Why do we have a bronchial tree with 23 levels of bifurcation?

A simple one-dimensional mass transfer model has been proposed for the oxygen transport through a bronchial tree to alveolar tissues as well as the carbon dioxide removal from the tissues in the human respiratory system. The proposed model mathematically describes the mass transfer between the airway inlet and the red blood cell interior in the pulmonary capillaries. The quasi steady one-dimensional analysis based on the model reveals that the bronchial tree is constructed such that it promotes the easiest access to the external air. Naturally, there exists the optimal number of the bifurcation levels, namely, 23, that yields the minimum overall mass transfer resistance for the mass transport from the external air to the red blood cells.     

A study on interstitial heat transfer in consolidated and unconsolidated porous media

The Nusselt number expressions are presented for the interstitial heat transfer coefficients for both consolidated and unconsolidated porous media. A boundary layer consideration is made for unconsolidated porous media to derive a general Nusselt number correlation, which shows its square root dependence of the Reynolds number, and matches fairly well with existing experimental data and correlations. As for low density consolidated porous media, rigorous mathematical arguments based on the volume averaging theory are provided, so as to explain the reason why the Reynolds number exponent of the Nusselt number expression for the case of low density consolidated porous media is much greater than that of unconsolidated porous media. The resulting expressions are compared against available experimental data and empirical correlations, and found to be in good accord with them.     

Fast swelling/deswelling kinetics of comb-type grafted poly(N-isopropylacrylamide) hydrogels

The synthesis and characterization of comb-type grafted thermo-sensitive hydrogels is presented. These hydrogels were synthesized by polymerization of N-isopropylacrylamide (IPAAm) with a PIPAAm macromonomer. This process leads to a crosslinked IPAAm backbone polymer, copolymerized with highly mobile comb-type PIPAAm chains. These new thermo-responsive copolymers displayed higher equilibrium swellings at lower temperatures and rapid deswelling kinetics at elevated temperatures. The swelling/deswelling for comb-type gels is dependent on the graft chain lengths, in contrast to normal PIPAAm gel lacking the graft chains. As the temperature is increased above the critical temperature, the dehydrated graft chains aggregated due to hydrophobic attraction. Rapid and reversible kinetics of the graft-type gel were observed in response to stepwise temperature changes within short time cycles: phenomena not observed in normal crosslinked thermo-sensitive gels. The influence of freely mobile graft chains on both the equilibrium and dynamic properties of comb-type PIPAAm gel is demonstrated. Possible application of graft-type gel is discussed for actuator systems.     

Copolymerization of 2‐butene and ethylene with catalysts based on titanium and zirconium complexes

The polymerization of 2‐butene and its copolymerization with ethylene have been investigated using four kinds of dichlorobis(β‐diketonato)titanium complexes, [ArN(CH₂)₃NAr]TiCl₂ (Ar = 2,6‐ⁱPr₂C₆H₃) and typical metallocene catalysts. The obtained copolymers display lower melting points than those produced of homopolyethylene under the same polymerization conditions. ¹³C NMR analysis indicates that 9.3 mol‐% of 2‐butene units were incorporated into the polymer chains with Ti(BFA)₂Cl₂‐MAO as the catalyst system. With the trans‐2‐butene a higher copolymerization rate was observed than with cis‐2‐butene. A highly regioselective catalyst system for propene polymerization, [ArN(CH₂)₃NAr]TiCl₂ complex using a mixture of triisobutylaluminium and Ph₃CB(C₆F₅)₄ as cocatalyst, was found to copolymerize a mixture of 1‐butene and trans‐2‐butene with ethylene up to 3.1 mol‐%. Monomer isomerization‐polymerization proceeds with typical metallocene catalysts to produce copolymers consisting of ethylene and 1‐butene.