Time-dependent shear response in dilute suspensions

Soft matter is ubiquitous in our daily lives and describes materials that aren`t really liquid or solid, but somewhere in between. The defining property is that these can easily be mechanically deformed, such as are gels, foams and emulsions. The soft matter research area includes condensed matter physics, chemistry, materials science, and engineering. The central question for such materials, as in this research project, is the flow behavior under shear. Whereas in Newtonian fluids the shear stress is proportional to the shear rate, many soft-matter systems are characterized by nonlinear flow curves. Well-known examples of non-Newtonian liquids are ketchup, which typically either does not flow at all and gets stuck in the bottle, or pours out all at once. The unusual behavior of soft materials is due to their structure, particles a few 100nm in size are in solution in a liquid. The arrangement of the particles changes under shear and counteracts the driving forces. In principle, the resulting shear stress can be calculated from the microscopic structure. In general, however, this is a formidable problem and requires computer simulations. However, analytical progress can be made for dilute systems, since then only pairs of two particles have to be considered, whereas the probability for pairs of 3 and higher can be neglected. This is exactly where the research project comes in. We want to determine the time-dependent shear stress in response to a shear rate that is suddenly imposed but is then time-independent. Unfortunately, the two-particle problem does not allow for a fully analytical solution either, and direct numerical methods become inefficient or imprecise for small or large shear rates. However, there is a procedure (boundary element method) which allows the problem to be reduced to the region where two particles touch, instead of working out the solution for the whole space. This method is novel for the shear problem and the challenge is to implement it with great numerical accuracy. For small shear rates one expects that it is sufficient to calculate to linear order only, for which the result is known analytically. However, the question arises as to what small really means here, i.e. small compared to what? For similar problems it has been shown that the behavior at even the smallest rates differs qualitatively from the linear prediction for long time scales, i.e. the range of validity of the prediction shrinks to zero. A central research question is now to be clarified, whether this scenario can be transferred to the case of dilute solutions under time-dependent shearing and which time scales are relevant in the problem.