A diffusing barrier creates a new universality class for interfacial growth

Research suggests that the surface properties of growing cell membranes and expanding bacterial colonies, for example, are fundamentally distinct.

Growing interfaces are dynamic boundaries - usually between two different phases of matter - which represent many nonequilibrium phenomena.

Almost all growing interfaces fall into the celebrated Kardar-Parisi-Zhang (KPZ) universality class. One feature of KPZ interfaces is that in one dimension the interface reaches a stationary state in which it has the statistical properties of a random walk:  the lateral width of the interface scales with the square root of its length.

A fascinating realisation of a growing interface is the lamellipodium, which is the leading edge of a growing mesh of actin filaments in a motile cell. The lamellipodium is an unusual growing interface in that it pushes against a constraining cell wall, producing a ratcheting effect, and enables the cell to move.

Inspired by the lamellipodium interacting with a cell wall, Justin Whitehouse (Condensed Matter CDT PhD student), Richard Blythe (Reader in Complexity Science) and Professor Martin Evans (Chair of Statistical Physics) have investigated the fundamental properties of an interface that is impeded by a diffusing barrier that either lies ahead of the interface (as in the case of the cell wall) or behind the interface (as in the case of a growing bacterial colony). When the diffusing barrier is ahead of the interface (and interacts with its peaks), they find the classic KPZ behaviour. The situation changes when the barrier is behind, interacting with the interfacial troughs:  this creates a new universality class where the interface is less rough than a random walk, scaling as the cube root of its length.

The paper was made the Editors' Suggestion in Physical Review Letters.