Dispersion resulting from flow through spatically periodic porous media II. Surface and intraparticle transport

1982 ◽  
Vol 307 (1498) ◽  
pp. 149-200 ◽  
Keyword(s):  
Periodic Structures ◽  
Brownian Particle ◽  
Tracer Particle ◽  
Continuous Phase ◽  
Tracer Transport ◽  
Tracer Particles ◽  
Spatially Periodic ◽  
Discontinuous Phase ◽  
External Forces ◽  
Transfer Problems

A rigorous theory of Brownian particle flow and dispersion phenomena in spatially periodic structures is presented within the context of generalized Taylor dispersion theory. The analysis expands upon a prior work, which was limited to transport within the continuous phase, to include convective and diffusive transport of the tracer particle within the interior of the discontinuous phase, as well as surface adsorption and transport along the phase boundary separating the discontinuous and continuous phases. Incorporated within the generalization are considerations of tracer particles of non-zero size, and situations wherein external forces act upon the tracer, the novel effect of each being to cause the tracer to move with a different velocity from that of the fluid in which it is suspended. Applications to various chromatographic separation phenomena are cited. Extensions of the analysis to heat-transfer problems and to situations involving homogeneous, first-order chemical reactions are also made. Both Eulerian and Lagrangian interpretations of the tracer transport phenomena are given.

Tracer trajectories and displacement due to a micro-swimmer near a surface

2015 ◽  
Vol 773 ◽  
pp. 498-519 ◽  
Author(s):  
A. J. T. M. Mathijssen ◽  
D. O. Pushkin ◽  
J. M. Yeomans
Keyword(s):  
Particle Transport ◽  
Numerical Study ◽  
Tracer Particle ◽  
Persistence Length ◽  
Theoretical Work ◽  
Solid Boundary ◽  
Tracer Transport ◽  
Tracer Particles ◽  
Recent Theoretical Work ◽  
Run And Tumble

We study tracer particle transport due to flows created by a self-propelled micro-swimmer, such as a swimming bacterium, alga or a microscopic artificial swimmer. Recent theoretical work has shown that as a swimmer moves in the fluid bulk along an infinite straight path, tracer particles far from its path perform closed loops, whereas those close to the swimmer are entrained by its motion. However, in biologically and technologically important cases tracer transport is significantly altered for swimmers that move in a run-and-tumble fashion with a finite persistence length, and/or in the presence of a free surface or a solid boundary. Here we present a systematic analytical and numerical study exploring the resultant regimes and their crossovers. Our focus is on describing qualitative features of the tracer particle transport and developing quantitative tools for its analysis. Our work is a step towards understanding the ecological effects of flows created by swimming organisms, such as enhanced fluid mixing and biofilm formation.

Percolation phase transition of static and growing networks under a weighted function

2016 ◽  
Vol 27 (07) ◽  
pp. 1650082 ◽  
Author(s):  
Xiao Jia ◽  
Jin-Song Hong ◽  
Ya-Chun Gao ◽  
Hong-Chun Yang ◽  
Chun Yang ◽  
...  
Keyword(s):  
Phase Transition ◽  
Continuous Phase ◽  
Weighted Function ◽  
Percolation Process ◽  
Practical Applications ◽  
Network Intervention ◽  
Growing Networks ◽  
Discontinuous Phase ◽  
And Control ◽  
Growing Network

We investigate the percolation phase transitions in both the static and growing networks where the nodes are sampled according to a weighted function with a tunable parameter [Formula: see text]. For the static network, i.e. the number of nodes is constant during the percolation process, the percolation phase transition can evolve from continuous to discontinuous as the value of [Formula: see text] is tuned. Based on the properties of the weighted function, three typical values of [Formula: see text] are analyzed. The model becomes the classical Erdös–Rényi (ER) network model at [Formula: see text]. When [Formula: see text], it is shown that the percolation process generates a weakly discontinuous phase transition where the order parameter exhibits an extremely abrupt transition with a significant jump in large but finite system. For [Formula: see text], the cluster size distribution at the lower pseudo-transition point does not obey the power-law behavior, indicating a strongly discontinuous phase transition. In the case of growing network, in which the collection of nodes is increasing, a smoother continuous phase transition emerges at [Formula: see text], in contrast to the weakly discontinuous phase transition of the static network. At [Formula: see text], on the other hand, probability modulation effect shows that the nature of strongly discontinuous phase transition remains the same with the static network despite the node arrival even in the thermodynamic limit. These percolation properties of the growing networks could provide useful reference for network intervention and control in practical applications in consideration of the increasing size of most actual networks.

TRACER TIME DISTRIBUTION OF PARTICLES IN POROUS MEDIA

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 1075-1079
Author(s):  
MARIELA ARAUJO
Keyword(s):  
Porous Medium ◽  
Transit Time ◽  
Power Law ◽  
Time Distribution ◽  
Tracer Particle ◽  
Power Law Distribution ◽  
Low Velocity ◽  
Constant Flow Rate ◽  
Variable Permeability ◽  
Tracer Particles

We study the transit time distributions of tracer particles in a porous medium through which a constant flow rate is established. Our model assumes that non-Gaussian dispersion is due to the presence of low velocity zones or channels in parallel with a faster flow path. Each channel is represented as a trap and simulates the existence of variable permeability blocks inside the porous medium. The time the tracer particle spends inside each channel is related to the heterogeneity of the sample, and is assumed here to have a power-law distribution. We compare the transit time distribution of these particles for the case in which the traps are Poisson distributed with the one in which the trap distribution is a power-law function.

scholarly journals Water-in-Water Emulsion as a New Approach to Produce Mesalamine-Loaded Xylan-Based Microparticles

2019 ◽  
Vol 9 (17) ◽  
pp. 3519
Author(s):  
Bartolomeu S. Souza ◽  
Henrique R. Marcelino ◽  
Francisco Alexandrino ◽  
Silvana C. C. Urtiga ◽  
Karen C. H. Silva ◽  
...  
Keyword(s):  
Small Molecules ◽  
Drug Loading ◽  
Continuous Phase ◽  
Clinical Use ◽  
Water Emulsion ◽  
New Approach ◽  
Emulsion Method ◽  
Discontinuous Phase ◽  
Rapid Diffusion ◽  
Full Factorial

The water-in-water emulsion method has been reported as a technique able to prepare microparticles without using harmful solvents. However, there are few reports showing the encapsulation of small molecules into microparticles produced within this technique. The probable reason relays on the rapid diffusion of these molecules from the discontinuous phase to the continuous phase. In the present study, xylan microparticles containing mesalamine were produced and the doubled crosslinking approach, used to promote higher encapsulation rates, was disclosed. To achieve this goal, a 23 full factorial design was carried out. The results revealed that all formulations presented spherical-shaped microparticles. However, at specific conditions, only few formulations reached up to 50% of drug loading. In addition, the new xylan-based microparticles formulation retained almost 40% of its drug content after 12 h of a dissolution assay likely due to the degree of crosslinking. Thus, the doubled crosslinking approach used was effective on the encapsulation of mesalamine and may pave the way to successfully produce other polysaccharide-based carriers for clinical use.

Laser-Induced Spatially Periodic Structures on the Titanium Surface in n-Hexane at Different Pressures

2020 ◽  
Vol 46 (8) ◽  
pp. 779-782
Author(s):  
D. A. Kochuev ◽  
K. S. Khor’kov ◽  
A. S. Chernikov ◽  
R. V. Chkalov ◽  
V. G. Prokoshev
Keyword(s):  
Titanium Surface ◽  
Periodic Structures ◽  
Spatially Periodic

Dispersion resulting from flow through spatially periodic porous media

1980 ◽  
Vol 297 (1430) ◽  
pp. 81-133 ◽  
Keyword(s):  
Porous Media ◽  
Velocity Vector ◽  
Tracer Particle ◽  
Fluid Velocity ◽  
Complex Structure ◽  
Molecular Diffusivity ◽  
Spatially Periodic ◽  
Flow Through ◽  
Limiting Case ◽  
Interstitial Velocity

A rigorous theory of dispersion in both granular and sintered spatially-periodic porous media is presented, utilizing concepts originating from Brownian motion theory. A precise prescription is derived for calculating both the Darcy-scale interstitial velocity vector v* and dispersivity dyadic D* of a tracer particle. These are expressed in terms of the local fluid velocity vector field v at each point within the interstices of a unit cell of the spatially periodic array and, for the dispersivity, the molecular diffusivity of the tracer particle through the fluid. Though the theory is complete, numerical results are not yet available owing to the complex structure of the local interstitial velocity field v. However, as an illustrative exercise, the theory is shown to correctly reduce in an appropriate limiting case to the well-known Taylor-Aris results for dispersion in circular capillaries.

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