Complex or structured fluids—such as granular media, emulsions, wormlike micelles, and even metals under certain conditions—can behave as solids or liquids, depending on the way they are deformed. These materials display complex flow behavior near the solid-liquid transition, and it is often impossible to capture the flow behavior with continuum models that consider only “local” information about the material stress state.
Instead, one must also consider “non-local” effects when predicting flow, as flow in one location is also determined by how the material flows elsewhere. To capture these non-local effects in continuum models, two components are necessary: (1) stress or strain gradients, which distribute information across some spatial extent, and (2) the length scale over which these fields work. Even after these two pieces are determined, there still remains the additional question of what microscopic physics causes them.
In this Research Topic, we aim to bring together mini-reviews or perspectives on the relevance and state of the art of non-local modeling in different disciplines. The articles should touch upon any of the following content: what kind of gradient field modeling has been shown to be effective or useful? How to determine the length scale for the gradient fields? To gain insights into non-local modeling, which types of continuous or discontinuous flows can be considered? What are possible microscopic mechanisms that determine non-local features? What are the open experimental, numerical and theoretical challenges in this broad but coherent theme?
Complex or structured fluids—such as granular media, emulsions, wormlike micelles, and even metals under certain conditions—can behave as solids or liquids, depending on the way they are deformed. These materials display complex flow behavior near the solid-liquid transition, and it is often impossible to capture the flow behavior with continuum models that consider only “local” information about the material stress state.
Instead, one must also consider “non-local” effects when predicting flow, as flow in one location is also determined by how the material flows elsewhere. To capture these non-local effects in continuum models, two components are necessary: (1) stress or strain gradients, which distribute information across some spatial extent, and (2) the length scale over which these fields work. Even after these two pieces are determined, there still remains the additional question of what microscopic physics causes them.
In this Research Topic, we aim to bring together mini-reviews or perspectives on the relevance and state of the art of non-local modeling in different disciplines. The articles should touch upon any of the following content: what kind of gradient field modeling has been shown to be effective or useful? How to determine the length scale for the gradient fields? To gain insights into non-local modeling, which types of continuous or discontinuous flows can be considered? What are possible microscopic mechanisms that determine non-local features? What are the open experimental, numerical and theoretical challenges in this broad but coherent theme?