Heat loss corrections for heat capacity flow calorimeters

A single equation describes all linear thermal models for the heat losses in heat capacity flow calorimeters. This equation is used to correct for heat losses by extrapolating the apparent heat capacity to the zero value of a modified reciprocal flow rate. The method, which does not require an auxiliary pump, has been successfully tested for aqueous sodium chloride solutions to 300.8°C, with the derived apparent molar heat capacities being in agreement with literature values. Aqueous solutions of 2-methylpropan-2-ol (t-butanol) gave anomalous results requiring further investigation. Two other correction methods are both consistent with the new method but apply less generally and require care in the evaluation of the correction factors.     

Theoretical analysis of electrokinetic flow and heat transfer in a microchannel under asymmetric boundary conditions

The main theme of the present work is to investigate the electrokinetic effects on liquid flow and heat transfer in a flat microchannel of two parallel plates under asymmetric boundary conditions including wall-sliding motion, unequal zeta potentials, and unequal heat fluxes on two walls. Based on the Debye-Huckel approximation, an electrical potential solution to the linearized Poisson-Boltzmann equation is obtained and employed in the analysis. The analytic solutions of the electrical potential, velocity distributions, streaming potential, friction coefficient, temperature distribution, and heat transfer rate are obtained, and thereby the effects of electrokinetic separation distance (K), zeta-potential level (zeta;(1)), ratio of two zeta potentials (r(zeta) identical with zeta;(2)/zeta;(1)), wall-sliding velocity (u(w)), and heat flux ratio (r(q) identical with q"(2)/q"(1)) are investigated. The present results reveal the effects of wall-sliding and zeta-potential ratio on the hydrodynamic nature of microchannel flow, and they are used to provide physical interpretations for the resultant electrokinetic effects and the underlying electro-hydrodynamic interaction mechanisms. In the final part the results of potential and velocity fields are applied in solving the energy equation. The temperature distributions and heat transfer characteristics under the asymmetrical kinematic, electric, and thermal boundary conditions considered presently are dealt with.     

Estimation of zeta potential by electrokinetic analysis of ionic fluid flows through a divergent microchannel

The streaming potential is generated by the electrokinetic flow effect within the electrical double layer of a charged solid surface. Surface charge properties are commonly quantified in terms of the zeta potential obtained by computation with the Helmholtz-Smoluchowski (H-S) equation following experimental measurement of streaming potential. In order to estimate a rigorous zeta potential for cone-shaped microchannel, the correct H-S equation is derived by applying the Debye-Hückel approximation and the fluid velocity of diverging flow on the specified position. The present computation provides a correction ratio relative to the H-S equation for straight cylindrical channel and enables us to interpret the effects of the channel geometry and the electrostatic interaction. The correction ratio decreases with increasing of diverging angle, which implies that smaller zeta potential is generated for larger diverging angle. The increase of Debye length also reduces the correction ratio due to the overlapping of the Debye length inside of the channel. It is evident that as the diverging angle of the channel goes to nearly zero, the correction ratio converges to the previous results for straight cylindrical channel.     

Heat flux and the calorimetric-respirometric ratio as measures of catabolic flux in mammalian cells

It is advocated that cellular heat flow rate (Ø = dQ/dt, where Q is heat) be expressed as an intensive quantity specific to cell size (X) and termed heat flux (J_Ø/X). It has been the practice to cite such data on a ‘per cell’ basis, but it would be preferable to use biomass (cellular volume or mass). This quantity is shown to be a measure of metabolic activity and, more accurately, catabolic rate coupled to the demand for ATP in anabolic processes and work in the cell. Recent developments in flow microcalorimetry and dielectric spectroscopy reveal that heat flux can be measured on-line, with the potential of industrial use as a control variable in the growth of hybridoma and genetically engineered cells. This is because the enthalpy change of growth can be regarded as a unique kind of stoichiometric coefficient directly related to the mass coefficients in the growth reaction. This can be verified by an enthalpy balance comparing data for material fluxes of catabolites with the value for heat flux. Information revealed by the stoichiometric growth equation can be used to improve medium design.

The ratio of heat flux to oxygen consumption (flux) is known as the calorimetric-respirometric (CR) ratio. It detects anaerobic processes when the value is more negative than −450 (±5%) kJ mol⁻¹ O₂. These processes are found in cells growing under fully aerobic conditions, because glycolysis provides biosynthetic precursors with lactate as the byproduct. It is suggested that the CR ratio would be a powerful on-line control variable for the growth of animal cells in bioreactors.     

Electroosmotic flow in a capillary annulus with high zeta potentials

The electroosmotic flow through an annulus is analyzed under the situation when the two cylindrical walls carry high zeta potentials. The analytical solutions for the electric potential profile and the electroosmotic flow field in the annulus are obtained by solving the Poisson-Boltzmann equation and the Stokes equation under an analytical scheme for the hyperbolic sine function. A mathematical expression for the average electroosmotic velocity is derived in a fashion similar to the Smoluchowski equation. Hence, a correction formula is introduced to modify the Smoluchowski equation, taking into account contributions due to the finite thickness of the electric double layer (EDL) and the geometry ratio-dependent correction. Specifically, under a circumstance when the two annular walls are oppositely charged, the flow direction can be determined from the sign of such correction formula, and there exists a zero-velocity plane inside the annulus. With the assumption of large electrokinetic diameters, the location of the zero-velocity plane can be estimated from the analytical expression for the velocity distribution. In addition, the characteristics of the electroosmotic flow through the annulus are discussed under the influences of the EDL parameters and geometric ratio of the inner radius to the outer radius of the annulus.     

Frequency-dependent laminar electroosmotic flow in a closed-end rectangular microchannel

This article presents an analysis of the frequency- and time-dependent electroosmotic flow in a closed-end rectangular microchannel. An exact solution to the modified Navier-Stokes equation governing the ac electroosmotic flow field is obtained by using the Green's function formulation in combination with a complex variable approach. An analytical expression for the induced backpressure gradient is derived. With the Debye-Hückel approximation, the electrical double-layer potential distribution in the channel is obtained by analytically solving the linearized two-dimensional Poisson-Boltzmann equation. Since the counterparts of the flow rate and the electrical current are shown to be linearly proportional to the applied electric field and the pressure gradient, Onsager's principle of reciprocity is demonstrated for transient and ac electroosmotic flows. The time evolution of the electroosmotic flow and the effect of a frequency-dependent ac electric field on the oscillating electroosmotic flow in a closed-end rectangular microchannel are examined. Specifically, the induced pressure gradient is analyzed under effects of the channel dimension and the frequency of electric field. In addition, based on the Stokes second problem, the solution of the slip velocity approximation is presented for comparison with the results obtained from the analytical scheme developed in this study.     

Effect of testing conditions on the laser flash thermal diffusivity measurements of ceramics

Several experimental techniques either under steady state or transient heat transfer conditions, have been developed to evaluate thermal conductivity and thermal diffusivity of materials. However, testing difficulties resulting from specimen size, extended testing time and heat losses, have somewhat impaired the applicability of many of them. In this respect, the use of the laser flash technique for thermal diffusivity measurements, is a very convenient alternative, considering its basic modeling equation is independent of the temperature gradient as well as the heat flow, and in addition the heat losses can be analytically treated. Another important advantage of the technique is its rapid experimental execution. In this work, it is presented as an investigation concerning how the testing conditions such as specimen coating, laser power and pulse duration, base line adoption, heat losses correction methods, and specimen thickness, may affect the thermal diffusivity measurements of some ceramic materials using the laser flash technique.     

Numerical modelling of sample–furnace thermal lag in dynamic mechanical analyser

Due to dynamic nature of processes taking place during the experiment (chemical reaction and physical processes, heat flow, gas flow, etc.) the results obtained by thermal methods may considerably depend on the conditions used during the experiment. Therefore, whenever the results of thermal analysis are reported, the experimental conditions used should be stated. In this paper we have studied the heat transfer from the furnace to the sample and through the sample during dynamic mechanical analysis measurements. Numerical modelling of the heat transfer was done using an own computer program based on the heat conduction equation, solved numerically applying the finite difference methods. The calculated values of the thermal lag between the furnace and the sample were compared with the values experimentally determined on samples of a composite polymeric energetic material (double-base rocket propellant). Also, the temperature distribution within the sample as a function of the heating rate was analysed using the same numerical model. It was found out that using this model and temperature dependent heat transfer coefficient, experimentally obtained values of the thermal lag between the furnace and the sample can be satisfactory described. It was also shown that even at slow heating rates, such is, e.g. 2 °C min⁻¹, the thermal lag between the furnace and the sample can reach several degrees, while the thermal gradient within 3-mm thick rectangular sample can reach 0.4 °C.     

A new version of differential flow heat capacity calorimeter; tests of heat loss corrections and heat capacities of aqueous NaCl from T = 300 K to T = 623 K

A new differential flow heat capacity calorimeter was constructed. It is designed to operate at temperatures up to 700 K and pressures up to 35 MPa and its primary use is for determining the massic heat capacities at constant pressure of dilute aqueous solutions. The instrument works in the so-called isoperibol regime, where the fluid sample flowing through the cell is heated by an electrical heater and the power necessary to provide a constant temperature rise is measured relative to that for a reference fluid (water). From the two values of power for sample and water the ratio of massic heat capacities of the sample to that of water can be calculated. A thorough investigation of calibration techniques showed that the calorimetric performance is very sensitive to the thermal conductivities of the sample and reference fluids. Measurements under turbulent flow conditions are questionable since there is no guarantee that by changing the flow rate the experiments and the calibrations would be performed at the same flow conditions. The procedure is very accurate and sensitive when measuring the difference in heat capacity between a solvent and a dilute solution of solute in the same solvent. The calorimeter was used to measure heat capacities of aqueous solutions of NaCl at eight temperatures up to 623 K and pressures to 30 MPa. The newly obtained values show consistency with previously published results and enlarge the database of experimental values aboveT =  573 K, where experimental data are rare.     

Mechanisms of surface processes in silicon etching

A unified view on the mechanism allowing one to explain the experimental features governing spontaneous silicon etching by atomic fluorine is presented. Analysis of the phenomenological equation of adsorption shows a significant difference between etching mechanisms at high and low heat of adsorption on the surface being etched. As follows from the parameter estimates, one or another case can be realized under different experimental conditions. At steady-state the etching is argued to be determined only by the processes taking place on the SiF. film surface. To describe the process, it is necessary to understand the mechanism of overcoming the surface barrier for fluorine penetration into the film. At low heat of fluorine adsorption the barrier is overcome by thermal activation. In the opposite case the etching mechanism includes electron tunneling from silicon to adatoms and creation of a surface electric field. The field lowers the high energetic barrier for fluorine penetration. Based on the kinetic equations describing the electronic and atomic processes on the surface, the equation of the field strength is obtained. This equation is analyzed in different limit cases. The observed features are shown to be reproduced at some conditions on the parameters. Definite predictions on the temperature dependence of the etch rate are made.     

Electrical currents and liquid flow rates in micro-reactors

For micro-reactor devices in which liquids are pumped by electro-osmotic flow (EOF), in situ monitoring of the electrical currents in the channel networks provides a valuable diagnostic tool. We demonstrate here that the voltage-current characteristics of a micro-reactor channel network can be accurately modelled using measurements of the full 3-D geometry of the channel network, the liquid conductivity and the channel wall-liquid surface conductivity. It is shown that surface conductivity provides a significant contribution to the overall measured electrical currents in channel networks for which the ratio of surface area to volume is high. Following correction for surface conductivity, the electrical currents are proportional to the liquid volumetric flow rates measured in the different branches of the channel network. The constant of proportionality is related to the zeta potential of the channel wall-liquid surface. Measurements of the variation of electrical currents and volumetric flow rates as a function of the applied voltages allows the determination of the surface conductivity and zeta potential within the micro-reactor which enables the prediction of the voltages required to produce the desired flow rates in any channel section. In situ logging of the electrical currents, incorporated within the control system, allows continuous monitoring of the liquid flow rates during micro-reactor operation.     

Thermocrystallization flow of nonfreezing water films on the surface of capillaries

The rates of mass transfer under the influence of a temperature gradient between the menisci of ice in a thin quartz capillary are measured. The mass transfer rate is determined by the diffusion of vapor and by the flow of a nonfrozen polymolecular adsorption film over the capillary surface. It is shown that the flow of the film is attributable neither to the thermoosmotic nor to the thermocapillary flow. The flow rate of a nonfrozen film is well described by a thermocrystallization transfer equation derived earlier, the thermocrystallization transfer being controlled by the water-ice phase transition heat.     

Diffusion and Brownian motion in Lagrangian coordinates

In this paper we consider the convection-diffusion problem of a passive scalar in Lagrangian coordinates, i.e., in a coordinate system fixed on fluid particles. Both the convection-diffusion partial differential equation and the Langevin equation are expressed in Lagrangian coordinates and are shown to be equivalent for uniform, isotropic diffusion. The Lagrangian diffusivity is proportional to the square of the relative change of surface area and is related to the Eulerian diffusivity through the deformation gradient tensor. Associated with the initial value problem, we relate the Eulerian to the Lagrangian effective diffusivities (net spreading), validate the relation for the case of linear flow fields, and infer a relation for general flow fields. Associated with the boundary value problem, if the scalar transport problem possesses a time-independent solution in Lagrangian coordinates and the boundary conditions are prescribed on a material surface/interface, then the net mass transport is proportional to the diffusion coefficient. This can be also shown to be true for large Peclet number and time-periodic flow fields, i.e., closed pathlines. This agrees with results for heat transfer at high Peclet numbers across closed streamlines.     

Using the Transfer Function of an Isoperibolic Reaction Calorimeter for Thermo-kinetic Analysis

It is an aim of the present work to determine the chemical heat flow rate of a reaction without explicitly solving the heat balance equations. Therefore, it is necessary to calculate the heat flow rate directly from the temperature course of an experimentally determined reaction. For this transformation the transfer function of the calorimeter is needed 1 . An isoperibol reaction calorimeter was used for the experiments. With different calibrations and gained transfer functions, it is shown that the chemical heat flow rate can be determined from the temperature course of a reaction. The evaluation is fast and easy to use, which improves automation and prevents possible input errors.     

Determination of the surface potential for hollow-fiber membranes by the streaming-potential method

A procedure has been proposed for measuring the surface potential of hollow-fiber membranes by the streaming-potential method under the conditions of a tangential flow of a solution. The zeta-potential and surface charge of nanofiltration hollow-fiber polyacrylonitrile membranes have been measured. The measurements have been performed for membranes with different porosities, which were obtained by partial drying of initial humid membranes. The porosity has been determined from the electrical conductivity of a membrane. An equation has been proposed for calculating the charge transfer by a solution flow in a porous layer. It has been shown that the use of the proposed equation makes it possible to obtain more correct values of the membrane surface potential.     

Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet

We study the effects of Marangoni stresses on the flow in an evaporating sessile droplet, by extending a lubrication analysis and a finite element solution of the flow field in a drying droplet, developed earlier. The temperature distribution within the droplet is obtained from a solution of Laplace's equation, where quasi-steadiness and neglect of convection terms in the heat equation can be justified for small, slowly evaporating droplets. The evaporation flux and temperature profiles along the droplet surface are approximated by simple analytical forms and used as boundary conditions to obtain an axisymmetric analytical flow field from the lubrication theory for relatively flat droplets. A finite element algorithm is also developed to solve simultaneously the vapor concentration, and the thermal and flow fields in the droplet, which shows that the lubrication solution with the Marangoni stress is accurate for contact angles as high as 40 degrees. From our analysis, we find that surfactant contamination, at a surface concentration as small as 300 molecules/microm(2), can almost entirely suppress the Marangoni flow in the evaporating droplet.     

Calibration burning of wood crib under ISO9705 hood

Wood cribs free burning tests were conducted under ISO9705 hood. From the tests, the heat release rate of these cribs was grouped as 0.5, 1.0 and 1.5 MW. This result was used to correct an empirical formula for peak heat release rate calculation. The correction achieves acceptable accuracy for the typical wood. The test result also shown heat release rate curve can be normalized by the total combustion surface of the wood crib. This can also be used to predict the HRR of wood crib of certain sizes and structures.     

Extinction of diffusion flames adjacent to flat surfaces of burning polymers

Extinction of the diffusion flames in the stagnation-point flow above the commercial polymers, poly(methyl methacrylate), polyoxymethylene (two types), polyethylene (three types), and polystyrene, is studied. The extinction data are used in a theory developed to obtain overall rate parameters for gas-phase combustion of these fuels. Calculated overall rate parameters are corrected for surface heat loss by radiation. It is found that radiation corrections are most significant for polyethylene and polystyrene, in part because of their somewhat higher surface temperatures. Surface regression rates and corresponding surface temperatures are measured to aid in the radiation correction. The results are also used in an Arrhenius-type rate expression to obtain overall activation energies for the thermal degradation of these polymers for comparison with the literature. Effects of surface losses on flame extinction are discussed.     

Uses of the transit time distribution in kinetic flow systems

We investigate the distribution of transit or residence times of a trace reactant in laminar flow. We present measurements of this distribution for hydrogen atoms in a typical flow system, and show that the results are consistent with known theory and previous measurements of the diffusion coefficient. The use of the measured distribution as a diagnostic of flow behavior is discussed. It is also shown that the measured or calculated transit time distribution can provide a convenient means of correcting results of kinetic measurements for the departure from plug flow. In the case of firstorder, and also second-order decay of a single reactant, this correction is a useful approximation to the more rigorous solution of the partial differential equation for diffusion and reaction in laminar flow. Effects of the deviation from plug flow on a complex rection system are illustrated qualitatively for the H + NO₂ titration system.