(229h) An Example of How the Scientific Research Provide New Material in the Teaching of Transport Phenomena

Scientific research in the engineering area, normaly, is carried out independently to the university teaching. This means that the scientist achieves new scientific knowledge and they are reported in scientific papers, divulgated in conferences or congresses, but rarely the new procedures implied or deducted in the scientific research are taken to the classrooms or to the undergraduate laboratories

This means that the priority of the researcher is not to use his findings to reinforce the teaching, but his research line.

In this material, two examples are provided how the results derived from a scientific work are going to pose a didactic problem that can be used in the transport phenomena classes, to illustrate a mass transfer problem.

The research work is related with hydrogen production through water dissociation using heterogeneous photocatalysis. This is a very important topic due the oil is going to be depleted and it is mandatory to look for alternative energies, such as solar, eolic, nuclear, geothermal, biomass, hydrogen, etc. Hydrogen is an energy vector, with a very high calorific value and its combustion does not generate CO₂. It can be produced using the methods: Electrochemical, biomass, catalytic reforming of hydrocarbons, photocatalysis, etc. This last one is a big promise due it has the potential of using the solar light, water, and zero ambient contamination.

The experiments were carried out in a reactor so called Photo – CREC- Water II- Modified, using water, ethanol as electron scavenger and novel catalysts made with titanium dioxide doped with palladium (0.5, 1, 2%). The samples taken from the reactor were analyzed in a gas chromatograph, and the obtained compounds were hydrogen, CO₂, CO and methane.

Heterogeneous Photocatalysis is performed illuminating the titanium dioxide with UV-A light (365 nm), to excite the semiconductor and to promote an electron from the valence to the conduction band. In this way, a couple of electrical charges are generated, an electron and a positive hole. The electron is going to reduce other species such as oxygen or a proton. The hole will oxidize the negative ion OH to convert it in a free radical OH, which will react with the scavenger (ethanol). In this form, reduction- oxidation reactions will be carried out.

Water is dissociated in the proton and the negative radical OH^- due the natural value of pH. To produce hydrogen, the proton reacts with the generated electron and the OH^- with the positive hole, producing a free radical H°. Then, two free radicals H° associate in a covalent bond to produce molecular hydrogen. By the other side, the negative radical OH^- is oxidized by the positive hole, generating a free radical OH° which will oxidize the methanol to eventually produce water and CO₂, the total oxidation.

It is necessary to avoid the presence of air or oxygen in the system, due the oxygen will compete with the proton for the electrons, and we want to favor the proton reduction only.

Experimental results indicate that hydrogen profiles with time have a linear behavior for all the used catalysts, and for TiO₂ doped with 2%Pd, 1.2 micromoles are obtained in 6 hours of reaction, which

indicates the photocatalysts can produce hydrogen and now it is important to improve the technology.

Now the challenge is to predict the transport of the protons from the liquid phase to the surface of the catalyst, and to determine the molar fraction of the protons in the boundary layer surrounding the catalytic particle, to determine the expression for the molar flux of the protons arriving to the limit of the boundary layer and then that for the produced molecular hydrogen, its transport in the liquid to the liquid-gas interphase, and then its transport in the gas phase where a sample is collected by the syringe needle. Also, it is important to determine the pH value at which the reaction rate is controlling and the transport of the protons is fast.

Problem one.

The algebraic development that follows can be incorporated as a pedagogic example that could be taught in classroom, or incorporated as examples or proposed in the section of problems to solve by the student.

A mass balance can be established: The transfer of protons from the liquid to the surface are equal to the reaction rate of the electrons with the protons plus the accumulation of protons, and the equations are written, achieving a ratio between a dimensionless number containing the intrinsic kinetic rate and other number containing the mass transfer coefficient in the boundary layer. This ratio must be less than 1 if the controlling step is the chemical reaction and the fast step is the transport of the protons in the boundary layer. This means that the numerator, containing the reaction rate is lesser than the denominator, with the mass transfer coefficient. This condition is meet with pH values lesser than 4.

The next step is to get the values of the terms involved in the inequality and the following procedure was followed. Particle diameter of the agglomerate of TiO₂, m = cm. To get the value of the mass transfer coefficient, the general mass balance was analyzed for a spherical particle in a fluid, without reaction, no convection. The differential equation was solved to find the concentration profile, using as boundary conditions that in the surface of the particle, the concentration is C_R and for an infinite radius, the concentration is cero. Using Fick law, the mass transfer of the protons was calculated to calculate the molar flux.

The mass transfer coefficient is defined as the proportionality constant between the flux and the difference of concentration between that in the surface and in the fluid. Then, with an equation of mass analogous to the Newton´s cooling law, we deduct the mass transfer coefficient and calculate it with the given information.

Using one concentration profile of protons, the reaction rate was calculated, and substituting the proton concentration at pH = 4 in the rate , the value was 0.389 (less than one). In this way, the mass transport is rapid and the reaction rate is slow and is the controlling step. This occurs for pH less than 4. For pH bigger than 4, this inequality is not meet, and the mass transport controls. Then, at pH lesser than one, the ions transport in the boundary layer is enhanced and increase the reaction rate. This is corroborated by the experimental data.

Problems two.

We are aware the molecular hydrogen is produced on the surface of the catalytic particle, then, it needs to cross the boundary layer surrounding the particle, to transport in the liquid phase, to cross the liquid – gas interphase, then to transport in the gas phase until reaching the syringe needle where the sample is collected. Then, the goal is to calculate the molecular hydrogen that is in the gas phase, using the existing theory.

The catalytic particle is surrounded by a boundary layer which offer resistance to the proton mass transport. Fick law including diffusion and convection and a mass balance in a differential element are used to obtain the differential equation describing the change of molar fraction of the protons. Solving it and using the appropriate boundary conditions, the molar fraction profile is obtained, and then the expression to calculate the molar flux in the limit of the boundary layer. This equation allows calculate the proton flow crossing the limit of the boundary coming from the water, in direction to the catalyst surface. The corresponding data are substituted. Certainly, there is uncertainty in several data assumed to do the calculations.

According to the stoichiometry, it is possible to determine the flux of molecular H₂ in the limit of the boundary layer, and then to predict the transport in the liquid phase to reach the gas – liquid interphase. Raoult law is used to calculate the molar fraction of molecular hydrogen in the liquid, assuming the flux is constant from the limit of the boundary layer to the interphase liquid – gas. It is assumed the liquid is quiet and the convective term is neglected. An equilibrium curve is used to relate the molar fraction of hydrogen in water and in nitrogen.

To analyze the transport in the gas phase of nitrgen, it is assumed the flux is constant and is the same than that in the liquid phase. Besides, it is considered the gas is quiet and there is not convection. With the Fick law, the molar fraction of the hydrogen is calculated in the gas phase, and it is compared with that measured by the gas chromatograph. The error is round the 80%, and this can be attributed to the uncertainty in some data assumed due the lack of information.

In this way, the prediction of the experimental results obtained in this research line, use a procedure and calculations relatively simples than can be used in the programs of mass transport in undergraduate program of chemical engineering.