23.01.24 - Alessio Zaccone "Complex fluids in shear flow and other external fields"

Complex fluids in shear flow and other external fields

I will start from the fundamental (Smoluchowski) equations governing the dynamics of colloidal (Brownian) particles and/or molecules in shear flows for which an accurate solution at the two-body level has been found using the method of matched-asymptotics for both high and low Peclet numbers [1]. These solutions give access to the distorted pair correlation function and structure factor of colloidal suspensions as a function of shear rate/Peclet number. This solution can then be implemented into the integral equation theory of liquids to predict the pair correlation function and structure factor of dense colloids in shear flow, again in good agreement wtih numerics (Stokesian simulations) [2]. Possible shear-induced isotropic-to-inhomogeneous (e.g. laning) transitions à la Brazovskii are also predicted.

The same type of solutions can be used to predict the shear-induced aggregation of charge-stabilized colloidal particles thus extending the DLVO theory of colloidal stability to systems under shear flow [3], and to make predictions for crystal nucleation in shear flow [4] that have been recently verified experimentally in detail [5].

In the final part of the talk I will address the problem of how to extend the fluctuation-dissipation relations to systems in external fields (e.g. AC electric fields [6]) and shear flow [7], when both the tagged particle and the bath as well “respond” to the field. In both cases, new fluctuation-dissipation relations are derived from first principles using a Caldeira-Leggett Hamiltonian modified with terms that represent the external fields. Non-markovian memory in external fields appear to be the rule rather than the exception.

[1]  L. Banetta, A. Zaccone Physical review E 99, 052606 (2019); L. Banetta, A. Zaccone Colloid and Polymer Science 298, 761-771 (2020); S. Riva, L. Banetta, A. Zaccone Physical Review E 105 (5), 054606

[2] L. Banetta, F. Leone, C. Anzivino, M.S. Murillo, A Zaccone Physical Review E 106 (4), 044610 (2022)

[3] A. Zaccone, H. Wu, D. Gentili, and M. Morbidelli Phys. Rev. E 80, 051404 (2009)

[4] F. Mura and A. Zaccone Phys. Rev. E 93, 042803 (2016)

[5] R. Debuysschère, B. Rimez, A. Zaccone, and B. Scheid Cryst. Growth Des. 23, 7, 4979–4989 (2023)

[6] B. Cui and A. Zaccone Phys. Rev. E 97, 060102(R) (2018)

[7] S. Pelargonio and A. Zaccone Phys. Rev. E 107, 064102 (2023)