Diffusion in Biological Systems

Drug Delivery ◽  
2001 ◽  
Author(s):  
W. Mark Saltzman
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Molecular Diffusion ◽  
Biological Systems ◽  
Biological Tissues ◽  
Solute Concentration ◽  
Diffusion Resistance ◽  
Experimental Conditions ◽  
Composition Structure ◽  
Reliable Mechanism

Drug diffusion is an essential mechanism for drug dispersion throughout biological systems. Diffusion is fundamental to the migration of agents in the body and, as we will see in Chapter 9, diffusion can be used as a reliable mechanism for drug delivery. The rate of diffusion (i.e., the diffusion coefficient) depends on the architecture of the diffusing molecule. In the previous chapter a hypothetical solute with a diffusion coefficient of 10-7 cm2/s was used to describe the kinetics of diffusional spread throughout a region. Therapeutic agents have a multitude of sizes and shapes and, hence, diffusion coefficients vary in ways that are not easily predictable. Variability in the properties of agents is not the only difficulty in predicting rates of diffusion. Biological tissues present diverse resistances to molecular diffusion. Resistance to diffusion also depends on architecture: tissue composition, structure, and homogeneity are important variables. This chapter explores the variation in diffusion coefficient for molecules of different size and structure in physiological environments. The first section reviews some of the most important methods used to measure diffusion coefficients, while subsequent sections describe experimental measurements in media of increasing complexity: water, membranes, cells, and tissues. Diffusion coefficients are usually measured by observing changes in solute concentration with time and/or position. In most situations, concentration changes are monitored in laboratory systems of simple geometry; equally simple models (such as the ones developed in Chapter 3) can then be used to determine the diffusion coefficient. However, in biological systems, diffusion almost always occurs in concert with other phenomena that also influence solute concentration, such as bulk motion of fluid or chemical reaction. Therefore, experimental conditions that isolate diffusion—by eliminating or reducing fluid flows, chemical reactions, or metabolism—are often employed. Certain agents are eliminated from a tissue so slowly that the rate of elimination is negligible compared to the rate of dispersion. These molecules can be used as “tracers” to probe mechanisms of dispersion in the tissue, provided that elimination is negligible during the period of measurement. Frequently used tracers include sucrose [1, 2], iodoantipyrene [3], inulin [1], and size-fractionated dextran [3, 4].

scholarly journals Specific features of eddy turbulence in the turbopause region

2014 ◽  
Vol 32 (4) ◽  
pp. 431-442 ◽  
Author(s):  
M. N. Vlasov ◽  
M. C. Kelley
Keyword(s):  
Diffusion Coefficient ◽  
Heat Transport ◽  
Diffusion Coefficients ◽  
Transport Coefficient ◽  
Molecular Diffusion ◽  
Eddy Diffusion ◽  
Cooling Rates ◽  
Eddy Diffusion Coefficient ◽  
Eddy Heat Transport ◽  
The Mean

Abstract. The turbopause region is characterized by transition from the mean molecular mass (constant with altitude) to the mean mass (dependent on altitude). The former is provided by eddy turbulence, and the latter is induced by molecular diffusion. Competition between these processes provides the transition from the homosphere to the heterosphere. The turbopause altitude can be defined by equalizing the eddy and molecular diffusion coefficients and can be located in the upper mesosphere or the lower thermosphere. The height distributions of chemical inert gases very clearly demonstrate the transition from turbulent mixing to the diffusive separation of these gases. Using the height distributions of the chemical inert constituents He, Ar, and N2 given by the MSIS-E-90 model and the continuity equations, the height distribution of the eddy diffusion coefficient in the turbopause region can be inferred. The eddy diffusion coefficient always strongly reduces in the turbopause region. According to our results, eddy turbulence above its peak always cools the atmosphere. However, the cooling rates calculated with the eddy heat transport coefficient equaled to the eddy diffusion coefficient were found to be much larger than the cooling rates corresponding to the neutral temperatures given by the MSIS-E-90 model. The same results were obtained for the eddy diffusion coefficients inferred from different experimental data. The main cause of this large cooling is the very steep negative gradient of the eddy heat transport coefficient, which is equal to the eddy diffusion coefficient if uniform turbulence takes place in the turbopause region. Analysis of wind shear shows that localized turbulence can develop in the turbopause region. In this case, eddy heat transport is not so effective and the strong discrepancy between cooling induced by eddy turbulence and cooling corresponding to the temperature given by the MSIS-E-90 model can be removed.

Diffusion Coefficients from Capillary Flow

1963 ◽  
Vol 3 (03) ◽  
pp. 256-266 ◽  
Author(s):  
H.R. Bailey ◽  
W.B. Gogarty
Keyword(s):  
Differential Equation ◽  
Diffusion Coefficient ◽  
Numerical Solution ◽  
Diffusion Coefficients ◽  
Molecular Diffusion ◽  
Capillary Flow ◽  
Molecular Diffusion Coefficient ◽  
Flow Method ◽  
And Diffusion ◽  
Flow Experiments

Abstract Methods are presented for determining molecular diffusion coefficients by using data from capillary flow experiments. These methods are based on a numerical solution (presented in a previous paper) of the partial differential equation describing the combined mechanisms of flow and diffusion. Results from this numerical solution are given and compared with the approximate analytical solution of G. I. Taylor. The numerical solution is valid over a much larger time range. These methods are applied to experimental results for the fluid pairs water-potassium permanganate solution and amyl acetateorthoxylene. Both of these fluid pairs have approximately equal densities and viscosities. Graphical and numerical techniques are presented for deters mining diffusion coefficients from the flow data. Values obtained by these techniques are compared with values obtained by other methods. Introduction The molecular diffusion coefficient is known to be a variable in determining the amount of mixing in a miscible displacement process. The effect of molecular diffusion on dispersion in longitudinal flow through porous media has been examined by different investigators. These investigators concluded that at low velocities of flow, the amount of dispersion is approximately proportional to the molecular diffusion coefficient. The influence of diffusion on fingering, channeling, and overriding has been mentioned by other investigators. Recent studies have been made on the effects of molecular diffusion in connection with the problem of gravity segregation. Many different methods have been developed for the experimental determination of molecular diffusion coefficients. These methods differ mainly according to boundary conditions selected and analytical procedures used. Nevertheless, all of these methods have the condition in common that the bulk fluids in which diffusion is occurring are stationary with respect to each other. In connection with a series of papers on mixing in capillary flow, Taylor suggested the use of a flow method for determining molecular diffusion coefficients. Additional studies have been conducted on miscible displacements in capillary tubes, but the data from these studies were not used for the specific purpose of determining diffusion coefficients. The flow method proposed by Taylor results in a single value of the diffusion coefficient for the fluid pair used in the displacement experiments. This single value represents the true value for the fluid pair when the diffusion coefficient is independent of concentration. If the diffusion coefficient is a function of concentration, the single value obtained by the flow method gives an average value for the coefficient of the fluid pair. These average values are based on diffusion taking place over the entire range of concentration, i.e., from 0 per cent of one fluid to 100 per cent of that same fluid. In field applications of the miscible displacement process, gradients occur over the same range of concentration as are found in the displacements in capillary tubes. Molecular diffusion coefficients obtained from the capillary flow method should, therefore, be especially relevant to field operations. This investigation was undertaken to evaluate the feasibility of obtaining molecular diffusion coefficients from capillary flow experiments. In making this evaluation, diffusion coefficients were first determined for two systems from data obtained in capillary flow experiments. These values of the diffusion coefficient were then compared to values obtained by other methods. MIXING IN CAPILLARY FLOW-THEORETICAL The theoretical basis for determining molecular diffusion coefficients from capillary flow experiments is the partial differential equation relating the mechanisms of flow and diffusion. SPEJ P. 256^

Determination of Concentration Dependent Diffusion Coefficients of Carbon in Expanded Austenite

2008 ◽  
Vol 273-276 ◽  
pp. 306-311 ◽  
Author(s):  
Thomas S. Hummelshøj ◽  
Thomas L. Christiansen ◽  
Marcel A.J. Somers
Keyword(s):  
Diffusion Coefficient ◽  
Weight Change ◽  
Diffusion Coefficients ◽  
Input Data ◽  
Accurate Determination ◽  
Experimental Conditions ◽  
Thin Foils ◽  
Expanded Austenite ◽  
Aisi 316

In the present paper various experimental procedures to experimentally determine the concentration dependent diffusion coefficient of carbon in expanded austenite are evaluated. To this end thermogravimetric carburization was simulated for various experimental conditions and the evaluated composition dependent diffusivity of carbon derived from the simulated experiments was compared with the input data. The most promising procedure for an accurate determination is shown to be stepwise gaseous carburizing of thin foils in a gaseous atmosphere; the finer the stepsize, the more accurate the approximation of the diffusivity. Thermogravimetry was applied to continuously monitor the weight change of thin foils of AISI 316 during carburizing in CO-H2 gas mixtures for one of the simulated experimental procedures.

Biological Agent Detection Using Optical Diffusometry Methods

2006 ◽  
Author(s):  
Aloke Kumar ◽  
Venu Gorti ◽  
Steve Wereley
Keyword(s):  
Diffusion Coefficient ◽  
Constant Temperature ◽  
Particle Tracking ◽  
Diffusion Coefficients ◽  
Pathogen Detection ◽  
Biological Agent ◽  
Optical Traps ◽  
Hydrodynamic Drag ◽  
Experimental Conditions ◽  
Particle Tracking Algorithm

Biological agent detection has captured the attention of many researchers over the last few years. The present research explores the possibility of directly measuring the diffusion coefficients of sub-micron particles as a means of pathogen detection. At a constant temperature, the diffusion coefficient is simply a function of the drag on the particle. If the particles are functionalized with antibodies against a specific analyte and introduced into a sample containing that analyte, binding of the analyte with the particles will increase the particles' hydrodynamic drag. This results in a decrease in diffusion, which is measured by a particle tracking algorithm. The reduction in diffusion is correlated with the amount of analyte present. Sensitivity to experimental conditions is also explored and it is shown that alternate methods like optical traps provide an even better technique for biological agent detection.

Diffusion and Drug Dispersion

Drug Delivery ◽  
2001 ◽  
Author(s):  
W. Mark Saltzman
Keyword(s):  
Statistical Physics ◽  
Molecular Diffusion ◽  
Bulk Composition ◽  
Mass Conservation ◽  
Biological Tissues ◽  
Solute Concentration ◽  
Conservation Equations ◽  
Drug Molecules ◽  
Molecular Movement ◽  
Typical Cell

Most biological processes occur in an environment that is predominantly water: a typical cell contains 70-85% water and the extracellular space of most tissues is 99%. Even the brain, with its complex arrangement of cells and myelinated processes, is ≈ 80% water. Drug molecules can be introduced into the body in a variety of ways; the effectiveness of drug therapy depends on the rate and extent to which drug molecules can move through tissue structures to reach their site of action. Since water serves as the primary milieu for life processes, it is essential to understand the factors that determine rates of molecular movement in aqueous environments. As we will see, rates of diffusive transport of molecules vary among biological tissues within an organism, even though the bulk composition of the tissues (i.e., their water content) may be similar. The section begins with the random walk, a useful model from statistical physics that provides insight into the kinetics of molecular diffusion. From this starting point, the fundamental relationship between diffusive flux and solute concentration, Fick’s law, is described and used to develop general mass-conservation equations. These conservation equations are essential for analysis of rates of solute transport in tissues. Molecules that are initially localized within an unstirred vessel will spread throughout the vessel, eventually becoming uniformly dispersed. This process, called diffusion, occurs by the random movement of individual molecules; molecular motion is generated by thermal energy.

ANALYSIS OF SUGAR EXTRACTION KINETICS WITH CONCENTRATION-DEPENDENT DIFFUSION COEFFICIENT

2020 ◽  
Author(s):  
Е.Г. СТЕПАНОВА ◽  
С.Е. КОШЕВАЯ
Keyword(s):  
Diffusion Coefficient ◽  
Sherwood Number ◽  
Diffusion Coefficients ◽  
Molecular Diffusion ◽  
Sucrose Concentration ◽  
Linear Equations ◽  
Nonlinear Problems ◽  
Extraction Process ◽  
Nonlinear Dependence ◽  
Nonlinearity Parameter

Приведен численный анализ данных экстрагирования сахарозы и установлена нелинейная зависимость коэффициента внутренней диффузии от концентрации сахарозы D = D(С). Рассмотрена возможность прогнозирования диффузионных свойств стружки в процессе экстрагирования при наложении термических и электрохимических воздействий, что позволит получить диффузионные соки с заданными параметрами чистоты соков 82–84% и минимальные потери сахара в жоме – 0,35%. Для решения второго закона Фика при определенных начальных и граничных условиях построена математическая модель. Приведены методика и результаты расчетов коэффициентов диффузии сахарозы для свекловичной стружки в форме пластины. Проанализированы кинетические зависимости значений коэффициентов молекулярной диффузии от концентрации сахарозы при значениях параметра нелинейности от 0,07 до 148,4. При анализе результатов численного эксперимента концентрационная зависимость коэффициента диффузии аппроксимирована в виде линейной комбинации полиномов Лежандра. Показано, что вблизи состояния равновесия процесс описывается линейными уравнениями. Получена графическая зависимость числа Шервуда от числа Фурье Sh = f(Fо). Установлено, что для решения линейных и нелинейных задач внутреннего массопереноса число Шервуда асимптотически приближается к Sh ® р2/2. A numerical analysis of sucrose extracting data is given and a nonlinear dependence of the internal diffusion coefficient on the sucrose concentration D = D(C) is established. The possibility of predicting the diffusion properties of chips in the extraction process when applying thermal and electrochemical influences is considered, which will allow to obtain diffusion juices with the specified parameters of juice purity of 82–84% and minimum sugar loss in the pulp – 0,35%. A mathematical model is constructed to solve the second Fick’s law under certain initial and boundary conditions. The method and results of calculations of sucrose diffusion coefficients for beet chips in the form of a plate are given. The kinetic dependences of the values of the molecular diffusion coefficients on the sucrose concentration are analyzed for the values of the nonlinearity parameter from 0,07 to 148,4. When analyzing the results of a numerical experiment, the concentration dependence of the diffusion coefficient is approximated as a linear combination of Legendre polynomials. It is shown that the process is described by linear equations near the equilibrium state. A graphical dependence of the Sherwood number on the Fourier number Sh = f(Fo) is obtained. It is found that for solving linear and nonlinear problems of internal mass transfer, the Sherwood number asymptotically approaches Sh > р2/2.

scholarly journals Determination of Diffusion Coefficients from Observations on Grenade Glow Clouds

1963 ◽  
Vol 16 (4) ◽  
pp. 490 ◽  
Author(s):  
ER Johnson ◽  
KH Lloyd
Keyword(s):  
Diffusion Coefficient ◽  
Theoretical Model ◽  
Gaussian Distribution ◽  
Diffusion Coefficients ◽  
Molecular Diffusion ◽  
Particle Density ◽  
Altitude Range ◽  
Explosion Products ◽  
Thin Cloud

Glows have been observed at Woomera when grenades ejected from Skylark rockets have been detonated in the altitude range 90-170 km. Using results obtained from these glows by a special scanning photometer located on the ground, an estimate has been made of the diffusion coefficient in the region 120-160 km. The theoretical model which is used to describe the behaviour of the explosion products incorporates the assumptions of molecular diffusion, a Gaussian distribution of particle density, and an optically thin cloud. The effects of consumption of the cloud particles are included in the model.

scholarly journals Effect of Modification on the Fluid Diffusion Coefficient in Silica Nanochannels

Molecules ◽  
2021 ◽  
Vol 26 (13) ◽  
pp. 4030
Author(s):  
Gengbiao Chen ◽  
Zhiwen Liu
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Surface Effect ◽  
Bulk Water ◽  
Self Diffusion ◽  
Average Diffusion Coefficient ◽  
Average Diffusion ◽  
Chain Lengths ◽  
Fluid Diffusion ◽  
Self Diffusion Coefficient

The diffusion behavior of fluid water in nanochannels with hydroxylation of silica gel and silanization of different modified chain lengths was simulated by the equilibrium molecular dynamics method. The diffusion coefficient of fluid water was calculated by the Einstein method and the Green–Kubo method, so as to analyze the change rule between the modification degree of nanochannels and the diffusion coefficient of fluid water. The results showed that the diffusion coefficient of fluid water increased with the length of the modified chain. The average diffusion coefficient of fluid water in the hydroxylated nanochannels was 8.01% of the bulk water diffusion coefficient, and the diffusion coefficients of fluid water in the –(CH2)3CH3, –(CH2)7CH3, and –(CH2)11CH3 nanochannels were 44.10%, 49.72%, and 53.80% of the diffusion coefficients of bulk water, respectively. In the above four wall characteristic models, the diffusion coefficients in the z direction were smaller than those in the other directions. However, with an increase in the silylation degree, the increased self-diffusion coefficient due to the surface effect could basically offset the decreased self-diffusion coefficient owing to the scale effect. In the four nanochannels, when the local diffusion coefficient of fluid water was in the range of 8 Å close to the wall, Dz was greater than Dxy, and beyond the range of 8 Å of the wall, the Dz was smaller than Dxy.

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