A suspension of elastic chains of small beads in a Newtonian fluid is a common model for a viscoelastic polymer solution. The configuration of these multibead chains is described by a distribution function that evolves according to a Liouville or Fokker–Planck equation. The evolution of these multibead-chain suspensions is described using a double bracket formulation with a Hamiltonian functional. The conservative part of the dynamics is described by a Poisson bracket, and the dissipative part by an additional symmetric bracket. We treat the configuration space of multibead chains as a higher order tangent bundle. Lifting the fluid velocity field to the bundle leads naturally to a semidirect product Lie–Poisson bracket for the conservative dynamics. The elastic stress exerted by the multibead chains on the fluid then follows directly from the same Hamiltonian functional that governs the internal dissipative mechanics of the multibead chains. For chains with three or more beads, the possible bending of the chain introduces an angular momentum flux that is absent for chains with two beads. This flux appear as an asymmetric elastic stress whose antisymmetric part is the divergence of a rank-3 tensor, as in the Cosserats’ theory of couple stresses in media with no internal angular momentum density. We investigate the possibility of an exact closure, passing from a distribution function description to a closed internal state variable description of the fluid suspension, and obtain some sufficient conditions for their existence. The resulting exactly closable models are generalisations of the upper-convected Maxwell model to Hookean bead–spring chains instead of Hookean bead–spring pairs.

小珠的弹性链在牛顿流体中的悬浮液是粘弹性聚合物溶液的常用模型。这些多珠链的构型由根据Liouville或Fokker-Planck方程演化的分布函数描述。使用具有汉密尔顿函数的双托架公式描述了这些多珠链悬浮液的演变。动力学的保守部分用泊松括号描述，而耗散部分用附加的对称括号描述。我们将多珠链的配置空间视为高阶切线束。将流体速度场提升到管束自然会导致保守动力学的半直接乘积李-泊松括号。然后，多珠链施加在流体上的弹性应力直接来自控制多珠链内部耗散力学的同一哈密顿函数。对于具有三个或更多珠子的链，链的可能弯曲会引入角动量通量，而对于具有两个珠子的链则不存在。该通量表现为非对称弹性应力，其反对称部分是3级张量的发散，就像Cosserats在无内部角动量密度的介质中的耦合应力理论中一样。我们研究了从流体分布的分布函数描述到内部状态变量描述的精确封闭的可能性，并为它们的存在获得了足够的条件。