E.James Davis

Analyses of mass transfer in hemodialyzers for laminar blood flow and homogeneous dialysate

Abstract Theoretical analyses of mass transfer in hemodialyzers which contain flowing blood and dialysate streams separated by a semi-permeable membrane are presented. Semi-infinite parallel-plate and cylindrical tube geometries are considered. Solutions are obtained in terms of well-known functions, a method which avoids difficulties associated with computing the higher eigenvalues encountered in previous analyses. Applications of the mathematical model to systems used in clinical practice are discussed.

THE EFFECTS OF AXIAL CONDUCTION IN THE WALL ON HEAT TRANSFER WITH LAMINAR FLOW

Abstract Wall conduction effects on steady-state laminar flow heat-transfer experiments are examined, and an analysis of heat transfer with axial conduction in the wall bounding a fluid in laminar flow is developed to determine the effects of the conduction in the wall on heat transfer with Poiseuille-Couette flow between parallel plates. The parameters that determine the relative importance of axial conduction are found to be the Peclet number of the fluid, the thickness to length ratio of the wall and the parameter β = k 2 δ 1 k 1 L . The Couette flow analysis and experiments that correspond to heat transfer with Couette flow are shown to be in good agreement, and comparisons of the interfacial temperature distribution and local Nusselt numbers obtained by accounting for axial conduction are made with the results determined by neglecting axial conduction.

Submicron droplet evaporation in the continuum and non-continuum regimes

Abstract Precise measurements of the evaporation rates of single submicron low-volatility liquid droplets have been made to test available theoretical and semi-theoretical analyses of aerosol evaporation in the diffusion-controlled and Knudsen aerosol regimes. By suspending a charged droplet in an electric field in a polarized laser beam the droplet size was determined as a function of time using Mie theory to interpret the light-scattering data. New data for dibutyl sebacate (DBS) evaporating into helium, nitrogen and carbon dioxide and data reported earlier for dioctyl phthalate (DOP) evaporating into helium and nitrogen are compared with theoretical predictions of aerosol evaporation rates. The results for DBS and DOP are consistent with an evaporation coefficient of order unity in the free-molecule regime, and the data in the diffusion-controlled regime are used to determine the diffusivities of DBS in He, N 2 and CO 2 as well as the Lennard-Jones interaction parameters and the vapor pressure of DBS.

Interfacial conditions and evaporation rates of a liquid droplet

Abstract The problem of unsteady state evaporation of a liquid droplet suddenly exposed to an unsaturated gaseous medium is solved in terms of integral equations. By taking into account the nonuniform temperature field in the droplet and the nonuniform temperature and concentration fields in the continuum surrounding the droplet the temperature history of the droplet surface is predicted. The effect of the time-varying surface temperature on the evaporation rate is determined, and the time required for the interfacial temperature to reach an asymptotic limit is calculated. The novel feature of this solution is that it rigorously takes into account the temperature distribution inside the drop as well as an enthalpy balance on the drop. By rigorously taking into account the appropriate material and energy balances the physically impossible discontinuities of some previous solutions are avoided.

The solution of conjugated multiphase heat and mass transfer problems

Abstract Three types of conjugated boundary value problems that arise when heat and/or mass are transferred between contiguous phases are analyzed by means of integral equation formulations. The systems are classified according to the type of differential equation that describes the temperature or concentration field in a phase, and systematic methods of solution are illustrated for each type of conjugated system. These include parabolic-parabolic systems, illustrated by a laminar gas/laminar liquid gas absorption problem, and parabolic-elliptic systems of which heat transfer from a thick-walled tube to a laminar flow is an example. The third type, which is more frequently encountered in chemical engineering, involves the conjugation of a partial differential equation with an ordinary differential equation. The temperature distribution in the falling film reactor is examined from this point of view.

Knudsen aerosol evaporation

Abstract The evaporation kinetics of submicron aerosol droplets has been studied by measuring the size of single droplets as a function of time using laser light scattering from the droplet. By suspending a charged droplet in an electric field in a light scattering cell, precise measurements of droplet size have been made over a range of total pressures corresponding to diffusion-controlled evaporation and Knudsen aerosol evaporation. The results are compared with available theoretical and semitheoretical predictions for Knudsen aerosol transport processes. For the systems studied, dioctyl phthalate in helium and in nitrogen, the results are consistent with an evaporation coefficient of unity. Furthermore, the technique can be used to determine diffusion coefficients and vapor pressures for relatively nonvolatile species.

Determination of diffusion coefficients by submicron droplet evaporation

Lennard‐Jones potential function constants, diffusion coefficients, and vapor pressures for relatively nonvolatile organics in gaseous media have been determined by measuring the evaporation rates of submicron droplets suspended in an electric field in a laser beam. A light‐scattering method was used to obtain the droplet size as a function of time for diffusion‐controlled evaporation.

The effects of bubble translation on vapor bubble growth in a superheated liquid

Abstract A theoretical analysis of vapor bubble growth in a uniformly superheated liquid has been carried out to determine the effects of translational motion of the bubble on the bubble growth rate. Assuming potential flow in the region surrounding the bubble the appropriate convective diffusion equation is solved by means of a new similarity transformation. The results of the theoretical analysis are compared with available experimental data and with analyses of the limiting cases of no bubble translation and quasi steady state bubble growth. The analysis is shown to reduce to the Plesset and Zwick or Scriven analysis for stationary growing bubbles. The effects of translation are found to be significant when the translational velocity is sufficiently high at moderate Jakob numbers, but for high Jakob numbers radial convection predominates and translation has little effect on the growth rates. The analysis predicts results in good agreement with experimental data available in the literature.

Diffusion-controlled growth or collapse of moving and stationary fluid spheres

Abstract The problem of diffusion-controlled growth or collapse of a bubble or droplet that is moving relative to a surrounding fluid is solved by means of a similarity transformation previously proposed by Ruckenstein. The cases of low Reynolds number flow ( Re Re

The enhancement of heat transfer by waves in stratified gas-liquid flow

Abstract An experimental investigation of heat transfer from a flat plate to horizontal cocurrent airwater flow has been carried out to assess the effects of the different flow regimes on the effectiveness of the heat transfer. The results for smooth liquid film flow and two-dimensional wavy flow of the liquid phase are shown to agree with the theoretical analysis of heat transfer to smooth films. Three-dimensional waves and roll waves are shown to increase the Nusselt number (compared with smooth films) by more than 100 per cent. By using a surface-active agent to stabilize the flow direct comparison between wavy flow heat transfer and smooth flow heat transfer is obtained. At sufficiently low gas phase Reynolds numbers and at sufficiently high wall heat fluxes Rayleigh-like instability due to buoyant forces is shown to occur.