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.
Part of the book: Desalination
Dissipative Dynamics of Granular Materials
Granules are inelastic particles, undergoing dissipative and repulsive forces on contact. A granular state consists of a conglomeration of discrete, non-Brownian particles in a combined state of solid, liquid, and gas. Modern theoretical physics lacks general theories for the granular states. Simulation methods for particle dynamics include molecular dynamics (MD), Brownian dynamics (BD), Stokesian dynamics (SD), dissipative particle dynamics (DPD), and dissipative hydrodynamics (DHD). These conventional methods were originally designed to mimic the small-particle motion being less influenced by the gravitational force. There are three reasons that a conventional method cannot be directly applied to investigate granular dynamics. First, volume exclusion forces between colliding particles are often disregarded due to strong repulsive forces between negatively charged colloids and nanoparticles. Second, the gravitational force is not significant as applied to small, light particles, and therefore it is often discarded in force/torque calculations. Third, energy conservation in an equilibrium state is not guaranteed for the granular system due to the inelastic and frictional nature of the granular materials. In this light, this chapter discusses the fundamentals of particle dynamics methods, formulates a robust theoretical framework for granular dynamics, and discusses the current applications and future directions of computational granular dynamics.
Part of the book: Granular Materials
Temperature Effect on Forward Osmosis
Forward osmosis, or simply, osmosis, refers to a process by which a solvent moves across a semipermeable membrane due to the difference in the solute concentration established across the membrane. Because of its spontaneous nature, forward osmosis has received immense attention during the last few decades, particularly for its diverse applications, which include municipal wastewater treatment, seawater desalination, membrane bioreactor, potable water purification, food processing, drug delivery, energy generation, and so forth. Of many parameters that determine the performance of the forward osmosis process, the most fundamental factor that impacts performance is temperature. Considering the importance of the temperature on the forward osmosis process, there have been only a limited number of studies about the effect of temperature on the osmosis-driven process. In this chapter, we discuss the temperature effect on the forward osmosis process from two main aspects. First, we provide an extensive and in-depth survey on the currently available studies related to the anisothermal osmosis phenomena. Second, we then discuss a state-of-the-art theoretical framework that describes the anisothermal forward osmosis process that may shed light on achieving an enhanced performance via temperature control.
Part of the book: Osmotically Driven Membrane Processes
A Coupling Algorithm of Computational Fluid and Particle Dynamics (CFPD)
Computational fluid dynamics (CFD) and particle hydrodynamics (PHD) have been developed almost independently. CFD is classified into Eulerian and Lagrangian. The Eulerian approach observes fluid motion at specific locations in the space, and the Lagrangian approach looks at fluid motion where the observer follows an individual fluid parcel moving through space and time. In classical mechanics, particle dynamic simulations include molecular dynamics, Brownian dynamics, dissipated particle dynamics, Stokesian dynamics, and granular dynamics (often called discrete element method). Dissipative hydrodynamic method unifies these dynamic simulation algorithms and provides a general view of how to mimic particle motion in gas and liquid. Studies on an accurate and rigorous coupling of CFD and PHD are in literature still in a growing stage. This chapter shortly reviews the past development of CFD and PHD and proposes a general algorithm to couple the two dynamic simulations without losing theoretical rigor and numerical accuracy of the coupled simulation.
Part of the book: Advanced Computational Fluid Dynamics for Emerging Engineering Processes
Fundamentals of Irreversible Thermodynamics for Coupled TransportView all chapters
Engineering phenomena occur in open systems undergoing irreversible, non-equilibrium processes for coupled mass, energy, and momentum transport. The momentum transport often becomes a primary or background process, on which driving forces of physical gradients govern mass and heat transfer rates. Although in the steady state no physical variables have explicit variation with time, entropy increases with time as long as the systems are open. The degree of irreversibility can be measured by the entropy-increasing rate, first proposed by L. Onsager. This book conceptually reorganizes the entropy and its rate in broader aspects. Diffusion is fully described as an irreversible, i.e., entropy increasing, phenomenon using four different physical pictures. Finally, an irreversible thermodynamic formalism using effective driving forces is established as an extension to the Onsager’s reciprocal theorem, which was applied to core engineering phenomena of fundamental importance: solute diffusion and thermal flux. In addition, the osmotic and thermal fluxes are explained in the unified theoretical framework.
Part of the book: Non-Equilibrium Particle Dynamics