Testing predictions of macroscopic binary diffusion coefficients using lattice models with site heterogeneity

Quantitatively predicting mass transport rates for chemical mixtures in porous materials is important in applications of materials such as adsorbents, membranes, and catalysts. Because directly assessing mixture transport experimentally is challenging, theoretical models that can predict mixture diffusion coefficients using Only single-component information would have many uses. One such model was proposed by Skoulidas, Sholl, and Krishna (Langmuir, 2003, 19, 7977), and applications of this model to a variety of chemical mixtures in nanoporous materials have yielded promising results. In this paper, the accuracy of this model for predicting mixture diffusion coefficients in materials that exhibit a heterogeneous distribution of local binding energies is examined. To examine this issue, single-component and binary mixture diffusion coefficients are computed using kinetic Monte Carlo for a two-dimensional lattice model over a wide range of lattice occupancies and compositions. The approach suggested by Skoulidas, Sholl, and Krishna is found to be accurate in situations where the spatial distribution of binding site energies is relatively homogeneous, but is considerably less accurate for strongly heterogeneous energy distributions.

A unified friction description and its application to the simulation of frictional instability using the finite element method

This article first summarizes some available experimental results on the frictional behaviour of contact interfaces, and briefly recalls typical frictional experiments and relationships, which are applicable for rock mechanics, and then a unified description is obtained to describe the entire frictional behaviour. It is formulated based on the experimental results and applied with a stick and slip decomposition algorithm to describe the stick-slip instability phenomena, which can describe the effects observed in rock experiments without using the so-called state variable, thus avoiding related numerical difficulties. This has been implemented to our finite element code, which uses the node-to-point contact element strategy proposed by the authors to handle the frictional contact between multiple finite-deformation bodies with stick and finite frictional slip, and applied here to simulate the frictional behaviour of rocks to show its usefulness and efficiency.

The lattice solid model to simulate the physics of rocks and earthquakes: Incorporation of friction

The particle-based lattice solid model developed to study the physics of rocks and the nonlinear dynamics of earthquakes is refined by incorporating intrinsic friction between particles. The model provides a means for studying the causes of seismic wave attenuation, as well as frictional heat generation, fault zone evolution, and localisation phenomena. A modified velocity-Verlat scheme that allows friction to be precisely modelled is developed. This is a difficult computational problem given that a discontinuity must be accurately simulated by the numerical approach (i.e., the transition from static to dynamical frictional behaviour). This is achieved using a half time step integration scheme. At each half time step, a nonlinear system is solved to compute the static frictional forces and states of touching particle-pairs. Improved efficiency is achieved by adaptively adjusting the time step increment, depending on the particle velocities in the system. The total energy is calculated and verified to remain constant to a high precision during simulations. Numerical experiments show that the model can be applied to the study of earthquake dynamics, the stick-slip instability, heat generation, and fault zone evolution. Such experiments may lead to a conclusive resolution of the heat flow paradox and improved understanding of earthquake precursory phenomena and dynamics. (C) 1999 Academic Press.

Local shell-side coefficients in shell and tube exchanges the use of a mass transfer technique

A diffusion-controlled electrochemical mass transfer technique has been employed in making local measurements of shell-side coefficients in segmentally baffled shell and tube heat exchangers. Corresponding heat transfer data are predicted through the Chilton and Colburn heat and mass transfer analogy. Mass transfer coefficients were measured for baffle spacing lengths of individual tubes in an internal baffle compartment. Shell-side pressure measurements were also made. Baffle compartment average coefficients derived from individual tube coefficients are shown to be in good agreement with reported experimental bundle average heat transfer data for a heat exchanger model of similar geometry. Mass transfer coefficients of individual tubes compare favourably with those obtained previously by another mass transfer technique. Experimental data are reported for a variety of segmental baffle configurations over the shell-side Reynolds number range 100 to 42 000. Baffles with zero clearances were studied at three baffle cuts and two baffle spacings. Baffle geometry is shown to have a large effect on the distribution of tube coefficients within the baffle compartment. Fluid "jetting" is identified with some baffle configurations. No simple characteristic velocity is found to correlate zonal or baffle compartment average mass transfer data for the effect of both baffle cut and baffle spacing. Experiments with baffle clearances typical of commercial heat exchangers are also reported. The effect of leakage streams associated with these baffles is identified. Investigations were extended to double segmental baffles for which no data had previously been published. The similarity in the shell-side characteristics of this baffle arrangement and two parallel single segmental baffle arrangements is demonstrated. A general relationship between the shell-side mass transfer performance and pressure drop was indicated by the data for all the baffle configurations examined.

Statnote 15: the non-parametric correlation coefficients

If in a correlation test, one or both variables are small whole numbers, scores based on a limited scale, or percentages, a non-parametric correlation coefficient should be considered as an alternative to Pearson’s ‘r’. Kendall’s t and Spearman’s rs are similar tests but the former should be considered if the analysis is to be extended to include partial correlations. If the data contain many tied values, then gamma should be considered as a suitable test.

Transfer coefficients over inclined tube banks

The thesis presents experimental results for shell-side transfer coefficients and pressure drops across four different tube banks, using small-scale models, with yawed tubes, as found in many types of heat exchangers, boilers and nuclear reactors. The tube banks investigated have a staggered tube layout on a rotated square pitch, with a 1.25 pitch-to-diameter ratio. The angle of attack was varied between 45o and 90o. An extensive range of Reynolds number, i.e. 0.5. to 12,600, covering so-called laminar, transition and turbulent flows, was investigated. A diffusion-controlled electrochemical mass transfer technique has been employed to measure mass transfer coefficients. The heat transfer coefficients may be then readily obtained from the mass transfer values by applying the well-established Chilton-Colburn analogy. The results for the normal tube bank, which forms the base case for the study on inclined tube banks, show close agreement with previous work. The transfer coefficients and pressure drops of the inclined tube banks are compared with results from the ideal normal tube bank to examine the effect of inclination angle on heat transfer and pressure drop variations. The variation of the transfer coefficients row-by-row and the entrance and exit effects have also been investigated. An auxilary investigation has been carried out on the role of natural convection. A preliminary correlation of transfer coefficients and pressure drops against the variation in the yaw angle has been attempted. The results are discussed in the light of the few existing theoretical treatments and experimental data for these situations, and recommendations made for future work.

Autocatalytic deposition of composite coatings

The deposition and properties of electroless nickel composite coatings containing graphite, PTFE and chromium were investigated. Solutions were developed for the codeposition of graphite and chromium with electroless nickel. Solutions for the deposition of graphite contained heavy metal ions for stability, with non-ionic and anionic surfactants to provide wetting and dispersion of the particles. Stability for the codeposition of chromium particles was achieved by oxidation of the chromium. Thin oxide layers of 200 nm thick prevented initiation of the electroless reaction onto the chromium. A mechanism for the formation of electroless composite coatings was considered based on the physical adsorption of particles and as a function of the adsorption of charged surfactants and metal cations from solution. The influence of variables such as particle concentration in solution, particle size, temperature, pH, and agitation on the volume percentage of particles codeposited was studied. The volume percentage of graphite codeposited was found to increase with concentration in solution and playing rate. An increase in particle size and agitation reduced the volume percentage codeposited. The hardness of nickel-graphite deposits was found to decrease with graphite content in the as-deposited and heat treated condition. The frictional and wear properties of electroless nickel-graphite were studied and compared to those of electroless nickel-PTFE. The self-lubricating nature of both coatings was found to be dependent on the ratio of coated area to uncoated area, the size and content of lubricating material in the deposit, and the load between contacting surfaces. The mechanism of self-lubrication was considered, concluding that graphite only produced an initial lubricating surface due to the orientation of flakes, unlike PTFE, which produced true self-lubrication throughout the coating life. Heat treatment of electroless nickel chromium deposits at 850oC for 8 and 16 hours produced nickel-iron-chromium alloy deposits with a phosphorus rich surface of high hardness. Coefficients of friction and wear rates were intially moderate for the phosphorus rich layer but increased for the nickel-iron-chromium region of the coating.