Abstract
We demonstrate that the spatial correlations of microscopic stresses in 2D model colloidal gels obtained in computer simulations can be quantitatively described by the predictions of a theory for emergent elasticity of pre-stressed solids (vector charge theory). By combining a rigidity analysis with the characterization provided by the stress correlations, we show that the theoretical predictions are able to distinguish rigid from floppy gels, and quantify that distinction in terms of the size of a pinch-point singularity emerging at large length scales, which, in the theory, directly derives from the constraints imposed by mechanical equilibrium on the internal forces. We also use the theoretical predictions to investigate the coupling between stresstransmission and rigidity, and we explore the possibility of a Debye-like screening mechanism that would modify the theory predictions below a characteristic length scale.
The loss of rigidity in particulate gels can be quantified by the disappearance of a characteristic pinch-point singularity in the gel stress-stress correlation function.