Flow of liquid/liquid dispersions in a Hele-Shaw cell

Flow of liquid/liquid dispersions have been investigated in a Hele-Shaw cell which contained a thin disk held between two parallel plates. This device offers a well defined flow field and also permits visual observation of the dispersed drop movement. The dispersed drops coalesce with the disk for the systems where the dispersed phase wets the disk surface. The dispersed phase accumulate at the downstream end of the disk and they detach from there as blobs. Through an accurate measurement of accumulated dispersed phase volume, the coalescence rate was determined. The coalescence efficiency in the Hele Shaw cell is determined by dividing the coalescence hate by the undisturbed flow rate of the dispersed phase through an area equal to the projected area of the disk on a plane normal to the flow direction. The coalescence efficiency first increases and then decreases with the flow rate of dispersion. The coalescence rate/disk dimensions increases with the decrease in the disk dimensions. The rate of coalescence increases with the increase in the dispersed drop diameter and it decreases with the increase in the continuous phase viscosity. The presence of surfactants reduces the coalescence rate. All these results are quantitatively explained through a model, which takes into account several important features like various mechanism of drainage, the roles of dispersion and continuous phase viscosities, and the drop deformation.

Stability of a Random Diffusion with Linear Drift

We consider a Linear system with Markovian switching which is perturbed by Gaussian type noise, If the linear system is mean square stable then we show that under certain conditions the perturbed system is also stable, We also shaw that under certain conditions the linear system with Markovian switching can be stabilized by such noisy perturbation.

Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks

Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM.

Studies of Phosphazenes. Part 13.' Thermal Rearrangement Reactions of Some Met hoxycyclo phosp hazenes

The methoxycyclophosphazenes [NP(OMe),], (n = 3-6) rearrange on heating to give oxocyclophosphazanes, [N(Me)PO(OMe)],. Isomeric products are formed when n = 4-6. The lH, ,lP, and 13C n.m.r. data for the starting materials and the products are presented. The ethoxy- and n-propoxy-derivatives N,P,( OR)* do not undergo the above rearrangement. The geminal derivatives N,P,R,(OMe), (R = Ph or NHBut) on heating yield both fully and partially rearranged products, namely dioxophosphaz-1 -enes and oxophosphazadienes, as shown by 270- MHz lH n.m.r. spectroscopy. The non-geminal derivative N,P,( NMe,),(OMe), gives only the fully rearranged product N,Me,P,(NMe,),O,(OMe), whose structure has been established from its lH and 31P n.m.r. spectra.

Studies of phosphazenes. Part 14. The tautomerism of oxocyclotriphosphazadienes

The tautomeric behaviour of monohydroxycyclotriphosphazatrienes has been investigated by 31P n.m.r. spectroscopy. These derivatives exist as oxocyclotriphosphazadiene tautomers in which the hydrogen atom is attached to a ring nitrogen atom to the phosphoryl group. Three types of prototropic behaviour are observed : (a) no exchange is detected and only one tautomer is present [e.g. N3HP3(NHBut)2R3O (R = OMe or OEt)]; (b) exchange takes place between two equivalent sites and only one tautomer is observed [e.g. N3HP3R5O (R = OMe or OPh); N3HP3Ph4RO (R = OMe or OEt)]; and (c) exchange occurs between two non-equivalent sites and two tautomers are present [e.g. N3HP3Ph2R3O (R = OMe, OEt, or OPrn)]. It is shown that basicity calculations using substituent constants have predictive value since they are in good agreement with the spectroscopic observations.

Studies of phosphazenes. Part 10. Spirocyclic derivatives of cyclotriphosphazatrienes

The reactions of hexachlorocyclotriphosphazatriene, N3P3Cl6, and its geminal bis-t-butylamino- and diphenyl derivatives, with ethylenediamine and ethanolamine are reported. In each case, both chlorine atoms attached to the same phosphorus atoms are replaced, giving rise to spirocyclic derivatives. A small quantity of a bis spirocyclic derivative, N3P3(NHCH2CH2O)2Cl2, is also obtained; this compound occurs in both cis and trans forms. Attempts to prepare fully substituted tris spirocyclic derivatives have been unsuccessful and only resinous materials were obtained. The 1H and 31P n.m.r. spectra of the products are discussed.

Tautomeric forms of hydroxycyclotriphosphazatrienes; X-ray crystal structure of N3P3Ph2(OMe)3OH

The prefered tautomer(s) of hydroxycyclotriphosphazatrienes and prototropic exchange in solution have been established by 31P n.m.r. spectroscopy, thus confirming predictions deduced from basicity calculations; the X-ray structure of N3P3Ph2(OMe)3OH shows that it exists as the hydrogen-bonded dimer of the oxophosphazadiene tautomer in which a proton is adjacent to the PPh2 group.

Semimicro determination of selenium and tellurium by chloramine-T oxidation

Finely divided selenium and tellurium undergo oxidation to selenic and orthotelluric acids by a concentrated solution of chloramine-T in acid medium. An analytical procedure (accurate to <1 %) has been developed based on this reaction.

Spirocyclic phosphazenes derived from the reaction of N3P3Cl6 and N4P4Cl8 with bifunctional reagents

Four possible reaction paths may be envisaged when a chlorocyclophosphazene reacts with a bifunctional reagent (FIGURE). He have shown recently that 1,2-diaminoethane and ethanolamine react initially with N3P3CI 6 to give the spirocyclic derivatives, N3P3CI4(HNCH2CH2X) X = NH, 0 (I). Further reaction with these bifunctional reagents leads to the formation of non-crystalline resins [reaction (iii)] albeit two isomeric bls(spirocyclic)- ethanolamino derivatives were isolated in low yields (vSZ).

Aromatic amines and their derivatives. Part 3. The synthesis and crystal structure of 4,4-NN-tetramethyl-NN-dinitroso-2,2-methylenedianiline

The synthesis of 4,4,N,N-tetramethyl-NN-dinitroso-2,2-methylenedianiline (1) by the route p-MeC6H4NH2+ HCHO + OH–(p-MeC6H4NMe)2CH2(7b); (7b)+ acid at 70 °C 4,N-dimethyl-6-(N-methyl-p-toluidinomethyl)aniline (4b); (4b)+ acid at 130 °C 4,4,NN-tetramethyl-2,2-methylenedianiline (3b); (3b)+ HNO2(1), is described. Aspects of the 1H n.m.r. spectra of the above and related compounds are discussed. A crystal-structure analysis of compound (1) shows one of the N-nitroso-groups to be disordered with the endo-form being in preponderance (4 : 1) over the exo-form. The other N-nitroso-group is exclusively exo in the solid state. There is little or no resonance between the benzene ring and the nitroso-group attached to the ring, the two groups being almost perpendicular to each other. In one of the N-nitroso-groups, the nitrogen atom deviates significantly from the plane of the benzene ring to which it is attached. Both amide nitrogen atoms show some pyramidal character.

Studies of phosphazenes. Part I. Reactions of octachlorocyclotetraphosphazatetraene with ethylamine

The reaction of octachlorocyclotetraphosphazatetraene, N4P4Cl8, with ethylamine has been investigated. Seven derivatives, N4P4Cl8–n(NHEt)n[n= 1, 2 (two isomers), 3, 4 (two isomers), and 8] have been isolated and their structures established by 1H and 31P n.m.r. spectroscopy. A non-geminal chlorine atom replacement scheme is observed. Attempts to prepare penta- or hexa-ethylamino derivatives were unsuccessful: only sticky, non-crystalline resins were obtained from 1 : 10 or 1 : 12 reactions. The preparation and n.m.r. spectroscopic data of mixed ethylamino(methoxy)-derivatives. N4P4(NHEt)–8-n(OMe)n[n= 6, 4 (two isomers)], and an ethylamino-(dimethylamino)-derivative, N4P4(NHEt)2(NMe2)6, are generally consistent with the proposed structures. The reaction pattern is discussed.

Improved procedures for static and dynamic analyses of wrinkled membranes

An analysis of large deformations of flexible membrane structures within the tension field theory is considered. A modification-of the finite element procedure by Roddeman et al. (Roddeman, D. G., Drukker J., Oomens, C. W J., Janssen, J. D., 1987, ASME J. Appl. Mech. 54, pp. 884-892) is proposed to study the wrinkling behavior of a membrane element. The state of stress in the element is determined through a modified deformation gradient corresponding to a fictive nonwrinkled surface. The new model uses a continuously modified deformation gradient to capture the location orientation of wrinkles more precisely. It is argued that the fictive nonwrinkled surface may be looked upon as an everywhere-taut surface in the limit as the minor (tensile) principal stresses over the wrinkled portions go to zero. Accordingly, the modified deformation gradient is thought of as the limit of a sequence of everywhere-differentiable tensors. Under dynamic excitations, the governing equations are weakly projected to arrive at a system of nonlinear ordinary differential equations that is solved using different integration schemes. It is concluded that, implicit integrators work much better than explicit ones in the present context.

The 31p nmr Spectra of Isomeric Diaminohexa-hlorocyclotetraphosphazatetraenes; Examples of a2b2 and aa'bb' spin Systems

The 31P nmr spectra of 2,4- and 2,6-diamino-derivatives of octachlorocyclotetraphosphazatetraene, N4P4Cl6(NR1R2)2 (R1 = H, R2 = But; R1 = H, R2 = CH2Ph; R1 = Me, R2 = Ph), have been measured. The 2,4- and 2,6-isomers were analysed as AA'BB' and A2B2 spin systems respectively. In the 2,4-isomers the spin-spin couplings 2J(PNP) and 4J(PNPNP) were of opposite sign.