- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- UBC Undergraduate Research /
- Modelling Diffusion in a Physically Constrained System...
Open Collections
UBC Undergraduate Research
Modelling Diffusion in a Physically Constrained System : A Numerical Approach Jozefiak, Adam Daniel; Li, Jim Zhang Hao
Abstract
Diffusion has been described on a microscopic scale by Einstein as a probabilistic collision of particles. On a macroscale, diffusion has been thoroughly described by Fick’s laws. However, the solutions to Fick’s laws are limited to idealized physical systems. The aim of this experimental study is to provide a mathematical model for diffusion which incorporates both macroscopic and microscopic properties to effectively model diffusion in a geometrically constrained two-dimensional system. Based on macroscopic and microscopic properties, two-dimensional diffusion was modelled as a summation of equally probable paths of diffusion. The point source diffusion of hydrochloric acid in an arena with variable barrier dimensions was monitored continuously using a pH probe. The numerical solution of the mathematical model for each experimental condition was determined and the pre-exponential factor was fit to the measurements. The average pre-exponential value was determined for each experimental condition, and t-scores were calculated to compare the average pre-exponential values which were found to be statistically similar. This indicates that the proposed model is an accurate model as it predicts identical pre-exponential values between experimental conditions, accounting for all variants that it attempts to model. This model provides a bridge between the microscopic and macrcoscopic theoretical descriptions of diffusion that were independently postulated by Einstein and Fick. Applications of the model include the approximation of locations of leakage in hydraulic systems.
Item Metadata
Title |
Modelling Diffusion in a Physically Constrained System : A Numerical Approach
|
Creator | |
Date Issued |
2016-03-24
|
Description |
Diffusion has been described on a microscopic scale by Einstein
as a probabilistic collision of particles. On a macroscale, diffusion
has been thoroughly described by Fick’s laws. However, the solutions
to Fick’s laws are limited to idealized physical systems. The
aim of this experimental study is to provide a mathematical model
for diffusion which incorporates both macroscopic and microscopic
properties to effectively model diffusion in a geometrically
constrained two-dimensional system. Based on macroscopic and
microscopic properties, two-dimensional diffusion was modelled
as a summation of equally probable paths of diffusion. The point
source diffusion of hydrochloric acid in an arena with variable barrier
dimensions was monitored continuously using a pH probe. The
numerical solution of the mathematical model for each experimental
condition was determined and the pre-exponential factor was fit to
the measurements. The average pre-exponential value was determined
for each experimental condition, and t-scores were calculated
to compare the average pre-exponential values which were
found to be statistically similar. This indicates that the proposed
model is an accurate model as it predicts identical pre-exponential
values between experimental conditions, accounting for all variants
that it attempts to model. This model provides a bridge between the
microscopic and macrcoscopic theoretical descriptions of diffusion
that were independently postulated by Einstein and Fick. Applications
of the model include the approximation of locations of leakage
in hydraulic systems.
|
Subject | |
Genre | |
Type | |
Language |
eng
|
Series | |
Date Available |
2017-01-31
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0319147
|
URI | |
Affiliation | |
Campus | |
Citation |
Jozefiak, A. D., & Li, Z. H. (2016). Modelling Diffusion in a Physically Constrained System: A Numerical Approach. STEM Fellowship Journal, 2(1), 38-48.
|
Publisher DOI |
10.17975/sfj-2016-008
|
Peer Review Status |
Reviewed
|
Scholarly Level |
Undergraduate
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International