Diffusion Fundamentals (E-Journal)

Abad, Enrique

Campos, Daniel

Méndez, Vicenç

Yuste, Santos Bravo

Lindenberg, Katja

The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application
Mortal creepers searching for a target  
 
E. Abad1*, D. Campos2, V. Méndez2, S.B. Yuste3, K. Lindenberg4 
 
1Universidad de Extremadura, Mérida, Spain 
2Universitat Autònoma de Barcelona, Bellaterra, Spain 
3Universidad de Extremadura, Badajoz, Spain 
4University of California, San Diego, USA 
*eabad@unex.es 
 
In biology and ecology, target search processes where the lifetime of the searchers is shorter or 
comparable to the typical time needed to reach the target by diffusion are a common occurrence (e.g., 
oocyte fertilization by sperm). Here, we present a simple paradigm for detection of an immobile target 
by a Continuous Time Random Walker with a finite lifetime, which we alternatively call a mortal 
creeper [1]. The motion of the creeper is characterized by linear displacements at a fixed speed and 
exponentially distributed duration, interrupted by random changes in the direction of motion and 
resumption of motion in the new direction with the same speed. The mortal creeper may die at any 
time during its motion according to an exponential decay law characterized by a finite mean death rate 
ωm. While still alive, the creeper has a finite mean frequency ω of change of the direction of motion. 
In particular, we consider the efficiency of the target search process, characterized by the probability 
that the creeper will eventually detect the target. Analytic results confirmed by numerical results show 
that there is an ωm-dependent optimal frequency ω=ωopt that maximizes the probability of eventual 
target detection. We work primarily in one-dimensional (d=1) domains and examine the role of initial 
conditions and of finite domain sizes. Numerical results in d=2 domains confirm the existence of an 
optimal frequency of change of direction, thereby suggesting that the observed effects are robust to 
changes in dimensionality. In the d=1 case, explicit expressions for the probability of target detection 
in the long time limit are given. In the case of an infinite domain, we compute the detection 
probability for arbitrary times and study its early- and late-time behavior. We further consider the 
survival probability of the target in the presence of many independent creepers beginning their motion 
at the same location and at the same time. We also consider a version of the standard "target problem" 
in which many creepers start at random locations at the same time. In this latter case, no optimal 
frequency ωopt>0  is found. 
 
 
Figure 1: The optimal frequency of reorientation ωopt maximizing the probability of eventual target detection 
becomes non-zero for intermediate values of the mortality rate ωm. 
References 
[1] D. Campos, E. Abad, V. Méndez, S. B. Yuste, and K. Lindenberg: Mortal walkers searching for a target. 
ArXiV:1503.02013 (2015).  
 
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1


English

Mortal creepers searching for a target

Al-Naji, Majd

Goepel, Michael

Roibu, Anca

Gläser, Roger

The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application
Reduction of p-Nitrophenol to p-Aminophenol over Supported 
Monometallic Catalysts as a Model Reaction for Mass-Transfer 
Investigations 
 
Majd Al-Naji*, Michael Goepel, Anca Roibu, Roger Gläser 
 
Institute of Chemical Technology, Universität Leipzig, Leipzig, Germany. 
*majd.al-naji@uni-leipzig.de 
 
Generally, mass-transfer limitations play an important role for a valid determination of the reaction 
rate of liquid-phase catalytic hydrogenation reactions [1]. Catalytic hydrogenations are considered one 
of the most important reactions in many industrial processes such as upgrading of biomass and 
transformation of unsaturated to saturated hydrocarbons. Moreover, the reduction of -NO2 and -C=O 
groups in organic compounds are common conversions in chemicals and pharmaceuticals production 
[1-2]. Usually, the catalytic hydrogenation reactions require laborious experiments involving high-
pressure reactors, elevated temperatures, organic solvents and long experimentation times. Therefore, 
the assessment of the catalytic activity of supported metal catalysts utilizing the hydrogenation of p-
nitrophenol (PNP) to p-aminophenol (PAP) using NaBH4 as a reduction agent as a model reaction is 
presented. This conversion can be readily conducted in shorter reaction time (20 min), ambient 
pressure and temperature and with water as a solvent. Furthermore, the progress of the reaction can be 
easily monitored using on-line UV/Vis spectroscopy [2-3].  
This work was, thus, devoted to investigate the 
effect of external mass-transfer limitations on the 
reaction rate of hydrogenation of PNP to PAP 
using NaBH4 as reduction agent. Catalysts used 
for this study were 2.2Pt/SiO2, 3.9Pt/γ-Al2O3, 
2.1Pd/Al-MCF and 2.0Pd/Al-SBA-15 with 
different textural properties.   
The catalysts were thoroughly characterized via 
N2-sorption, elemental analysis, XRD, SEM and 
TEM. The initial reaction rates of PNP 
hydrogenation over the supported Pt catalysts 
obtained at different stirring speed were 
calculated (Figure 1). Monometallic 2.2Pt 
supported on SiO2 shows a correlation between 
the initial reaction rate and the stirring speed 
indicating the presence of external mass-transfer 
limitation. In contrast, the initial reaction rate 
using 3.9Pt/γ-Al2O3 does not increase for stirring 
speeds above 1000 min–1. Therefore, it can be assumed that under these conditions external mass-
transfer is not limiting the reaction rate due to different morphological properties (i.e., smaller catalyst 
grains) as well as a lower catalytic activity.  
 
References 
 [1] M. Goepel, H. Kabir, C. Küster, E. Saraçi, P. Zeigermann, R. Valiullin, C. Chmelik, D. Enke, J. Kärger, R. 
Gläser: Improving mass-transfer in controlled pore glasses as supports for the platinum-catalyzed aromatics 
hydrogenation. Catal. Sci. Technol. 5, 3137-3146 (2015). 
[2] M. Goepel, M. Al-Naji, P. With, G. Wagner, O. Oeckler, D. Enke, R. Gläser, Hydrogenation of p-
nitrophenol to p-aminophenol as a test reaction for the catalytic activity of supported Pt catalysts. Chem. Eng. 
Technol. 37, 551-554 (2014). 
[3] M. Al-Naji, A. M. Balu, A. Roibu, M. Goepel, W. D. Einicke, R. Luque, R. Gläser, Mechanochemical 
preparation of advanced catalytically active bifunctional Pd-containing nanomaterials for aqueous phase 
hydrogenation. Catal. Sci. Technol. 5, 2085-2091 (2015).  
400 600 800 1000 1200 1400
0.04
0.06
0.08
0.10
r 0
 / 
(m
m
ol
 m
-3
 m
in
-1
)
Stirring Speed / min-1
 2.2Pt/SiO2
 3.9Pt/γ−Al2O3
 
 
Figure 1: Influence of the stirring speed on the 
initial reaction rate for the reduction of PNP using 
2.2Pt/SiO2 and 3.9Pt/γ-Al2O3.  
Reaction conditions: cPNP = 0.18 mmol l
-1, cNaBH4 = 
0.6 mmol l-1, T = 298 K, mcatalyst = 150 mg. 
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1


Reduction of p-Nitrophenol to p-Aminophenol over supported
monometallic catalysts as a model reaction for mass-transfer
investigations

Angı, Deniz

Yeresikli, Alev Güneş

Özkan, Fehime Çakıcıoğlu

The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application
Evaluation of CO2 diffusion on aluminum based metal organic frameworks  
Deniz Angı1, Alev Güneş Yeresikli2, Fehime Çakıcıoğlu Özkan2* 
1Izmir Institute of Technology, Dept. of  Materials Sci. and Eng., Izmir, TURKEY 
2Izmir Institute of Technology, Dept. of Chemical Eng., Izmir, TURKEY 
*Corresponding author (fehimeozkan@iyte.edu.tr) 
 
     Metal-organic frameworks(MOFs), highly porous crystalline materials, are composed of metal 
clusters connected by organic linkers. As they have high porosity, large surface area and large pore 
volume, a considerable amount of specific gases can be adsorbed onto these pores. Hydrogen, a clean 
energy fuel can be produced by Steam Methane Reformer (SMR) processes. Steam methane reformer 
off-gas, gas produced by steam methane reformer contains mainly H2 besides to  CO2, (10-25%v/v), 
CH4 (1.3-8%v/v), CO (0.25-10%v/v) as impurities.  It is critical to remove CO2 from the gas mixture 
not only for up-grading  of  SMR-off gas but also natural gas to obtain high purity H2 or CH4, 
respectively. MOFs are considered as a potential adsorbent material to be used in gas purification and 
separation. Zero Length Column (ZLC) technique was conducted to measure the intraparticle diffusion 
properties of porous adsorbents. The response curve, yielded from quadrupole mass spectrometer, is 
used to determine adsorption parameters such as Henry’s constant and diffusion coefficient.The 
adsorption kinetics of CO2, on aluminum based organic framework was studied at 30 
oC. The flow 
rates of inert carrier gas Helium will be changed as 30, 50, 70 and 100 ml/min in order to determine 
whether the system will be favored by equilibrium or kinetic control. CO2 adsorption kinetics of 
aluminum based organic framework synthesized were compared with the commercial one (MIL-
53(Al)). The results show that the calculated diffusivity values are weakly dependent on purge flow 
rate. The study reveals that transport is controlled by intracrystalline diffusion. The study shows that 
the ZLC method is an effective tool to investigate the diffusion kinetics of CO2 gas in MIL 53 (Al). 
 
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1


Evaluation of CO2 diffusion on aluminum based metal organic frameworks

Carter, David

Kruczek, Boguslaw

Tezel, F. Handan

The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application
Application of Maxwell Stefan equations to characterize silicalite membranes 
 
D. Carter, B. Kruczek, F. H. Tezel* 
 
Department of Chemical and Biological Engineering 
University of Ottawa, 161 Louis-Pasteur, Ottawa, Ontario K1N 6N5 CANADA 
Email: handan.tezel@uottawa.ca 
 
Inorganic membranes composed of zeolites such as silicalite are able to separate a wide variety of gas 
mixtures near atmospheric conditions and are therefore well suited to be used in tandem with, or to 
replace many gas separation processes such as absorption and cryogenic distillation. Due to the highly 
ordered and regular pore network inside zeolites, different gas molecules will interact with the zeolitic 
pores at different rates leading to the separation of gas mixtures by surface diffusion.  
 
In order to characterize silicalite membranes to be used for the separation of multi-component gas 
mixtures, a rigorous model is required that accounts for both intermolecular and intramolecular 
interactions, as well as interactions between the gas molecules and the adsorbent. To this end, the 
Maxwell Stefan equations have been used to calculate the exchange diffusivities between gas molecules 
in the presence of similar, and different molecular species in silicalite membranes.  
 
In this study, defect free membranes were fabricated by impregnating silicalite particles into ceramic 
supports composed of TiO2. The membranes were then characterized by conducting binary gas 
permeation experiments at different feed pressures and compositions using synthetic post combustion flue 
gas mixtures composed of CO2 and N2. For a membrane whose CO2 permeance was found to be a 
maximum of 2.64 x 10-6 [mol·m-2·Pa-1·s-1], the exchange diffusivity of CO2 in the presence of N2 was 
found to decrease from   2.32 x 10-10 to 2.5 x 10-11 [m2·s-1] as a function of CO2 log mean partial pressure 
difference, and the exchange diffusivity of N2 in the presence of CO2 was found to increase as a function 
of N2 log mean partial pressure difference without bound beyond 3.2 x 10
-11[m2·s-1]. Although these 
diffusivities are not independent of operating conditions as desired, the observed trends better describe the 
transport of gas molecules as required for industrial separation process design. 
 
 
 
 
 
 
 
  
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1


Application of Maxwell Stefan equations to characterize silicalite membranes

Nguyen, Tien Quang

Glorius, Maja

Breitkopf, Cornelia

The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application
Transport of isopropanol in H-ZSM5 by impedance spectroscopy 
 
T.Q. Nguyen*, M. Glorius, C. Breitkopf 
 
Technical Thermodynamics, Dresden University of Technology 
01062 Dresden, Germany 
*tien_quang.nguyen@mailbox.tu-dresden.de  
 
The transport of gases/liquids in meso- and micropores of catalysts is the first important step in the 
microkinetic cycle. Diffusion processes may significantly influence the catalytic activity and 
selectivity. As zeolite structures are well-known, those materials are used for studying the influence of 
diffusion on the catalytic activity. H-ZSM5 represents a well-defined material with strong Brønsted 
acid sites. It has two types of pores: mesopores and micropores [1]. Due to the complexity of the 
mechanism of diffusion processes in different pore structures in such zeolites, traditional techniques 
(such as TAP, FR) are restricted with respect to the range of diffusion coefficients. New approaches 
are needed for revealing exact values of diffusion coefficients.  
Electrochemical impedance spectroscopy is a powerful tool for understanding gas/liquid transport 
phenomena in porous materials. By using a small perturbation of the voltage amplitude within a large 
range of frequencies, the method can exploit transport processes under steady-state conditions in 
grains, grain boundaries and interfaces. Based on a model in space charge relaxation of dielectric 
materials, the value of diffusion coefficients of charged carriers/molecules can be determined [2].    
In this study, the molecular diffusion coefficient of isopropanol over H-ZSM5 (prepared by [3]) was 
characterized by impedance spectroscopy. The results are compared to literature data. The 
adsorption/diffusion mechanism of isopropanol in the zeolite inside the micropore structure as well as 
the electrical characterization and the activation energy are discussed. FTIR spectroscopy supports the 
characterization during isopropanol adsorption. Results will be shown in detail on the poster.  
 
 
References 
[1] Glazneva T. S., V. P. Isopropanol diffusion and dehydration in zeolite HZSM-5. Spectrokinetic study. 
Reaction Kinetics and Catalysis Letters, 94(1), 11-19 (2008). 
[2] Bandara, T. M. W. J., and B. E. Mellander. Evaluation of mobility, diffusion coefficient and density of 
charge carriers in ionic liquids and novel electrolytes based on a new model for dielectric response. 
INTECH Open Access Publisher, 383-406 (2011). 
[3] Schuricht, Falk, and Wladimir Reschetilowski. Simultaneous selective catalytic reduction (SCR) of NOx and 
N2O over Ag/ZSM-5-Catalytic studies and mechanistic implications. Microporous and Mesoporous 
Materials 164, 135-144 (2012). 
 
 
 
 
 
 
 
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1


Transport of isopropanol in H-ZSM5 by impedance spectroscopy

Saxton, Michael J.

The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application
Diffusion coefficient as a function of mass for globular macromolecules 
 
Michael J. Saxton1* 
 
1Dept of Biochemistry & Molecular Medicine, Univ of California, Davis, California, USA 
 
*mjsaxton@ucdavis.edu 
 
How well can the diffusion coefficient D of a globular biomolecule be predicted from its molecular 
mass MW?   
Diffusion measurements in heterogeneous systems can be improved by the use of scalable tracers, in 
which the size is varied alone at constant shape, surface properties, diffusion mechanism, 
deformability, and other properties affecting diffusion  [1].  Before trying to design a de novo series of 
scalable globular proteins, it is appropriate to examine how scalable the commonly used de antiquo 
globular proteins are.       
The widely-used compilation of experimental diffusion coefficients by Tyn and Gusek [2] was 
examined [1, supporting information].  This set — ranging from ribonuclease, 12640 Da, to tobacco 
mosaic virus, 50 MDa — was plotted as D versus log MW.  The obviously linear species were 
removed, and values of D and MW for the outliers were examined.  The plot yields a cloud of values 
of D versus log MW.  In such a plot, rigorously scalable tracers would give a single smooth curve of D 
versus log MW.  The extent of the cloud represents scatter due to nonscalablity and experimental error.  
Published values of D from hydrodynamic calculations by various laboratories are remarkably 
consistent with the cloud.   
The cloud prediction is certainly good enough for semi-quantitative estimates or for finding the 
camera frame rate required in single-particle tracking experiments.  For globular proteins of known 
structure, highly accurate values can be obtained from simulations, if required.  For a diffusion-
controlled reaction in dilute solution, the cloud prediction is close enough that the standard analysis of 
propagation of errors can be used.  But scalable tracers may be useful for diffusion measurements in 
cytoplasm, in particular to control surface interactions with cytoplasmic components.  Geometric 
scalability would be essential in a measurement of the percolation threshold of cytoplasm. 
The incomplete examination of the question here indicates what would be required for a complete 
examination.  (Supported in part by NIH grant GM038133) 
 
References 
[1] M .J. Saxton: Wanted: Scalable Tracers for Diffusion Measurements. J Phys Chem B 118, 12805-12817 
(2014). 
[2] M. T. Tyn, T. W. Gusek:  Prediction of Diffusion Coefficients of Proteins. Biotech Bioeng 35, 327–338 
(1990). 
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1


Diffusion coefficient as a function of mass for globular macromolecules

Sikorski, Andrzej

Polanowski, Piotr

The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application
Dynamics of Linear and Cyclic Chains in Two Dimensions 
 
Andrzej Sikorski1*, Piotr Polanowski2 
 
1Department of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland 
2Department of Molecular Physics, Technical University of Łódź, 90-924 Łódź, Poland 
*sikorski@chem.uw.edu.pl 
 
 
Extensive and systematic simulation studies of two-dimensional polymer systems were performed. In 
contrast to other works we focused on cooperative phenomena that occurred where the motion of 
particles takes place in a dense system. Comparison studies of athermal cyclic and linear polymer 
chains systems on the two-dimensional triangular lattice are presented. We studied various polymers 
concentrations with respect to an explicitly considered solvent. We employed the Dynamic Lattice 
Liquid (DLL) model [1], which can work at the highest system density, where all lattice sites are 
occupied and it allows to take into account coincidences of elementary molecular motion attempts 
resulting in local cooperative structural transformations. Both static and dynamic properties of the 
model systems are characterized [2]. We showed the differences between the dynamic behavior of 
rings and linear chains in solution and how the structure of these objects influence the dynamics of the 
inert solvent. The simulation results reflect molecular packing and other properties of monomolecular 
polymer layers, which can be relevant for these, obtained in some thin film formation techniques. 
 
References 
[1] P. Polanowski and T. Pakula, Studies of mobility, interdiffusion, and self-diffusion in two-
component mixtures using the dynamic lattice liquid model. J. Chem. Phys. 118, 11139-11146 
(2003). 
[2] P. Polanowski, J. K. Jeszka and A. Sikorski, Dynamic Properties of Linear and Cyclic Chains in 
Two Dimensions. Computer Simulation Studies, Macromolecules 47, 4830-4839 (2014). 
 
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1


Dynamics of linear and cyclic chains in two dimensions

Silva, Fabio

Stevens, Chris J.

Weisskopf, Alison

Castillo, Cristina

Qin, Ling

Bevan, Andrew

Fuller, Dorian Q.

The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application
Modelling the geographical origin of rice cultivation in Asia using the Rice 
Archaeological Database  
 
Fabio Silva1*, Chris J Stevens1, Alison Weisskopf1, Cristina Castillo1, Ling Qin2, Andrew Bevan1 
and Dorian Q Fuller1 
 
1UCL Institute of Archaeology, London, United Kingsom 
2Peking University, School of Archaeology and Museology, Beijing, China  
*fabio.silva@ucl.ac.uk 
 
An extensive database of archaeological evidence for rice across Asia, including 400 sites from 
mainland East Asia, Southeast Asia and South Asia (see [1] for an earlier version) is used to compare 
several models for the geographical origins of rice cultivation and infer the most likely region(s) for its 
origins and subsequent outward diffusion.  
The approach is based on regression modelling (eg. [2]) wherein goodness of fit is obtained from a 
quantile regression [3] of the archaeologically inferred age versus a least-cost distance from the 
putative origin(s). The Fast Marching method [4] is used to estimate the least-cost distances based on 
simple geographical features (cf. [5] and [6]) and the efficiency of different goodness of fit indices 
were compared using Monte Carlo simulations.  
The origin region that best fits the archaeobotanical data is also compared to other hypothetical 
geographical origins derived from the literature, including from genetics, archaeology and historical 
linguistics. The model that best fits all available archaeological evidence is a dual origin model with 
two centres for the cultivation and dispersal of rice focused on the Middle Yangtze and the Lower 
Yangtze valleys (cf. [7] and [8]).  
 
References 
[1] D. Q. Fuller, J. van Etten, K. Manning, C. Castillo, E. J. Kingwell-Banham, A. R. Weisskopf, L. Qin, Y. 
Sato, R. Hijmans. The contribution of rice agriculture and livestock pastoralism to prehistoric methane 
levels: an archaeological assessment. The Holocene 21, 743–759 (2011). doi: 10.1177/0959683611398052  
[2] J. Steele. Radiocarbon dates as data: quantitative strategies for estimating colonization front speeds and 
event densities. Journal of Archaeological Science 37(8), 2017–2030 (2010). doi: 10.1016/j.jas.2010.03.007  
[3] R. Koenker. Quantile Regression. Cambridge, Cambridge University Press (2005).  
[4] J. A. Sethian. A fast marching level set method for monotonically advancing fronts. Proceedings of the 
National Academy Sciences 93(4), 1591–1595 (1996). 
[5] F. Silva F and J. Steele. Modeling boundaries between converging fronts in prehistory. Advances in 
Complex Systems 15(01n02), 1150005 (2012). doi: 10.1142/S0219525911003293  
[6] F. Silva and J. Steele. New methods for reconstructing geographical effects on dispersal rates and routes 
from large-scale radiocarbon databases. Journal of Archaeological Science 52: 609–620 (2014). doi: 
10.1016/j.jas.2014.04.021  
[7] D. Q. Fuller and L. Qin. Water management and labour in the origins and dispersal of Asian rice. World 
Archaeology 41(1), 88–111 (2009). doi: 10.1080/00438240802668321  
[8] D. Q. Fuller, T. Denham, M. Arroyo-Kalin, L. Lucas, C. J. Stevens, L. Qin, R. G. Allaby and M. D. 
Purugganan. Convergent evolution and parallelism in plant domestication revealed by an expanding 
archaeological record. Proceedings of the National Academy of Sciences 111(17), 6147–6152 (2014). doi: 
10.1073/pnas.1308937110  
 
 
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1


Modelling the geographical origin of rice cultivation in Asia using the Rice
Archaeological Database

Sinder, Michael

Burshtein, Zeev

Pelleg, Joshua

The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application
Reaction fronts and ambipolar chemical diffusion in oxide crystals 
 
M. Sinder1*, Z. Burshtein1, J. Pelleg1 
 
1Ben Gurion University of the Negev, P. O. Box 653, Beer Sheva 84105, Israel 
*micha@bgu.ac.il 
 
   We study theoretically the impact of oxygen diffusion in oxide crystals on the dynamic changes of 
metal dopants in the ionic state, and on the crystal conduction type.  The analysis invokes ambipolar 
diffusion for all participating species: oxygen vacancies, metal dopant, holes and electrons.  The 
species dynamics are demonstrated for an oxide of 8 eV energy gap, electron and hole diffusivities 
being 105 times larger than the oxygen vacancy one, and the dopant energy level being 1.0 eV above 
or 1.0 eV below the mid-gap.  We obtain linkage between the oxygen chemical diffusivity and the 
occurrence of a reaction front. The necessary condition is the existence of a sufficiently long interval, 
where a power dependence of the oxygen chemical diffusivity on the ambient oxygen pressure exists. 
  In our demonstrated system, prominent reaction fronts occur at very low and at very high ambient 
oxygen pressures. The fronts relate to the reversible MeMe MeM ′⎯→⎯′+
←×  reaction at the low 
pressures, and to the reversible ×←• ⎯→⎯+′ MeMe MhM  reaction at high pressures, where M marks 
the dopant metal, and Me marks an oxide lattice constituent metal.  
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Reaction fronts and ambipolar chemical diffusion in oxide crystals

Zhu, Qingyong

Moggridge, Geoffrey D.

D’Agostino, Carmine

The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application
A local composition model for the prediction of mutual diffusion 
coefficients in binary liquid mixtures from tracer diffusion coefficients 
 
Q. Zhu1*, G.D. Moggridge1, C. D’Agostino1 
 
1University of Cambridge, Cambridge, UK 
*qz246@cam.ac.uk 
 
A local composition model is proposed based on cluster diffusion theory for prediction of mutual 
diffusion coefficients ( ) in binary liquid mixtures from tracer diffusivities (  and ): 
 
(1) 
In this equation, the effect of strong molecular association in mutual diffusion is accounted by using 
the local mole fractions (  and ). and  are the activity coefficient and mole fraction. The 
thermodynamic correction factor in bracket is scaled by 0.64 on the basis of critical point theory with 
which the concentration-dependence of diffusion driven by the chemical potential gradient is assumed 
to be similar to the transient concentration fluctuations near the consolute point. 
Equation 1 was validated for prediction of mutual diffusion coefficients for binary liquid mixtures in a 
wide range of non-ideality. Particular interest lies in the prediction for mixtures containing one self-
associating component and on non-polar component for which most of the existing models can not 
accurately predict the mutual diffusion coefficients (example shown in Figure 1).  
 
Figure 1: Prediction of mutual diffusion coefficients of methanol-benzene at 25 0C 
Equation 2 in Figure 1, developed by [3], is expressed as: 
 
(2) 
References 
[1] P.A. Johnson, A.L. Babb: Self-diffusion in liquids. I. concentration dependence in ideal and non-ideal 
binary solutions. Journal of Physical Chemistry 60, 14–19 (1956).  
[2] C.W. Caldwell, A.L. Babb: Diffusion in the system methanol-benzene. Journal of Physical Chemistry 59, 
1113-1114 (1955). 
[3] J. Li, H. Liu, Y. Hu: A mutual diffusion coefficient model based on local composition. Fluid Phase Equilibria 
187-188, 193–208 (2001). 
 
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1


A local composition model for the prediction of mutual diffusion
coefficients in binary liquid mixtures from tracer diffusion coefficients

Not a member yet

Mortal creepers searching for a target

Reduction of p-Nitrophenol to p-Aminophenol over supported monometallic catalysts as a model reaction for mass-transfer investigations

Evaluation of CO2 diffusion on aluminum based metal organic frameworks

Application of Maxwell Stefan equations to characterize silicalite membranes

Transport of isopropanol in H-ZSM5 by impedance spectroscopy

Diffusion coefficient as a function of mass for globular macromolecules

Dynamics of linear and cyclic chains in two dimensions

Modelling the geographical origin of rice cultivation in Asia using the Rice Archaeological Database

Reaction fronts and ambipolar chemical diffusion in oxide crystals

A local composition model for the prediction of mutual diffusion coefficients in binary liquid mixtures from tracer diffusion coefficients

1,189

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