scholarly journals Reaction-infiltration instability in a compacting porous medium

2018 ◽  
Vol 852 ◽  
pp. 5-36 ◽  
Author(s):  
David W. Rees Jones ◽  
Richard F. Katz
Keyword(s):  
Porous Medium ◽  
Host Rock ◽  
Numerical Solutions ◽  
Critical Conditions ◽  
Porous Flow ◽  
Magma Flow ◽  
Horizontal Length ◽  
Geological Features ◽  
Geologic Record

Certain geological features have been interpreted as evidence of channelized magma flow in the mantle, which is a compacting porous medium. Aharonov et al. (J. Geophys. Res., vol. 100 (B10), 1995, pp. 20433–20450) developed a simple model of reactive porous flow and numerically analysed its instability to channels. The instability relies on magma advection against a chemical solubility gradient and the porosity-dependent permeability of the porous host rock. We extend the previous analysis by systematically mapping out the parameter space. Crucially, we augment numerical solutions with asymptotic analysis to better understand the physical controls on the instability. We derive scalings for the critical conditions of the instability and analyse the associated bifurcation structure. We also determine scalings for the wavelengths and growth rates of the channel structures that emerge. We obtain quantitative theories for and a physical understanding of, first, how advection or diffusion over the reactive time scale sets the horizontal length scale of channels and, second, the role of viscous compaction of the host rock, which also affects the vertical extent of channelized flow. These scalings allow us to derive estimates of the dimensions of emergent channels that are consistent with the geologic record.

Capillary Imbibition Dynamics in Porous Media

2014 ◽  
Author(s):  
Swayamdipta Bhaduri ◽  
Pankaj Sahu ◽  
Siddhartha Das ◽  
Aloke Kumar ◽  
Sushanta K. Mitra
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Paper Strip ◽  
Capillary Imbibition ◽  
Flow Physics ◽  
Fundamental Understanding ◽  
Paper Based Microfluidics ◽  
To Come

The phenomenon of capillary imbibition through porous media is important both due to its applications in several disciplines as well as the involved fundamental flow physics in micro-nanoscales. In the present study, where a simple paper strip plays the role of a porous medium, we observe an extremely interesting and non-intuitive wicking or imbibition dynamics, through which we can separate water and dye particles by allowing the paper strip to come in contact with a dye solution. This result is extremely significant in the context of understanding paper-based microfluidics, and the manner in which the fundamental understanding of the capillary imbibition phenomenon in a porous medium can be used to devise a paper-based microfluidic separator.

Growth of fingers at an unstable diffusing interface in a porous medium or Hele-Shaw cell

1969 ◽  
Vol 39 (3) ◽  
pp. 477-495 ◽  
Author(s):  
R. A. Wooding
Keyword(s):  
Porous Medium ◽  
Numerical Solutions ◽  
Hyperbolic Equations ◽  
Saturated Porous Medium ◽  
Mean Amplitude ◽  
Wave Number ◽  
Two Fluids ◽  
Averaged Equations ◽  
The Mean ◽  
Hele Shaw Cell

Waves at an unstable horizontal interface between two fluids moving vertically through a saturated porous medium are observed to grow rapidly to become fingers (i.e. the amplitude greatly exceeds the wavelength). For a diffusing interface, in experiments using a Hele-Shaw cell, the mean amplitude taken over many fingers grows approximately as (time)2, followed by a transition to a growth proportional to time. Correspondingly, the mean wave-number decreases approximately as (time)−½. Because of the rapid increase in amplitude, longitudinal dispersion ultimately becomes negligible relative to wave growth. To represent the observed quantities at large time, the transport equation is suitably weighted and averaged over the horizontal plane. Hyperbolic equations result, and the ascending and descending zones containing the fronts of the fingers are replaced by discontinuities. These averaged equations form an unclosed set, but closure is achieved by assuming a law for the mean wave-number based on similarity. It is found that the mean amplitude is fairly insensitive to changes in wave-number. Numerical solutions of the averaged equations give more detailed information about the growth behaviour, in excellent agreement with the similarity results and with the Hele-Shaw experiments.

scholarly journals SIR Model for Dengue Disease with Effect of Dengue Vaccination

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Pratchaya Chanprasopchai ◽  
I. Ming Tang ◽  
Puntani Pongsumpun
Keyword(s):  
Mathematical Model ◽  
Mortality Rate ◽  
Dengue Virus ◽  
Numerical Solutions ◽  
Specific Treatment ◽  
Sir Model ◽  
Dengue Vaccine ◽  
Dengue Disease ◽  
Modelling Methods

The dengue disease is caused by dengue virus, and there is no specific treatment. The medical care by experienced physicians and nurses will save life and will lower the mortality rate. A dengue vaccine to control the disease is available in Thailand since late 2016. A mathematical model would be an important way to analyze the effects of the vaccination on the transmission of the disease. We have formulated an SIR (susceptible-infected-recovered) model of the transmission of the disease which includes the effect of vaccination and used standard dynamical modelling methods to analyze the effects. The equilibrium states and their stabilities are investigated. The trajectories of the numerical solutions plotted into the 2D planes and 3D spaces are presented. The main contribution is determining the role of dengue vaccination in the model. From the analysis, we find that there is a significant reduction in the total hospitalization time needed to treat the illness.

scholarly journals Remotely distinguishing and mapping endogenic water on the Moon

2017 ◽  
Vol 375 (2094) ◽  
pp. 20150391 ◽  
Author(s):  
Rachel L. Klima ◽  
Noah E. Petro
Keyword(s):  
Solar Wind ◽  
Spatial Distribution ◽  
Solar System ◽  
The Moon ◽  
Testing Hypotheses ◽  
Origin And Evolution ◽  
Lunar Interior ◽  
Geological Features ◽  
Insight Into

Water and/or hydroxyl detected remotely on the lunar surface originates from several sources: (i) comets and other exogenous debris; (ii) solar-wind implantation; (iii) the lunar interior. While each of these sources is interesting in its own right, distinguishing among them is critical for testing hypotheses for the origin and evolution of the Moon and our Solar System. Existing spacecraft observations are not of high enough spectral resolution to uniquely characterize the bonding energies of the hydroxyl molecules that have been detected. Nevertheless, the spatial distribution and associations of H, OH − or H 2 O with specific lunar lithologies provide some insight into the origin of lunar hydrous materials. The global distribution of OH − /H 2 O as detected using infrared spectroscopic measurements from orbit is here examined, with particular focus on regional geological features that exhibit OH − /H 2 O absorption band strengths that differ from their immediate surroundings. This article is part of the themed issue ‘The origin, history and role of water in the evolution of the inner Solar System’.

Intrapleural fluid movements described by a porous flow model

1992 ◽  
Vol 73 (6) ◽  
pp. 2511-2516 ◽  
Author(s):  
G. Miserocchi ◽  
D. Venturoli ◽  
D. Negrini ◽  
M. C. Gilardi ◽  
R. Bellina
Keyword(s):  
Porous Medium ◽  
Gamma Camera ◽  
Flow Model ◽  
Pleural Space ◽  
Interstitial Tissue ◽  
Hydraulic Pressure ◽  
Pressure Gradients ◽  
Hydraulic Radius ◽  
Porous Flow ◽  
Anesthetized Dogs

We injected technetium-labeled albumin (at a concentration similar to that of the pleural fluid) in the costal region of anesthetized dogs (n = 13) either breathing spontaneously or apneic. The decay rate of labeled activity at the injection site was studied with a gamma camera placed either in the anteroposterior (AP) or laterolateral (LL) projection. In breathing animals (respiratory frequency approximately 10 cycles/min), 10 min after the injection the activity decreased by approximately 50% on AP and approximately 20% on LL imaging; in apneic animals the corresponding decrease in activity was reduced to approximately 15 and approximately 3%, respectively. We considered label translocation from AP and LL imaging as a result of bulk flows of liquid along the costomediastinal and gravity-dependent direction, respectively. We related intrapleural flows to the hydraulic pressure gradients existing along these two directions and to the geometry of the pleural space. The pleural space was considered as a porous medium partially occupied by the mesh of microvilli protruding from mesothelial cells. Solution of the Kozeny-Carman equation for the observed flow velocities and pressure gradients yielded a mean hydraulic radius of the pathways followed by the liquid ranging from 2 to 4 microns. The hydraulic resistivity of the pleural space was estimated at approximately 8.5 x 10(5) dyn.s.cm-4, five orders of magnitude lower than that of interstitial tissue.

scholarly journals Extended logistic growth model for heterogeneous populations

2017 ◽  
Author(s):  
Wang Jin ◽  
Scott W McCue ◽  
Matthew J Simpson
Keyword(s):  
Cell Proliferation ◽  
Growth Model ◽  
Numerical Solutions ◽  
Cellular Level ◽  
Logistic Growth ◽  
Logistic Growth Model ◽  
Living Tissues ◽  
Discrete Mathematical Model ◽  
The Continuum

AbstractCell proliferation is the most important cellular-level mechanism responsible for regulating cell population dynamics in living tissues. Modern experimental procedures show that the proliferation rates of individual cells can vary significantly within the same cell line. However, in the mathematical biology literature, cell proliferation is typically modelled using a classical logistic equation which neglects variations in the proliferation rate. In this work, we consider a discrete mathematical model of cell migration and cell proliferation, modulated by volume exclusion (crowding) effects, with variable rates of proliferation across the total population. We refer to this variability as heterogeneity. Constructing the continuum limit of the discrete model leads to a generalisation of the classical logistic growth model. Comparing numerical solutions of the model to averaged data from discrete simulations shows that the new model captures the key features of the discrete process. Applying the extended logistic model to simulate a proliferation assay using rates from recent experimental literature shows that neglecting the role of heterogeneity can, at times, lead to misleading results.

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