Pores Of Finite Length Research Articles

New Model for Liquid Evaporation and Vapor Transport in Nanopores Covering the Entire Knudsen Regime and Arbitrary Pore Length.

Liquid evaporation and the associated vapor transport in micro/nanopores are ubiquitous in nature and play an important role in industrial applications. Accurate modeling of the liquid evaporation process in nanopores is critical to achieving a better design of devices for enhanced evaporation. Although having high impact on evaporation rate, vapor transport resistance in micro/nanopores remains incompletely understood. In this study, we proposed a new model which, for the first time, considered vapor transport in finite-length pores under various Knudsen regimes and then coupled the transport resistance to liquid evaporation. Direct Simulation Monte Carlo and laboratory experiments were conducted to provide validation for our model. The model successfully predicts the variation of pore transmissivity with Knudsen number and nanopore size, which cannot be revealed by prior theories. The relative error of model-predicted evaporation rate was within 1% in L/r = 0 cases and within 3.5% in L/r > 0 cases. Our model is featured by its applicability under the entire range of Knudsen numbers. The evaporation of various types of liquids in arbitrarily sized pores can be modeled using a universal relation.

On the existence of a hysteresis loop in open and closed end pores

We have studied the adsorption of argon at 87 K in slit pores of finite length with a smooth graphitic potential, open at both ends or closed at one end. Simulations were carried out using conventional GCMC (grand canonical Monte Carlo) or kMC (kinetic Monte Carlo) in the canonical ensemble with extremely long Markov chain, of at least 2 × 108 configurations; selected simulations with much longer Markov chains do not show any change in the results. When the pore width is in the micropore range (0.65 nm), type I isotherms are obtained for both pore models and for both simulation methods. However, wider pores (1, 2 and 3 nm in width) all exhibit hysteresis loops in the GCMC simulations, while in the canonical ensemble simulations, the isotherms pass through a sigmoid van der Waals type loop in the transition region. This loop locates the true equilibrium transition. For the pores with one closed end, this transition is close to, or coincides with, the adsorption branch of the GCMC hysteresis loop, but for the open-ended pores, it is more closely associated with the desorption branch. In a separate study of adsorption hysteresis in an infinitely long slit pore, using both simulation techniques, the van der Waals loop follows the adsorption branch of the GCMC isotherm to the transition, then reverts to a long vertical section that falls midway between the two hysteresis branches and finally moves to the desorption transition close to the evaporation pressure. An examination of molecular distributions inside the pores reveals two coexisting phases in the canonical simulations, whereas in the grand canonical simulations, the molecules are uniformly distributed along the length of the pores.

A Monte Carlo study of equilibrium transition in finite cylindrical pores

In this paper, we report a comprehensive analysis of the adsorption of argon in cylindrical pores of finite length having different dimensions and adsorbent energies. We determine the mechanisms of adsorption and desorption in the hysteresis region, and use the recently introduced mid-density scheme, as an approximate method, to determine the equilibrium transition, which is found to lie wholly within the loop and closer to the desorption branch. For a given loading in the hysteresis region, we determine the microscopic behaviour of two metastable states (one on the adsorption branch and the other on the desorption branch) and the stable equilibrium state. The adsorption metastable state is characterised by a bulging adsorbed layer, while the desorption metastable state is characterised by a liquid bridge with a meniscus at each end in the shape of a long elliptical cone. The equilibrium state has a configuration that displays a liquid bridge with hemispherically shaped menisci having areas less than those of the two menisci in the desorption metastable state.

Generalized Hydrodynamic Treatment of the Interplay between Restricted Transport and Catalytic Reactions in Nanoporous Materials

Behavior of catalytic reactions in narrow pores is controlled by a delicate interplay between fluctuations in adsorption-desorption at pore openings, restricted diffusion, and reaction. This behavior is captured by a generalized hydrodynamic formulation of appropriate reaction-diffusion equations (RDE). These RDE incorporate an unconventional description of chemical diffusion in mixed-component quasi-single-file systems based on a refined picture of tracer diffusion for finite-length pores. The RDE elucidate the nonexponential decay of the steady-state reactant concentration into the pore and the non-mean-field scaling of the reactant penetration depth.

Passage of a Small Air Bubble through a Circular Pore across the Plate of Finite Thickness

Experimental and theoretical studies are made on the passage of a small air bubble through a circular pore of finite length which connects two half-space chambers of viscous fluid, with an application to the transport of a drug-containing particle to a diseased cell through a cleft of endothelial cells in mind. Dependences of the change of shape and the translational velocity of the bubble on the deformability and the constriction size are examined.

Contact Angles, Pore Condensation, and Hysteresis: Insights from a Simple Molecular Model

We discuss the thermodynamics of adsorption of fluids in pores when the solid-fluid interactions lead to partial wetting of the pore walls, a situation encountered, for example, in water adsorption in porous carbons. Our discussion is based on calculations for a lattice gas model of a fluid in a slit pore treated via mean field density functional theory (MFDFT). We calculate contact angles for pore walls as a function of solid-fluid interaction parameter, alpha, in the model, using Young's equation and the interfacial tensions calculated in MFDFT. We consider adsorption and desorption in both infinite pores and in finite length pores in contact with the bulk. In the latter case, contact with the bulk can promote evaporation or condensation, thereby dramatically reducing the width of hysteresis loops. We show how the observed behavior changes with alpha. By using a value of alpha that yields a contact angle of about 85 degrees and maintaining the bulk fluid in a supersaturated vapor state on adsorption, we find an adsorption/desorption isotherm qualitatively similar to those for graphitized carbon black where pore condensation occurs at supersaturated bulk vapor states in the spaces between the primary particles of the adsorbent.

Flow through an orifice in a fibrous medium with application to fenestral pores in biological tissue

Slow viscous flow through a circular orifice in a plane wall bounded by a fibrous medium is studied using an effective medium approach, based on the Brinkman equation, using an integral equation technique. The solution is of more general interest because it describes the transition in behavior from the classic Sampson solution for creeping flow through an orifice to a potential flow solution for Darcy flow as the permeability parameter increases. Asymptotic analytical results for the total flux through the orifice for a given pressure difference are obtained for both small and large values of the permeability parameter α defined by a/ K p , where a is the orifice radius and K p the Darcy permeability. For intermediate values of α, the integral equation is solved numerically for the flux and velocity profile at the opening. For α≫ O(1), the velocity profile at the opening has a minimum at the orifice center, rises dramatically near the edge of the orifice and then experiences a boundary-layer-like correction of thickness O(1/ α) to satisfy the no-slip boundary condition. The close relation between pressure driven flow through a circular orifice and broadside translation of the complementary geometry, namely a circular disk in Stokes flow, is also discussed. The effect of the finite thickness of the orifice is taken into account using a simple model proposed by Dagan et al. (J. Fluid Mech. 115 (1982)) for Stokes flow through a pore of finite length. The present results are used to estimate the hydraulic conductance of orifice like pores in fenestrated capillaries and fenestral pores in the internal elastic lamina of the arterial intima.

Adsorption Hysteresis in Porous Solids

Hysteresis has been observed in adsorption isotherms for a number of gas–solid systems and, generally, is attributed to adsorption in mesoporous materials with capillary condensation. This behavior is classified as Type IV or Type V in the IUPAC classification scheme. Here, lattice theory is used to predict adsorption behavior in pores. The Ono–Kondo theory is used with appropriate boundary conditions for fluid adsorption in infinite and semi-finite slit-like pores. It is shown that there can be phase transitions in the adsorbed phase which lead to hysteresis in kinetically controlled experiments. However, hysteresis in equilibrium behavior is exhibited only in pores of finite length. For finite-length pores, the interface geometry is predicted to be different during the processes of adsorption and desorption and this difference in interface shape leads to hysteresis. This simple molecular model is able to predict the change in the interface geometry without invoking the Kelvin equation or the macroscopic concept of surface tension.

Impedance of porous electrodes

Equations describing potential and current distribution in semi-infinite- and finite-length cylindrical porous electrodes, assuming Butler-Volmer equation for the pore walls, are presented. In the case of finite-length pores, for arbitrary values of transfer coefficients, only numerical solutions exist. Ac impedances of these electrodes were also simulated for different kinetic and geometric parameters. Complex nonlinear least-squares fit of the simulated impedances to the de Levie's equation, which neglects the potential dependence of the charge transfer resistance, was studied and the approximation errors discussed. This procedure overestimates charge transfer resistances predicted by de Levie's equation (for the same pore geometry), at most by a factor of 2. The double-layer capacitances obtained are also larger than those assumed. Errors of approximations are discussed in relation to earlier experimental work.

Impedance analysis of the electrochemical doping of poly(3-methyl-thiophene) from aqueous solutions of KClO 4, KCl and K 2SO 4

Impedance spectra of poly(3-methyl-thiophene) (P3MeT) films on Pt electrodes in aqueous solutions of 0.1 M KClO 4, 0.1 M KCl and 0.1 M K 2SO 4 show that, in the undoped form, the polymer acts as an ion-insertion electrode. In the doped state, the behaviour in 0.1 M KClO 4 is similar to that of porous metal electrodes with finite-length pores, although the low frequency capacitance is too high to be explained as an ordinary double-layer capacitance at the polymer-solution interface. This capacitance is therefore interpreted as a redox capacity connected to the doping of the polymer. In KClO 4, the doping threshold found by stepwise coulometry is at least 250 mV lower than the transition to porous electrode behaviour seen in the impedance data. In 0.1 M KCl(aq) and 0.1 M K 2SO 4(aq) this doping threshold is ca. 200 mV higher than in 0.1 M KClO 4, paralleling voltammetric data. In the KCl and K 2SO 4 solutions, the same equivalent circuit can be used both above and below the onset potential for doping. However, a Warburg element present in this circuit may be interpreted as due to diffusion below the metal-insulator transition and as capacitive charging of electrode pores of apparent infinite depth above this transition. The impedance data indicate that the pore structure of P3MeT varies with the contacting electrolyte.

The sedimentation of a small particle through a fluid-filled pore of finite length

This paper investigates the axisymmetric sedimentation of a small slowly rotating and translating particle through a fluid-filled circular pore of finite length which communicates with two half-space chambers of fluid. In the quasi-steady Stokes approximation the particle is modelled by either a rotlet or Stokeslet, and potential-theoretic methods are used to reduce each problem to the solution of coupled infinite systems of linear equations. The numerical solutions of these sets of equations are used to compute approximations to the resistive torque and drag experienced by the particle.

Mass transfer in a plane finite pore on a broad interval of Knudsen numbers with allowance for condensation

The flow field and the flow rate of a gas in a two-dimensional plane pore of finite length are found numerically over a broad interval of Knudsen numbers with allowance for condensation on the walls.