We provide a derivation of several classes of boundary conditions for fluids of Korteweg-type using a simple and transparent thermodynamic approach that automatically guarantees that the derived boundary conditions are compatible with the second law of thermodynamics. The starting assumption of our approach is to describe the boundary of the domain as the membrane separating two different continua, one inside the domain, and the other outside the domain. With this viewpoint one may employ the framework of continuum thermodynamics involving singular surfaces. This approach allows us to identify, for various classes of surface Helmholtz free energies, the corresponding surface entropy production mechanisms. By establishing the constitutive relations that guarantee that the surface entropy production is non-negative, we identify a new class of boundary conditions, which on one hand generalizes in a nontrivial manner the Navier’s slip boundary conditions, and on the other hand describes dynamic and static contact angle conditions. We explore the general model in detail for a particular case of a Korteweg fluid where the Helmholtz free energy in the bulk is that of a van der Waals fluid. We perform a series of numerical experiments to document the basic qualitative features of the novel boundary conditions and their practical applicability to model phenomena such as the contact angle hysteresis.

我们使用简单透明的热力学方法提供Korteweg型流体的几种边界条件的推导，该方法自动保证导出的边界条件与热力学第二定律兼容。我们方法的初始假设是将区域的边界描述为将两个不同的连续体分开的膜，一个在区域内，另一个在区域外。基于这一观点，可以采用涉及奇异表面的连续热力学框架。这种方法使我们能够为各种类型的表面亥姆霍兹自由能确定相应的表面熵产生机理。通过建立本构关系以确保表面熵产生为非负，我们确定了一类新的边界条件，它一方面以非平凡的方式概括了Navier的滑移边界条件，另一方面描述了动态和静态接触角条件。我们将针对特定情况的Korteweg流体详细探讨通用模型，其中大量的Helmholtz自由能是van der Waals流体的自由能。我们进行了一系列数值实验，以证明新型边界条件的基本定性特征及其对诸如接触角磁滞等现象建模的实际适用性。我们将针对特定情况的Korteweg流体详细探讨通用模型，其中大量的Helmholtz自由能是van der Waals流体的自由能。我们进行了一系列数值实验，以证明新型边界条件的基本定性特征及其对诸如接触角磁滞等现象建模的实际适用性。我们将针对特定情况的Korteweg流体详细探讨通用模型，其中大量的亥姆霍兹自由能是范德华流体的自由能。我们进行了一系列的数值实验，以证明新型边界条件的基本定性特征及其对诸如接触角滞后等现象建模的实际适用性。