Reaction–diffusion description of biological transport processes in general dimension

1996 ◽  
Vol 104 (5) ◽  
pp. 1918-1936 ◽  
Author(s):  
W. Nadler ◽  
D. L. Stein
Keyword(s):  
Reaction Diffusion ◽  
Transport Processes ◽  
Biological Transport ◽  
General Dimension

Effect of non-uniform passive advection on A+B->C radial reaction-diffusion fronts 

2021 ◽  
Author(s):  
Alessandro Comolli ◽  
Anne De Wit ◽  
Fabian Brau
Keyword(s):  
Molecular Diffusion ◽  
Early Time ◽  
Reaction Diffusion ◽  
Transport Processes ◽  
Calcium Carbonate Precipitation ◽  
Atmospheric Reactions ◽  
Passive Advection ◽  
Reaction Fronts ◽  
Time Regime ◽  
Long Time

<p>The interplay between chemical and transport processes can give rise to complex reaction fronts dynamics, whose understanding is crucial in a wide variety of environmental, hydrological and biological processes, among others. An important class of reactions is A+B->C processes, where A and B are two initially segregated miscible reactants that produce C upon contact. Depending on the nature of the reactants and on the transport processes that they undergo, this class of reaction describes a broad set of phenomena, including combustion, atmospheric reactions, calcium carbonate precipitation and more. Due to the complexity of the coupled chemical-hydrodynamic systems, theoretical studies generally deal with the particular case of reactants undergoing passive advection and molecular diffusion. A restricted number of different geometries have been studied, including uniform rectilinear [1], 2D radial [2] and 3D spherical [3] fronts. By symmetry considerations, these systems are effectively 1D.</p><p>Here, we consider a 3D axis-symmetric confined system in which a reactant A is injected radially into a sea of B and both species are transported by diffusion and passive non-uniform advection. The advective field <em>v<sub>r</sub>(r,z)</em> describes a radial Poiseuille flow. We find that the front dynamics is defined by three distinct temporal regimes, which we characterize analytically and numerically. These are i) an early-time regime where the amount of mixing is small and the dynamics is transport-dominated, ii) a strongly non-linear transient regime and iii) a long-time regime that exhibits Taylor-like dispersion, for which the system dynamics is similar to the 2D radial case.</p><p>                                  <img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.ff5ab530bdff57321640161/sdaolpUECMynit/12UGE&app=m&a=0&c=360a1556c809484116c55812c8c06624&ct=x&pn=gnp.elif&d=1" alt="" width="299" height="299">                                                     <img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.671a6980bdff51231640161/sdaolpUECMynit/12UGE&app=m&a=0&c=c5a857c3fab835057e3af84001a91d15&ct=x&pn=gnp.elif&d=1" alt="" width="302" height="302"></p><p>                                                   Fig. 1: Concentration profile of the product C in the transient (left) and asymptotic (right) regimes.</p><p> </p><p>References:</p><p>[1] L. Gálfi, Z. Rácz, Phys. Rev. A 38, 3151 (1988);</p><p>[2] F. Brau, G. Schuszter, A. De Wit, Phys. Rev. Lett. 118, 134101 (2017);</p><p>[3] A. Comolli, A. De Wit, F. Brau, Phys. Rev. E, 100 (5), 052213 (2019).</p>

Evaluation of Lattice Boltzmann Method for Reaction-Diffusion Process in a Porous SOFC Anode Microstructure

2012 ◽  
Author(s):  
Hedvig Paradis ◽  
Bengt Sundén
Keyword(s):  
Porous Media ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Reaction Diffusion ◽  
Reaction Rates ◽  
Transport Processes ◽  
Microscopic Level ◽  
Reaction Diffusion Equation ◽  
Interaction Sites ◽  
Boltzmann Method

In the microscale structure of a porous electrode, the transport processes are among the least understood areas of SOFC. The purpose of this study is to evaluate the Lattice Boltzmann Method (LBM) for a porous microscopic media and investigate mass transfer processes with electrochemical reactions by LBM at a mesoscopic and microscopic level. Part of the anode structure of an SOFC for two components is evaluated qualitatively for two different geometry configurations of the porous media. The reaction-diffusion equation has been implemented in the particle distribution function used in LBM. The LBM code in this study is written in the programs MATLAB and Palabos. It has here been shown that LBM can be effectively used at a mesoscopic level ranging down to a microscopic level and proven to effectively take care of the interaction between the particles and the walls of the porous media. LBM can also handle the implementation of reaction rates where these can be locally specified or as a general source term. It is concluded that LBM can be valuable for evaluating the risk of local harming spots within the porous structure to reduce these interaction sites. In future studies, the information gained from the microscale modeling can be coupled to a macroscale CFD model and help in development of a smooth structure for interaction of the reforming reaction and the electrochemical reaction rates. This can in turn improve the cell performance.

Thermodynamic Structure of Nonlinear Macrokinetics in Reaction-Diffusion Systems

2004 ◽  
Vol 11 (02) ◽  
pp. 185-202 ◽  
Author(s):  
Stanisław Sieniutycz
Keyword(s):  
Chemical Reactions ◽  
Reaction Diffusion ◽  
Transport Processes ◽  
Mass Action ◽  
Nonlinear Kinetics ◽  
Reaction Diffusion Systems ◽  
Thermodynamic Structure ◽  
Far From Equilibrium ◽  
Physical Consequences ◽  
Kinetics Of

Affinity picture — new for transport phenomena — and the traditional Onsagerian picture are shown to constitute two equivalent representations for kinetics of chemical reactions and transfer processes. Two competing directions in elementary chemical or transport steps are analyzed. Nonequilibrium systems are described by equations of nonlinear kinetics of Marcelin-Kohnstamm-de Donder type that contain terms exponential with respect to the Planck potentials and temperature reciprocal. Simultaneously these equations are analytical expressions characterizing the transport of the substance or energy through the energy barrier. We regard kinetics of this sort as potential representations of a generalized law of mass action that includes the effect of transfer phenomena and external fields. We also consider physical consequences of these kinetics closely and far from equilibrium, and show how diverse processes can be described. In these developments we point out the significance of nonlinear symmetries and generalized affinity. Correspondence with the Onsager's theory is shown in the vicinity of thermodynamic equilibrium. Yet, the theory shows that far from equilibrium the rates of transport processes and chemical reactions cannot be determined uniquely in terms of their affinities because these rates depend on all state coordinates of the system.

scholarly journals Mean Transit Time and Mean Residence Time for Linear Diffusion–Convection–Reaction Transport System

2007 ◽  
Vol 8 (1) ◽  
pp. 37-49 ◽  
Author(s):  
Jacek Waniewski
Keyword(s):  
Exit Time ◽  
Mean Transit Time ◽  
Reaction Diffusion ◽  
Transport Processes ◽  
Linear Diffusion ◽  
Transit Times ◽  
Linear Reaction ◽  
Analytical Formulas ◽  
Reaction Transport ◽  
Diffusion Convection

Characteristic times for transport processes in biological systems may be evaluated as mean transit times (MTTs) (for transit states) or mean residence times (MRT) (for steady states). It is shown in a general framework of a (linear) reaction–diffusion–convection equation that these two times are related. Analytical formulas are also derived to calculate moments of exit time distribution using solutions for a stationary state of the system.

Long-distance biological transport processes through the air: can nature's complexity be unfolded in silico?

2005 ◽  
Vol 11 (2) ◽  
pp. 131-137 ◽  
Author(s):  
Ran Nathan ◽  
Nir Sapir ◽  
Ana Trakhtenbrot ◽  
Gabriel G. Katul ◽  
Gil Bohrer ◽  
...  
Keyword(s):  
In Silico ◽  
Transport Processes ◽  
Biological Transport ◽  
Long Distance

Biological transport processes for microhydraulic actuation

2007 ◽  
Vol 123 (2) ◽  
pp. 685-695 ◽  
Author(s):  
Vishnu Baba Sundaresan ◽  
Christopher Homison ◽  
Lisa M. Weiland ◽  
Donald J. Leo
Keyword(s):  
Transport Processes ◽  
Biological Transport

scholarly journals Analysis of dynamic morphogen scale invariance

2009 ◽  
Vol 6 (41) ◽  
pp. 1179-1191 ◽  
Author(s):  
David M. Umulis
Keyword(s):  
Scale Invariance ◽  
Reaction Diffusion ◽  
Cell Types ◽  
Transport Processes ◽  
Reaction Diffusion Equations ◽  
Local Concentration ◽  
Flux Dynamic ◽  
Multipotent Cells ◽  
Total Input ◽  
Distinct Cell

During the development of some tissues, fields of multipotent cells differentiate into distinct cell types in response to the local concentration of a signalling factor called a morphogen. Typically, individual organisms within a population differ in size, but their body plans appear to be scaled versions of a common template. Similarly, closely related species may differ by three or more orders of magnitude in size, yet common structures between species scale to have similar proportions. In standard reaction–diffusion equations, the morphogen range has a length scale that depends on a balance between kinetic and transport processes and not on the length or size of the field of cells being patterned. However, as shown here for a class of morphogen-patterning systems, a number of conditions lead to scale invariance of the morphogen distribution at equilibrium and during the transient approach to equilibrium. Equilibrium scale invariance requires conservation of the total binding site number and total input flux. Dynamic scale invariance additionally requires sufficient binding to slow the diffusion of ligand. The equations derived herein can be extended to the study of other perturbations to gain further insight into the processes regulating the robustness and scaling of morphogen-mediated pattern formation.

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