Date of Graduation


Document Type


Degree Type



Eberly College of Arts and Sciences



Committee Chair

Kenneth Showalter

Committee Co-Chair

Terry Gullion

Committee Member

Mikel Holcomb

Committee Member

Charles Jaffe

Committee Member

Justin Legleiter


In 1896, Raphael E. Liesegang discovered that precipitation reactions may produce striking precipi- tation rings and bands. More than a century later, propagating precipitation waves were discovered in similar reactions. The bands and rings discovered by Liesegang are static, but traveling precipitation waves exhibit complex spatiotemporal dynamics. Traveling waves are widespread and occur in both living and nonliving systems. Examples include calcium waves propagating through Xenopus laevis oocytes, cyclic AMP waves in colonies of Dictyostelium discordium cells, and spiral waves in propagating flames fronts. Recently, traveling waves were identified in a precipitation reaction involving AlCl3 and NaOH. The propagating precipitation waves observed in this reaction are the first of their kind to be reported. Since their discovery, other reactions have been shown to produce traveling precipitation waves. Examples of reactions that produce these waves are: NaAl(OH)4/HCl, GaCl3/NaOH, ZnCl 2/NaOH, and HgCl2/KI. In some configurations, propagating precipitation waves are remarkably similar to the propagating reaction-diffusion waves seen in the Belousov-Zhabotinsky (BZ) reaction. However, precipitation waves are distinctly different from reaction-diffusion waves, in both structure and dynamics.;A two-dimensional model is developed to characterize the behavior of precipitation waves in a cross-sectional configuration. The model is a modified sol-coagulation model that is based upon models of Liesegang bands and redissolution systems. The dynamics of precipitation waves is characterized in terms of growth and redissolution of a precipitation feature that travels through a migrating band of colloidal precipitate. Precipitation waves are fundamentally 3D in nature; thus, a 3D model is also developed. The 3D model refines the 2D model by identifying dominant processes and extending them to 3D. The 3D model is a general model of precipitation waves that it is capable of describing wave behavior in multiple precipitation systems.