We systematically explore near equilibrium, flow-driven, and flow-activity coupled dynamics of polar active liquid crystals using a continuum model. Firstly, we re-derive the hydrodynamic model to ensure the thermodyn...We systematically explore near equilibrium, flow-driven, and flow-activity coupled dynamics of polar active liquid crystals using a continuum model. Firstly, we re-derive the hydrodynamic model to ensure the thermodynamic laws are obeyed and elastic stresses and forces are consistently accounted. We then carry out a linear stability analysis about constant steady states to study near equilibrium dynamics around the steady states, revealing long-wave instability inherent in this model system and how active parameters in the model affect the instability. We then study model predictions for one- dimensional （1D） spatial-temporal structures of active liquid crystals in a channel subject to physical boundary conditions. We discuss the model prediction in two selected regimes, one is the viscous stress dominated regime, also known as the flow-driven regime, while the other is the full regime, in which all active mechanisms are included. In the viscous stress dominated regime, the polarity vector is driven by the prescribed flow field. Dynamics depend sensitively on the physical boundary condition and the type of the driven flow field. Bulk-dominated temporal periodic states and spatially homogeneous states are possible under weak anchoring conditions while spatially inhomogeneous states exist under strong anchoring conditions. In the full model, flow-orientation interaction generates a host of planar as well as out-of-plane spatial-temporal structures related to the spontaneous flows due to the molecular self-propelled motion. These results provide contact with the recent literature on active nematic suspensions. In addition, symmetry breaking pattems emerge as the additional active viscous stress due to the polarity vector is included in the force balance. The inertia effect is found to limit the long-time survival of spatial structures to those with small wave numbers, i.e., an asymptotic coarsening to long wave structures. A rich set of mechanisms for generating and limiting the flow structures as well as the spatial-temporal structures predicted by the model are displayed.展开更多
We merge classical kinetic theories [M. Doi and S. F. Edwards, The Theoryof Polymer Dynamics, 1986] for viscous dispersions of rigid rods, extended to semi-flexibility [A. R. Khokhlov and A. N. Semenov, Macromolecules...We merge classical kinetic theories [M. Doi and S. F. Edwards, The Theoryof Polymer Dynamics, 1986] for viscous dispersions of rigid rods, extended to semi-flexibility [A. R. Khokhlov and A. N. Semenov, Macromolecules, 17 (1984), pp. 2678-2685], and for Rouse flexible chains to model the hydrodynamics of polymer nano-rodcomposites (PNCs). A mean-field potential for the polymer-rod interface provides thekey coupling between the two phases. We restrict this first study to two-dimensionalconformational space. We solve the coupled set of Smoluchowski equations for threebenchmark experiments. First we explore how rod semi-flexibility and the polymer-rod interface alter the Onsager equilibrium phase diagram. Then we determine mon-odomain phase behavior of PNCs for imposed simple elongation and shear, respec-tively. These results inform the effects that each phase has on the other as parametricstrengths of the interactions are varied in the context of the most basic rheological ex-periments.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.DMS-1200487,DMR-1122483,and NIH 2R01GM078994-05A1)the Air Force Office of Scientific Research(AFOSR)(Grant No.FA9550-12-1-0178)the Army Research Office(Grant Nos.ARO-12-60317-MS and SC EPSCoR GEAR(CI and CRP))
文摘We systematically explore near equilibrium, flow-driven, and flow-activity coupled dynamics of polar active liquid crystals using a continuum model. Firstly, we re-derive the hydrodynamic model to ensure the thermodynamic laws are obeyed and elastic stresses and forces are consistently accounted. We then carry out a linear stability analysis about constant steady states to study near equilibrium dynamics around the steady states, revealing long-wave instability inherent in this model system and how active parameters in the model affect the instability. We then study model predictions for one- dimensional （1D） spatial-temporal structures of active liquid crystals in a channel subject to physical boundary conditions. We discuss the model prediction in two selected regimes, one is the viscous stress dominated regime, also known as the flow-driven regime, while the other is the full regime, in which all active mechanisms are included. In the viscous stress dominated regime, the polarity vector is driven by the prescribed flow field. Dynamics depend sensitively on the physical boundary condition and the type of the driven flow field. Bulk-dominated temporal periodic states and spatially homogeneous states are possible under weak anchoring conditions while spatially inhomogeneous states exist under strong anchoring conditions. In the full model, flow-orientation interaction generates a host of planar as well as out-of-plane spatial-temporal structures related to the spontaneous flows due to the molecular self-propelled motion. These results provide contact with the recent literature on active nematic suspensions. In addition, symmetry breaking pattems emerge as the additional active viscous stress due to the polarity vector is included in the force balance. The inertia effect is found to limit the long-time survival of spatial structures to those with small wave numbers, i.e., an asymptotic coarsening to long wave structures. A rich set of mechanisms for generating and limiting the flow structures as well as the spatial-temporal structures predicted by the model are displayed.
基金This research has been supported in part by the Air Force Office of Scientific Research,Air Force Materials Command,USAF,under grant number FA9550-06-1-0063,FA9550-08-1-0107 and the National Science Foundation through grants DMS-0605029,0626180,0548511 and 0604891,0724273 the Army Research Office contract 47089-MS-SR,and NASA URETI BIMat award No.NCC-1-0203.
文摘We merge classical kinetic theories [M. Doi and S. F. Edwards, The Theoryof Polymer Dynamics, 1986] for viscous dispersions of rigid rods, extended to semi-flexibility [A. R. Khokhlov and A. N. Semenov, Macromolecules, 17 (1984), pp. 2678-2685], and for Rouse flexible chains to model the hydrodynamics of polymer nano-rodcomposites (PNCs). A mean-field potential for the polymer-rod interface provides thekey coupling between the two phases. We restrict this first study to two-dimensionalconformational space. We solve the coupled set of Smoluchowski equations for threebenchmark experiments. First we explore how rod semi-flexibility and the polymer-rod interface alter the Onsager equilibrium phase diagram. Then we determine mon-odomain phase behavior of PNCs for imposed simple elongation and shear, respec-tively. These results inform the effects that each phase has on the other as parametricstrengths of the interactions are varied in the context of the most basic rheological ex-periments.
