Stability analysis of the 4th order Runge Kutta method in application to colloidal particle interactions

Colloidal particles have a wide range of industrial applications. This study is focused on the application to microstructured materials and the impact of external compressive forces on particles. Currently, in the large throughput manufacturing of microstructured materials, problems such as cracking are caused by these external forces. Numerical methods can be used to generate particle positions and obtain a better understanding of particle interactions under different conditions. The aim of this study was to obtain a better understanding of the stability limits of using the 4th order Runge Kutta method. By introducing the external forces as auxiliary functions, we were able to generate exact analytic solutions satisfying arbitrary hydrodynamic and interaction forces. This allowed rigorous comparison of the theoretical stability limits and the observed stability limits on time step. We found excellent agreement with the predicted and observed results.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Chemical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Velagala, Sindhuja

Contributors dc:contributor

• Higdon, Jonathan J.L.

• Colloidal Particles
• Stability
• 4th Order Runge Kutta

Statement dc:rights

• Copyright 2014 Sindhuja Velagala

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/72750

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/72750