论文标题
简单介电流体的连续模型：基于密度和连续力学方法之间的一致性
Continuum model of the simple dielectric fluid: Consistency between density based and continuum mechanics methods
论文作者
论文摘要
极性流体的基本连续体模型看似简单。自由能积分由四个术语组成：极化与外场的耦合，诱导的电场的静电能与自身相互作用以及在极化中储存的极化能二次。密度的局部功能解释了流体的机械状态。被视为数量密度和极化的非平衡自由能函数，在麦克斯韦场方程的约束下，这两种密度最小化应导致正确的平衡态。另一种选择是一种连续力学方法，其中机械自由度扩展到完全变形。我们表明，连续机电方法导致了力平衡方程，该方程与密度功能平衡方程一致。连续力学程序的要求更高。增益是由总能量变形得出的明确定义的压力张量。这解决了从力密度的整合获得的压力张量的不确定性问题，这是基于密度的热力学的常规方法。我们的推导基于Ericksen开发的变分静电方法（Arch。Mech。Anal。{\ BF 183} 299（2007））。
The basic continuum model for polar fluids is deceptively simple. The free energy integral consists of four terms: The coupling of polarization to an external field, the electrostatic energy of the induced electric field interacting with itself and the stored polarization energy quadratic in the polarization. A local function of density accounts for the mechanical state of the fluid. Viewed as a non-equilibrium free energy functional of number density and polarization, minimization in these two densities under constraints of the Maxwell field equations should lead the correct equilibrium state. The alternative is a continuum mechanics approach in which the mechanical degree of freedom is extended to full deformation. We show that the continuum electromechanics method leads to a force balance equation which is consistent with the density functional equilibrium equation. The continuum mechanics procedure is significantly more demanding. The gain is a well defined pressure tensor derived from deformation of total energy. This resolves the issue of the uncertainty in the pressure tensor obtained from integration of the force density, which is the conventional method in density based thermomechanics. Our derivation is based on the variational electrostatics approach developed by Ericksen (Arch. Rational Mech. Anal. {\bf 183} 299 (2007)).
