Microscopic origins of second normal stress difference in a colloidal gel under startup shear

To improve understanding of colloidal particle network physics during yielding, Brownian dynamics simulations incorporating multibody hydrodynamic interactions were performed to model colloidal gels and examine the relationship between microscopic particle dynamics and macroscopic stress responses, including normal stress differences. During shearing, shear and normal stresses exhibited overshoots at distinct strains, suggesting that each arises from a different microscopic mechanism in the yielding process. Statistical analyses using the number-weighted stress distribution and a screened bond orientation measure, motivated by rigidity theory, revealed that vertical alignment of bonds introduces an additional dynamic mechanism accompanied by larger local stress changes. Conventional analysis based on decomposition of the pair distribution function further supported these observations: net bond loss along the extensional axis is closely associated with bond rupture and dominates the shear stress response, whereas longer-lasting compression induces structural anisotropy and dominates the normal stress overshoot. Inspired by microscopic models of biopolymer networks, we proposed a phenomenological potential-energy metric that reasonably captures the origin of the normal stress overshoot. Taken together, this work provides particle-scale insight into how microstructural evolution and development of structural anisotropy are reflected in the shear and normal stress differences, which are governed by distinct dynamic mechanisms.