Analytic theory for the determination of velocity and stability of bubbles in a Hele-Shaw cell

An asymptotic theory is presented for the determination of velocity and linear stability of a steady symmetric bubble in a Hele-Shaw cell for small surface tension. In the first part, the bubble velocity U relative to the fluid velocity at infinity is determined for small surface tension T by determining a transcendentally small correction to the asymptotic series solution. It is found that for any relative bubble velocity U in the interval (U _c , 2), solutions exist at a countably infinite set of values of T (which has zero as its limit point) corresponding to the different branches of bubble solutions. The value of U _c decreases monotonically from 2 to 1 as the bubble area increases from 0 to . However, for a bubble of an arbitrarily given size, as T 0, a solution exists on any given branch with the relative bubble velocity U satisfying the relation 2–U=cT ^2/3, where c depends on the branch but is independent of the bubble area. The analytical evidence further suggests that there are no solutions for U>2. These results are in agreement with earlier analytical results for a finger.In Part II an analytic theory is presented for the determination of the linear stability of the bubble in the limit of zero surface tension. Only the solution branch corresponding to the largest possible U for given surface tension is found to be stable, while all the others are unstable, in accordance with earlier numerical results.This research has been supported by National Science Foundation Grant DMS-8713246. Partial support was also provided by the NASA Langley Research Center (NAS1-18605) while the author was in residence at the Institute of Computer Applications in Science and Engineering.     

An electrolytic device for preparation of hydrogen and oxygen from water for isotopic analysis

An electrolytic device for decomposition of water has been developed which readily gives hydrogen and oxygen for isotopic measurement with a mass spectrometer. A 20-mul sample can be decomposed quantitatively in 10 min with good reproducibility. The results produced are comparable with those obtained by reduction with uranium.     

Palladium(0)-catalyzed regioselective synthesis of alpha-dehydro-beta-amino esters from amines and allyl acetates: synthesis of a alpha-dehydro-beta-amino acid derived cyclic peptide as a constrained beta-turn mimic

Acetates derived from the adducts of the Baylis-Hillman reaction can be reacted in a regioselective manner with amines in the presence of palladium(0) catalyst to afford alpha-dehydro-beta-amino esters (2 and 3) in good yields. The regioselectivity of the reaction can be controlled by temperature and reaction medium leading to the synthesis of regioisomers 2 or 3. The alpha-dehydro-beta-amino acid 3 is a turn inducer, and the dipeptides 6 derived from it show the presence of an eight-membered intramolecular hydrogen bond. Also, cobalt(II) chloride catalyzes the cleavage of epoxy peptides with alpha-dehydro-beta-amino acid derivative 3b to afford the corresponding dipeptide derivatives 8, which exhibit an intramolecular hydrogen bond and thus mimic a beta-turn. This intramolecular hydrogen bonding preorganizes the corresponding diallylated peptide 8c for cyclization via ring-closing metathesis to afford the cyclic peptide 9 as a constrained mimic of a beta-turn.     

Dithiolate complexes of manganese and rhenium: X-ray structure and properties of an unusual mixed valence cluster Mn3(CO)6(mu-eta2-SCH2CH2CH2S)3

Treatment of Mn(2)(CO)(10) with 3,4-toluenedithiol and 1,2-ethanedithiol in the presence of Me(3)NO.2H(2)O in CH(2)Cl(2) at room temperature afforded the dinuclear complexes Mn(2)(CO)(6)(mu-eta(4)-SC(6)H(3)(CH(3))S-SC(6)H(3)(CH(3))S) (1), and Mn(2)(CO)(6)(mu-eta(4)-SCH(2)CH(2)S-SCH(2)CH(2)S) (2), respectively. Similar reactions of Re(2)(CO)(10) with 3,4-toluenedithiol, 1,2-benzenedithiol, and 1,2-ethanedithiol yielded the dirhenium complexes Re(2)(CO)(6)(mu-eta(4)-SC(6)H(3)(CH(3))S-SC(6)H(3)(CH(3))S) (3), Re(2)(CO)(6)(mu-eta(4)-SC(6)H(4)S-SC(6)H(4)S) (4), and Re(2)(CO)(6)(SCH(2)CH(2)S-SCH(2)CH(2)S) (5), respectively. In contrast, treatment of Mn(2)(CO)(10) with 1,3-propanedithiol afforded the trimanganese compound Mn(3)(CO)(6)(mu-eta(2)-SCH(2)CH(2)CH(2)S)(3) (6), whereas Re(2)(CO)(10) gave only intractable materials. The molecular structures of 1, 3, and 6 have been determined by single-crystal X-ray diffraction studies. The dimanganese and dirhenium carbonyl compounds 1-5contain a binucleating disulfide ligand, formed by interligand disulfide bond formation between two dithiolate ligands identical in structure to that of the previously reported dimanganese complex Mn(2)(CO)(6)(mu-eta(4)-SC(6)H(4)S-SC(6)H(4)S). Complex 6, on the other hand, forms a unique example of a mixed-valence trimangenese carbonyl compound containing three bridging 1,3-propanedithiolate ligands. The solution properties of 6 have been investigated by UV-vis and EPR spectroscopies as well as electrochemical techniques.     

Experimental study of effect of void volume fraction on neutron diffusion parameters in water

The dependence of the diffusion parameters including slowing down area, neutron diffusion length and migration length on the voided volume fraction in water has been studied experimentally. For this purpose, the PIEAS Neutron Transport Facility (PNTF) comprised of a 10 Ci Am–Be neutron source and a water filled aluminum tank with Perspex voided tubes has been designed and fabricated. A BF₃ detector was used for the neutron counting. The slowing down area was determined at the cadmium cutoff level. The diffusion parameters were determined first in the absence of voids. The experimentally measured values of the slowing down area, the diffusion length and the migration length have been found in good agreement with the corresponding values determined by other workers. By varying void volume fraction from 0% to 7.5%, the experimental measurements show a monotonic increase in the slowing down area from 58.71±2.6 to 71.28±3.2 cm², in the diffusion length from 2.95±0.13 to 3.11±0.13 cm and in the migration length from 8.21±0.165 to 8.99±0.169 cm. Our measurements show that the diffusion parameters exhibit a quadratic dependence on the void volume fraction.     

Ligand exchange reactions with η6-arene-η5-cyclopentadienyliron cations under thermal or photochemical conditions

Reactions of various η⁶-arene-η⁵-cyclopentadienyliron or substituted cyclopentadienyliron cations with trimethyl, triethyl or triphenyl phosphite under either thermal or photochemical conditions all resulted in the replacement of the arene ligand with three phosphite ligands to give η⁵-tris(trimethyl, triethyl or triphenyl phosphite)-η⁵-cyclopentadienyliron or substituted cyclopentadienyliron cations. The yields of the phosphite complexes were higher from photolysis than from the analogous thermolysis. Photolysis of the η⁶-chlorobenzene-η⁵-cyclopentadienyliron cation (IX) carried out in the presence of a more basic or more electron-rich aromatic ligand resulted in the exchange of the chlorobenzene of IX with the more basic arene, thus providing synthetic routes to cyclopentadienyliron complexes that may be difficult to prepare by other means. New complexes synthesized in this way are the η⁶-2-phenylethyl tosylate-η⁵-cyclopentadienyliron cation and the CpFe⁺ complexes of thiophene, 2-methylthiophene, 3-methylthiophene and 2,5-dimethylthiophene.     

Determination of Br,Rb, Cs,Sc and Na in various plant leaves located in an urban park by neutron activation analysis

In order to determine the effect of airborne emission of trace elements, e.g. Br, Rb Cs, Sc and Na on roadside ecosystem, concentrations were determined in different species of plants from an urban park at Lahore. For monitoring purpose attention was paid to the leaves ofSapindus mukorossis, Alstonia scholaris andDiospyros embryopteris. Different varieties of tissues were found to have different concentration of trace elements when compared among themselves. The concentration of trace element deposition was compared with the values reported in literature. Significant pollution was observed.     

Effect of various irradiation doses on some nutrients of Pakistani date

Summary Date samples were irradiated with different doses using a gamma-irradiator. Levels of moisture, protein, fibre and fats were determined on monthly basis for 5 months. Generally, the moisture contents of control date samples packed in white polythene decreased from 14.1±1.1 to 9.7±0.8% over a 5-month period while the irradiated samples were in the range of 10.4-11.2%, however, no proper pattern of change was observed. After 5-month storage, the protein level of irradiated samples was reduced to 1.00-1.30%, while the percent fibre levels were found to be in the range of 2.40-2.48. Similarly, the fat level decreases from 1.06±0.12 to 0.68±0.06 for control date sample while after 5-month the decrease in fat content was 0.45±0.04%, 0.44±0.04%, 0.44±0.05%, 0.42±0.05% and 0.40±0.04% for samples irradiated with 20, 50, 100, 200 and 300 krads, respectively.     

9,9-diphenyl-1,9,10,10a-tetrahydro-2H-phenaleno[1,9-bc]pyrans

Reaction between some naphtho[2,1-b]pyrans and 1,1-diphenylethene affords 9,9-diphenyl-1,9,10,10a-tetrahydro-2H-phenaleno[1,9-bc]pyrans.