Stirring a Cahn-Hilliard fluid in moving microdroplets

Biochemistry within living eukaryotic cells occurs in dynamic heterogeneous fluid environments containing macromolecules such as proteins, nucleic acids and sugars; most \textit{in-vitro} biochemical studies in dilute aqueous solutions do not capture this chemical and morphological complexity. Here, as an \textit{in-vitro} model for \textit{in-vivo} cellular environments, we investigate the dynamics of a phase separating aqueous polymer mixture within small moving droplets. We dispense aqueous mixtures of poly(ethylene glycol) (PEG) and dextran as droplets carried by an immiscible fluorinated oil at a microfluidic T-junction, and use high-speed optical microscopic imaging to observe dynamic phase behavior. In the static case, for off-critical compositions, this mixture separates via a spinodal mechanism into two phases- a PEG-rich phase and a dextran-rich phase. For moving drops, the polymer mixture exhibits a near continuum of flow and composition-dependent phase morphologies, from the `unmixed' static morphology to complex percolated morphologies resembling \textit{in vivo} cellular environments. We compare our measurements to previous theoretical and numerical studies of binary fluid mixing based on advective Cahn-Hilliard formulations.