Fluid-Solid Interaction Models

The singlet-level theories have also been applied to more sophisticated models of the fluid-solid interactions. In particular, the structure of associating fluids near partially permeable surfaces has been studied in Ref. 70. On the other hand, extensive studies of adsorption of associating fluids in a slit-like [71-74] and in spherical pores [75], as well as on the surface of spherical colloidal particles [29], have been undertaken. We proceed with the application of the theory to more sophisticated impermeable surfaces, such as those of crystalline solids. 

From this, the velocities of particles flowing near the wall can be characterized. However, the absorption parameter a must be determined empirically. Sokhan et al. [48, 63] used this model in nonequilibrium molecular dynamics simulations to describe boundary conditions for fluid flow in carbon nanopores and nanotubes under Poiseuille flow. The authors found slip length of 3nm for the nanopores [48] and 4-8 nm for the nanotubes [63]. However, in the first case, a single factor [4] was used to model fluid-solid interactions, whereas in the second, a many-body potential was used, which, while it may be more accurate, is significantly more computationally intensive. 

Instead of the classical approaches, a molecular-based statistical thermodynamic theory can be applied to allow a model of adsorption to be related to the microscopic properties of the system in terms of fluid-fluid and fluid-solid interactions, pore size, pore geometry and temperature. Using such theories the whole range of pore sizes measured can be calculated using a single approach. Two simulation... 

It should be noted that the introduction of fluid/solid interaction has no effect on the macroscopic equations since F2jt exists only at the fluid/solid interface. The relaxation time, tk, is estimated based on the viscosity and mass density representations given by Eqs. (20) and (21) of the Mi component and is detailed in Ref. [37, 43, 44], This model has been shown to satisfy Galilean invariance.44 Furthermore, in this interparticle potential model, the separation of a two-phase fluid into its components is automatic.37... 

The primary physical parameters, such as the fluid/fluid and fluid/solid interaction parameters, need apriori evaluation through model calibration using numerical experiments. The fluid/fluid interaction gives rise to the surface tension force and the fluid/ solid interaction manifests in the wall adhesion force. The fluid/fluid and fluid/solid interaction parameters are evaluated by designing two numerical experiments, bubble test in the absence of solid phase... 

First, a complete description of the adsorbent is required this must include details of its solid structure, surface chemical structure, pore size and shape. One starts by assuming that the pores in the model adsorbent are all of the same size and shape and that they are unconnected. Secondly, the nature of the fluid-fluid and fluid-solid interactions must be precisely defined since the validity of the calculations is dependent on the accuracy of the intermolecular potential functions. 

In this category, one may classify all the attempts in describing theoretically the fluid-solid interactions. The main characteristic of these models is a local description of the fluid flow hydrodynamics. Some models for the prediction of the liquid holdup are worth noting in this category. 

Despite these findings it is still common to arbitrarily assume infinite pore wall thickness in using the slit pore model, and the associated pore size dependent Steele 10-4-3 potential [6] is then employed for estimatiiig the potential energy profile in a pore of any size. The inappropriateness of this assumption has recently been demonstrated in our laboratory, where it has been shown [5] that in typical nanoporous carbons having surface area in the range important for practical application (>800 m /gm) the pore walls must actually be rather thin, and comprised of only a very small number (2-3) of graphene layers. For such small wall thicknesses the adsorption potential is much weaker than that obtained for the infinitely thick wall, and the adsorbed amoimts can be lower by factors of 2 or more, particularly at low pressures where fluid-solid interactions dominate [5]. 

Using the above fluid- fluid and fluid-solid potential models, the total interaction energy of a unit cell has been evaluated for various transitions. We considered close packed L-J particles forming a two-dimensional structure, comprising unit cells. To determine the total interaction potential for the unit cell, the following assumptions were applied... 

To test the above results and determine maximum deliveries from carbons, grand canonical (GCMC) Monte Carlo simulations were performed here for both slit pores and carbon nanotubes, for the case of hydrogen as well as methane storage. The Lennard-Jones model was enployed for the fluid-fluid as well as fluid-solid interactions, using the Lorentz-Berthelot mixing rules, and commonly used parameters listed elsewhere [18]. Isosteric heats were estimated in the simulations following the well-known fluctuation formula [18]. 

The central idea of MPTA is that the chemical potential of a component in the mixture results from two contributions a bulk-phase contribution, which is represented by a thermodynamic model (equation of state), and a potential energy contribution that depends on the distance between the gas component and the solid adsorbent (fluid-solid interactions). 

Thus, to be able to use the MPTA model in practice we need models to describe both fluid-fluid and fluid-solid interactions which are involved in the chemical potential in the adsorbed phase. For the fluid-fluid interactions, a thermodynamic model is used (typically in the form of equations of state like cubic equations of state, e.g. SRK). 

After introducing some types of moving-particle reactors, their advantages and disadvantages, and examples of reactions conducted in them, we consider particular design features. These relate to fluid-particle interactions (extension of the treatment in Chapter 21) and to the complex flow pattern of fluid and solid particles. The latter requires development of a hydrodynamic model as a precursor to a reactor model. We describe these in detail only for particular types of fluidized-bed reactors. 

Many of the present models used to describe fluid-solid phase equilibria require one to assume that the solute is at infinite dilution. That is, researchers have often assumed that solute-solute interactions are nonexistent. Recently, Brennecke et al. used the fluorescent probe pyrene to investigate the possibility of solute-solute interactions in C02, C2H4, and CF3H (7-9). Pyrene is an interesting probe because it can form a characteristic excited-state dimer (excimer) during its excited-state... 

Bridging the gap between micro- and macro-scale is the central theme of the first contribution. The authors show how a so-called Energy-Minimization Multi-Scale (EMMS) model allows to do this for circulating fluid beds. This variational type of Computational Fluid Dynamics (CFD) modeling allows for the resolution of meso-scale structures, that is, those accounting for the particle interactions, and enables almost grid-independent solution of the gas-solids two-phase flow. 

Figure 5. Interaction models between a TMI of a precursor complex and an oxide support (top) liquid (bottom) gas. The left- and right-hand sides represent the solid oxide and fluid phase respectively The vertical dotted lines represent the width of the interface, as explained in Ref 12.

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