Diffusion coefficient of a protein in a fluid membrane: numerical calculation

1985 ◽  
Vol 63 (1) ◽  
pp. 44-45 ◽  
Author(s):  
F. W. Wiegel ◽  
J. R. Heringa
Keyword(s):  
Diffusion Coefficient ◽  
Numerical Calculation ◽  
Asymptotic Formula ◽  
Effective Diffusion ◽  
Integral Membrane Protein ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Fluid Membrane ◽  
Parameter Values ◽  
Percent Relative Error

The drag force on an integral membrane protein is usually calculated with an asymptotic formula by Saffman. We have calculated this force by numerically solving the linearized Navier–Stokes equation. The results show that Saffman's formula is accurate within a few percent relative error for the usual range of parameter values. The mathematical equivalence of diffusion in an inhomogeneous membrane with the effective conduction of an inhomogeneous conductor is used to find a relation for the effective diffusion coefficient of a protein in an inhomogeneous membrane.

scholarly journals A new method for predicting transport properties of polar firn with respect to gases on the pore-space scale

2002 ◽  
Vol 35 ◽  
pp. 538-544 ◽  
Author(s):  
Johannes Freitag ◽  
Uwe Dobrindt ◽  
Josef Kipfstuhl
Keyword(s):  
Lattice Boltzmann ◽  
Diffusion Coefficients ◽  
Pore Space ◽  
Effective Diffusion ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Diffusive Transport ◽  
Navier Stokes Equation ◽  
The North ◽  
Effective Diffusion Coefficients

AbstractIn this study a powerful tool to investigate the permeabilities and effective diffusion coefficients of polar firn is presented using a combination of an experimental method for three-dimensional pore-structure reconstruction and two models to simulate advective and diffusive transports of gases through the pore space. the reconstruction follows a semi-automated digital analysis of serial surface sections. the simulations are based on a three-dimensional lattice Boltzmann formulation. They separately solve the Navier–Stokes equation and the diffusive transport equations. In a first application, effective diffusion coefficients and permeabilities are calculated from firn samples of a core drilled during the North Greenland Traverse 1993–95. the estimated relationships of diffusivity and permeability to the open porosity are expressed by power-law functions with exponents 2.1 and 3.4, respectively.

scholarly journals An Incompressible Polymer Fluid Interacting with a Koiter Shell

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Dominic Breit ◽  
Prince Romeo Mensah
Keyword(s):  
Moving Boundary ◽  
Classical Model ◽  
Elastic Shell ◽  
Planck Equation ◽  
Navier Stokes ◽  
Flexible Shell ◽  
Navier Stokes Equation ◽  
Shell System ◽  
Forward Equation ◽  
Polymer Fluid

AbstractWe study a mutually coupled mesoscopic-macroscopic-shell system of equations modeling a dilute incompressible polymer fluid which is evolving and interacting with a flexible shell of Koiter type. The polymer constitutes a solvent-solute mixture where the solvent is modelled on the macroscopic scale by the incompressible Navier–Stokes equation and the solute is modelled on the mesoscopic scale by a Fokker–Planck equation (Kolmogorov forward equation) for the probability density function of the bead-spring polymer chain configuration. This mixture interacts with a nonlinear elastic shell which serves as a moving boundary of the physical spatial domain of the polymer fluid. We use the classical model by Koiter to describe the shell movement which yields a fully nonlinear fourth order hyperbolic equation. Our main result is the existence of a weak solution to the underlying system which exists until the Koiter energy degenerates or the flexible shell approaches a self-intersection.

scholarly journals Effects of Salt Tracer Volume and Concentration on Residence Time Distribution Curves for Characterization of Liquid Steel Behavior in Metallurgical Tundish

Metals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 430
Author(s):  
Changyou Ding ◽  
Hong Lei ◽  
Hong Niu ◽  
Han Zhang ◽  
Bin Yang ◽  
...  
Keyword(s):  
Residence Time ◽  
Time Distribution ◽  
Residence Time Distribution ◽  
Mass Concentration ◽  
Distribution Curve ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Residence Time Distribution Curve ◽  
Tracer Solution ◽  
Time Distribution Curve

The residence time distribution (RTD) curve is widely applied to describe the fluid flow in a tundish, different tracer mass concentrations and different tracer volumes give different residence time distribution curves for the same flow field. Thus, it is necessary to have a deep insight into the effects of the mass concentration and the volume of tracer solution on the residence time distribution curve. In order to describe the interaction between the tracer and the fluid, solute buoyancy is considered in the Navier–Stokes equation. Numerical results show that, with the increase of the mass concentration and the volume of the tracer, the shape of the residence time distribution curve changes from single flat peak to single sharp peak and then to double peaks. This change comes from the stratified flow of the tracer. Furthermore, the velocity difference number is introduced to demonstrate the importance of the density difference between the tracer and the fluid.

Wavelet-distributed approximating functional method for solving the Navier-Stokes equation

1998 ◽  
Vol 115 (1) ◽  
pp. 18-24 ◽  
Author(s):  
G.W. Wei ◽  
D.S. Zhang ◽  
S.C. Althorpe ◽  
D.J. Kouri ◽  
D.K. Hoffman
Keyword(s):  
Stokes Equation ◽  
Functional Method ◽  
Navier Stokes ◽  
Navier Stokes Equation

scholarly journals Generalized Navier–Stokes Equations and Dynamics of Plane Molecular Media

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 288
Author(s):  
Alexei Kushner ◽  
Valentin Lychagin
Keyword(s):  
Carbon Dioxide ◽  
Internal Structure ◽  
Stokes Equation ◽  
Hydrogen Cyanide ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

Diffusion of Heavy Oil in SiO2 Model Catalyst and FCC Catalyst

2012 ◽  
Vol 550-553 ◽  
pp. 158-163 ◽  
Author(s):  
Zi Yuan Liu ◽  
Sheng Li Chen ◽  
Peng Dong ◽  
Xiu Jun Ge
Keyword(s):  
Diffusion Coefficient ◽  
Pore Size ◽  
Effective Diffusion Coefficient ◽  
Pore Diameter ◽  
Effective Diffusion ◽  
Model Catalyst ◽  
Average Pore ◽  
Diffusion Factor ◽  
Fcc Catalyst ◽  
Fcc Catalysts

Through the measured effective diffusion coefficients of Dagang vacuum residue supercritical fluid extraction and fractionation (SFEF) fractions in FCC catalysts and SiO2model catalysts, the relation between pore size of catalyst and effective diffusion coefficient was researched and the restricted diffusion factor was calculated. The restricted diffusion factor in FCC catalysts is less than 1 and it is 1~2 times larger in catalyst with polystyrene (PS) template than in conventional FCC catalyst without template, indicating that the diffusion of SFEF fractions in the two FCC catalysts is restricted by the pore. When the average molecular diameter is less than 1.8 nm, the diffusion of SFEF fractions in SiO2model catalyst which average pore diameter larger than 5.6 nm is unrestricted. The diffusion is restricted in the catalyst pores of less than 8 nm for SFEF fractions which diameter more than 1.8 nm. The tortuosity factor of SiO2model catalyst is obtained to be 2.87, within the range of empirical value. The effective diffusion coefficient of the SFEF fractions in SiO2model catalyst is two orders of magnitude larger than that in FCC catalyst with the same average pore diameter. This indicate that besides the ratio of molecular diameter to the pore diameter λ, the effective diffusion coefficient is also closely related to the pore structure of catalyst. Because SiO2model catalyst has uniform pore size, the diffusion coefficient can be precisely correlated with pore size of catalyst, so it is a good model material for catalyst internal diffusion investigation.

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