Govt. Exams
Entrance Exams
In the fast reaction regime where diffusion limits the overall rate, η ≈ 1/Φ for spherical pellets, indicating severe internal diffusion limitations.
The Langmuir model assumes monolayer adsorption on homogeneous surfaces with constant heat of adsorption, leading to saturation at high pressures.
For turbulent flow, empirical correlations show Sh ∝ Re^0.8·Sc^0.33 (or 0.5 depending on flow regime), derived from boundary layer theory and mass transfer analogies.
Lewis number Le = α/D_AB, where α is thermal diffusivity. It indicates the relative importance of heat and mass transfer in coupled processes. Le ≈ Sc/Pr for most gases.
Foam fractionation enrichment factor depends on surface activity (interfacial tension), protein hydrophobicity, and preferential adsorption of proteins at gas-liquid interfaces.
Shrinking core model applies: external diffusion, ash diffusion, and chemical reaction all contribute. Modern focus on clean energy requires optimized design.
Due to higher solute rejection, solutes accumulate near membrane surface, increasing local osmotic pressure and reducing driving force.
Φ = L√(k/D). When Φ >> 1, diffusion controls; when Φ << 1, kinetics controls. Critical for reactor design optimization.
η = (actual reaction rate)/(rate if all surface at bulk concentration). Important in catalytic reactors where diffusion and reaction compete.
Colburn analogy: j_D = (Sh)/(Re·Sc^(1/3)) ≈ j_H ≈ f/2 for smooth surfaces. Useful for correlating data when only one phenomenon is studied.