Hydrodynamic interactions between colloids in a wormlike micelle solution are memory-dependent, with a long-lived flow reversal after cessation that standard continuum models fail to capture.
On the causality and $K$-causality between measures
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abstract
Drawing from our earlier works on the notion of causality for nonlocal phenomena, we propose and study the extension of the Sorkin--Woolgar relation $K^+$ onto the space of Borel probability measures on a given spacetime. We show that it retains its fundamental properties of transitivity and closedness. Furthermore, we list and prove several characterizations of this relation, including the `nonlocal' analogue of the characterization of $K^+$ in terms of time functions. This generalizes and casts new light on our earlier results concerning the causal precedence relation $J^+$ between measures.
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Colloidal hydrodynamic interactions in viscoelastic fluids
Hydrodynamic interactions between colloids in a wormlike micelle solution are memory-dependent, with a long-lived flow reversal after cessation that standard continuum models fail to capture.