Wormlike micelles are self-assemblies of polymer chains that can break and recombine reversibly. In this paper, we derive a thermodynamically consistent two-species micro–macro model of wormlike micellar solutions by employing an energetic variational approach. The model incorporates a breakage and combination process of polymer chains into the classical micro–macro dumbbell model of polymeric fluids in a unified variational framework. We also study different maximum entropy closure approximations to the micro-macro model by “variation-then-closure” and “closure-then-variation” approaches. By imposing a proper dissipation in the coarse-grained level, the closure model, obtained by “closure-then-variation”, preserves the thermodynamical structure of both mechanical and chemical parts of the original system. Several numerical examples show that the closure model can capture the key rheological features of wormlike micellar solutions in shear flows.

蠕虫状胶束是聚合物链的自组装体，可断裂并可逆地重组。在本文中，我们通过采用能量变分方法，得出了蠕虫状胶束溶液的热力学一致的两种物种微观模型。该模型在统一的变分框架中将聚合物链的断裂和结合过程纳入了经典的聚合物流体的微-宏哑铃模型中。我们还通过“先变后闭”和“先变后闭”的方法研究了微宏模型的不同最大熵闭合近似。通过在粗粒度水平上施加适当的耗散，通过“先闭合后变化”获得的闭合模型可以保留原始系统的机械和化学部分的热力学结构。