ethylene oxide) (PEO), and hydroxyethylcellulose (HEC) probed using NanoSight nanoparticle tracking analysis. Results show that the diffusivity of nanoparticles is affected by their dimensions, medium viscosity, and, in particular, the specific interactions between nanoparticles and the macromolecules in solution; strong attractive interactions such as hydrogen bonding hamper diffusion. The water-soluble polymers retarded the diffusion of thiolated particles in the order PEO > PVP > PAA > HEC whereas for PEGylated silica particles retardation followed the order PAA > PVP = HEC > PEO. In the absence of specific interactions with the medium, PEGylated nanoparticles exhibit enhanced mobility compared to their thiolated counterparts despite some increase in their dimensions.

The role of location in knowledge creation and diffusion: evidence of centripetal and centrifugal forces in the City of London financial services agglomeration

In this paper we report on a major empirical study of centripetal and centrifugal forces in the City of London financial services agglomeration. The study sheds light on (1) the manner and magnitude of firm interaction in the agglomeration; (2) the characteristics of the agglomeration that aid the competitiveness of incumbent firms; and (3) the problems associated with agglomeration. In addressing these issues, we use the data to (1) test emerging theory that explains the high productivity and innovation of agglomerations in terms of their ability to generate and diffuse knowledge; and (2) evaluate the ‘end of geography’ thesis.

Strong armies, slow adaptation: civil-military relations and diffusion of military power

Why are some states more willing to adopt military innovations than others? Why, for example, were the great powers of Europe able to successfully reform their military practices to better adapt to and participate in the so-called military revolution of the sixteenth and seventeenth centuries while their most important extra-European competitor, the Ottoman Empire, failed to do so? This puzzle is best explained by two factors: civil-military relations and historical timing. In the Ottoman Empire, the emergence of an institutionally strong and internally cohesive army during the early stages of state formation—in the late fourteenth century—equipped the military with substantial bargaining powers. In contrast, the great powers of Europe drew heavily on private providers of military power during the military revolution and developed similar armies only by the second half of the seventeenth century, limiting the bargaining leverage of European militaries over their rulers. In essence, the Ottoman standing army was able to block reform efforts that it believed challenged its parochial interests. Absent a similar institutional challenge, European rulers initiated military reforms and motivated officers and military entrepreneurs to participate in the ongoing military revolution.

Simulation of a diffusion driven mobile robot

In this paper, we investigate the possibility to control a mobile robot via a sensory-motory coupling utilizing diffusion system. For this purpose, we implemented a simulation of the diffusion process of chemicals and the kinematics of the mobile robot. In comparison to the original Braitenberg vehicle in which sensorymotor coupling is tightly realised by hardwiring, our system employs the soft coupling. The mobile robot has two sets of independent sensory-motor unit, two sensors are implemented in front and two motors on each side of the robot. The framework used for the sensory-motor coupling was such that 1) Place two electrodes in the medium 2) Drop a certain amount of Chemical U and V related to the distance to the walls and the intensity of the light 3) Place other two electrodes in the medium 4) Measure the concentration of Chemical U and V to actuate the motors on both sides of the robot. The environment was constructed with four surrounding walls and a light source located at the center. Depending on the design parameters and initial conditions, the robot was able to successfully avoid the wall and light. More interestingly, the diffusion process in the sensory-motor coupling provided the robot with a simple form of memory which would not have been possible with a control framework based on a hard-wired electric circuit.

A traceable physical calibration of the vertical advection-diffusion equation for modelling ocean heat uptake

The classic vertical advection-diffusion (VAD) balance is a central concept in studying the ocean heat budget, in particular in simple climate models (SCMs). Here we present a new framework to calibrate the parameters of the VAD equation to the vertical ocean heat balance of two fully-coupled climate models that is traceable to the models’ circulation as well as to vertical mixing and diffusion processes. Based on temperature diagnostics, we derive an effective vertical velocity w∗ and turbulent diffusivity k∗ for each individual physical process. In steady-state, we find that the residual vertical velocity and diffusivity change sign in mid-depth, highlighting the different regional contributions of isopycnal and diapycnal diffusion in balancing the models’ residual advection and vertical mixing. We quantify the impacts of the time-evolution of the effective quantities under a transient 1%CO2 simulation and make the link to the parameters of currently employed SCMs.

POZylation: a new approach to enhance nanoparticle diffusion through mucosal barriers

The increasing use of nanoparticles in the pharmaceutical industry is generating concomitant interest in developing nanomaterials that can rapidly penetrate into, and permeate through, biological membranes to facilitate drug delivery and improve the bioavailability of active pharmaceutical ingredients. Here, we demonstrate that the permeation of thiolated silica nanoparticles through porcine gastric mucosa can be significantly enhanced by their functionalization with either 5 kDa poly(2-ethyl-2-oxazoline) or poly(ethylene glycol). Nanoparticle diffusion was assessed using two independent techniques; Nanoparticle Tracking Analysis, and fluorescence microscopy. Our results show that poly(2-ethyl-2-oxazoline) and poly(ethylene glycol) have comparable abilities to enhance diffusion of silica nanoparticles in mucin dispersions and through the gastric mucosa. These findings provide a new strategy in the design of nanomedicines, by surface modification or nanoparticle core construction, for enhanced transmucosal drug delivery.