Viscous effects on the acoustics and stability of a shear layer over an impedance wall

The effect of viscosity and thermal conduction on the acoustics in a shear layer above an impedance wall is investigated numerically and asymptotically by solving the linearised compressible Navier–Stokes equations (LNSE). It is found that viscothermal effects can be as important as shear, and therefore including shear while neglecting viscothermal effects by solving the linearised Euler equations (LEE) is questionable. In particular, the damping rate of upstream-propagating waves is found to be under-predicted by the LEE, and dramatically so in certain instances. The effects of viscosity on stability are also found to be important. Short wavelength disturbances are stabilised by viscosity, greatly altering the characteristic wavelength and maximum growth rate of instability. For the parameters considered here (chosen to be typical of aeroacoustic situations), the Reynolds number below which the flow stabilises ranges from 10$^{5}$ to 10$^{7}$. By assuming a thin but non-zero-thickness boundary layer, asymptotic analysis leads to a system of boundary layer governing equations for the acoustics. This system may be solved numerically to produce an effective impedance boundary condition, applicable at the wall of a uniform inviscid flow, that accounts for both the shear and viscosity within the boundary layer. An alternative asymptotic analysis in the high-frequency limit yields a different set of boundary layer equations, which are solved to yield analytic solutions. The acoustic mode shapes and axial wavenumbers from both asymptotic analyses compare well with numerical solutions of the full LNSE. A closed-form effective impedance boundary condition is derived from the high-frequency asymptotics, suitable for application in frequency domain numerical simulations. Finally, surface waves are considered, and it is shown that a viscous flow over an impedance lining supports a greater number of surface wave modes than an inviscid flow.E.J.B. gratefully acknowledges support from a Royal Society University Research Fellowship, and from a college lectureship from Gonville & Caius College, Cambridge. D.K. was supported by an EPSRC grant

Comparative evaluation of poly(pentafluoroaryl methacrylate)s and their non-fluorinated analogues as positive-working electron-beam resists

In order to rationalise the effects of fluorination on the performance of positive-working electron-beam resists based on methacrylate polymers, poly(pentafluorophenyl methacrylate) and poly(pentafluorobenzyl methacrylate) and their non-fluorinated analogues have been synthesized, and their electron-beam sensitivities and oxygen plasma etch rates determined for comparison with the corresponding parameters for alkyl methacrylate and fluoroalkyl methacrylate polymers reported in the literature. The fluoroaryl polymers were found to have enhanced dry-etch resistances, and in the case of poly(pentafluorophenyl methacrylate), to display a higher lithographic sensitivity than its parent non-fluorinated polymer. The plasma resistances and the lithographic sensitivities of the materials are considered, respectively, in terms of the potential for nucleophilic degradation of the ester side-groups, and of the thermochemistry of the available pathways for radiation-induced decomposition

Comparison of the Electron-Beam Lithographic Properties of a Range of Poly (Methacrylates) and Their Silicon-Containing Analogs

In order to understand and rationalise the difficulties encountered in achieving high lithographic sensitivity combined with dry-etch durability in electron-beam resists based on methacrylate polymers, the homologous series of n-alkyl methacrylates from methyl to butyl together with phenyl and benzyl methacrylates and the corresponding omega-trimethylsilylalkyl or p-trimethylsilylaryl methacrylates, where necessary, have been synthesized and polymerized using free-radical initiation. The polymer structures have been characterized using NMR spectroscopy and size-exclusion chromatography, and their thermal properties determined using differential scanning calorimetry. The polymers have been evaluated for their performance as electron-beam resists, both lithographically and in terms of their erosion rates in oxygen plasma processing; for these purposes, the performance of poly(methyl methacrylate) was used as a reference. Positive-working behaviour was observed for all the polymers with non-silylated ester functions, the lithographic sensitivities varying in the order butyl > ethyl > methyl approximately propyl > phenyl >> benzyl, and oxygen plasma etch rates being of the order of 2000 angstrom min-1. With the possible exception of poly(trimethylsilylmethyl methacrylate), the incorporation of trimethylsilyl groups in the alkyl ester functions is found to reduce significantly the lithographic sensitivities of the resists, and for the trimethylsilyl, ethyl, propyl and butyl polymers, a dominant negative-working behaviour pattern is revealed through judicious choice of developing solvents. In contrast, positive-working behaviour is maintained for the trimethylsilylaryl methacrylate polymers. The sensitivities of these are greater than those of the parent non-silylated polyesters, markedly so in the case of the benzyl polymer. With the exception of poly(trimethylsilylbenzyl methacrylate), the etch rate of which is still half that of the parent methacrylate polymer, oxygen plasma etch rates of all the polymers are reduced significantly by the incorporation of silicon. These effects are discussed in terms of the radiation chemistries of the various structures