Membrane Thermodynamics for Osmotic Phenomena

In this chapter, we briefly review the thermodynamic ensembles and associated energy functions using the seven thermodynamic variables. The energy E, the entropy S, and the system volume V are used to derive the temperature T and pressure P. The chemical potential μ is derived as the change of the system energy with respect to the number of matters N in the isobaric‐isothermal environment. A dilute solution is defined as a homogeneous mixture of solvent and inert solutes, where the total number and volume of solutes are much smaller than those of the solvent. Gibbs free energy of the dilute solution is used to rigorously derive the osmotic pressure by equilibrating chemical potentials of solutes and solvent. Nonequilibrium of the filtration systems is reviewed by introducing the irreversible thermodynamic model with Onsager’s reciprocal theorem. Direct applications of the irreversible thermodynamic model are currently limited due to the absence of the exact nonequilibrium statistical mechanics. We hope this chapter, containing a review of statistical mechanics, related to membrane separations and osmosis phenomena, helps researchers and especially graduate students, who seek an in‐depth understanding of membrane separation from the theoretical statistical physics as applied to chemical and environmental engineering

Task Space Control of Articulated Robot Near Kinematic Singularity: Forward Dynamics Approach

In this study, a forward dynamics-based control (FDC) framework is proposed for task space control of a nonredundant robot manipulator. The FDC framework utilizes forward dynamic robot simulation and an impedance controller to solve the inverse kinematics problem. For the practical use of the proposed control framework, the accuracy, robustness, and stability of robot motion are considered. Taking advantage of the stability of the implicit Euler method, a high-gain PD controller enables accurate end-effector pose tracking in the task space without losing stability even near the kinematic singularities. Also, the robustness of the controller is enhanced by borrowing the structure of the nonlinear robust internal-loop compensator. Lastly, the selective joint damping injection and spring force saturation are applied to the impedance controller so that the robot motion can always stay within the given dynamic constraints. This study suggests a new, effective solution for the kinematic singularity problem of non-redundant robot manipulators.1