To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships.

Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

In this paper we re-examine the problem of applying a thin layer of a power-law fluid to a solid substrate by means of a simple blade coater. Specifically we use lubrication theory to examine steady plane flow of a power-law fluid in the narrow nonuniform channel formed between a fixed blade of prescribed shape and a plane substrate moving parallel to itself. The first-order asymptotic solution for the case of a weakly non-Newtonian fluid is presented. An explicit expression is obtained for the first-order pressure gradient from which the first-order contributions to several important physical quantities including the thickness of the applied fluid layer and the forces on the blade are calculated for both plane and exponentially shaped blades. In particular, we find that, depending on the shape and height ratio of the coater, the effect of weakly non-Newtonian behavior can be either to increase or to decrease both the pressure and the load from their Newtonian values. We also re-examine the approximate solutions of Hwang [Trans. ASME J. Fluids Eng. 104, 469 (1982)] and Dien and Elrod [Trans. ASME J. Lubrication Technol. 105, 385 (1983)] and make a detailed comparison between their predictions and those of the exact solution in the weakly non-Newtonian limit. We find that in this limit the Dien and Elrod approximation is usually in significantly better agreement with the exact solution than Hwang’s approximation. In the Appendix we re-examine the Dien and Elrod approximate solution for the flow of a generalized Newtonian fluid.

Blade coating of a power-law fluid

Power law fluid model incorporated into elastohydrodynamic lubrication theory of line contact

Threshold of ribbing in a two-roll setup is investigated for non-Newtonian fluids. Two typical shear-thinning polymeric solutions are used, the first one exhibiting inelastic properties (Xanthan), the second one viscoelastic properties (polyacrylamide, PAAm). The effect of polymeric concentration and thus rheological parameters on the effective critical capillary number Ca ∗ at the onset of ribbing is described. For low polymer concentrations, only a small decrease of the onset is observed for both fluids. At larger concentrations, Ca ∗ remains constant for inelastic fluids, while for the elastic fluids, a continuous decrease up to a factor 10, with respect to the Newtonian case, is observed. Above threshold, a strong effect on elastic properties is also observed on the amplitude of ribbing. © 2002 Elsevier Science B.V. All rights reserved.

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Non-Newtonian effects on ribbing instability threshold

A study of optimum load capacity of slider bearings lubricated with power law fluids

A lubrication theory for the power law fluid is developed and analyzed. Only the infinite width gap is considered. Considered is flow between rigid walls of arbitrary shape under combined Couette and squeezing motion with a pressure gradient. equations appropriate to a thin film are derived by asymptotic integration of the three-dimensional equations of fluid mechanics. Further integration of these equations yields an algebraic equation for the pressure gradient. Working out the details of the structure of the equation enables us to develop a numerical algorithm for its solution

Analysis of Lubrication Theory for the Power Law Fluid

Abstract
This study proposed an alternative method to earthquake ground motion characterization based on composite-intensity index spectrum. It is a combination of spectral acceleration (Sa(T)), duration (D05-95) and peak ground velocity (PGV). The spectrum, considering the effect of three-component motions, was firstly introduced in the paper. It was established based on thirty-one three-component strong earthquake records that were collected worldwide. The index was further related to the modified Mercalli intensity scales to assign its damage potentials. The method revealed more meaningful interpretations of earthquake ground motion characterization than other procedures.
Keywords: Earthquake motion characterization, three components, composite-intensity index, acceleration spectrum, duration, peak ground velocity, MMI.
Abstrak
Studi ini mengusulkan metode alternatif terkait karakterisasi gelombang gempa berdasarkan spektrum indeks intensitas komposit. Indeks ini adalah gabungan dari spektra percepatan (Sa(T)), durasi (D05-95) dan kecepatan puncak permukaan (PGV). Spektrum indeks intensitas komposit, dengan tinjauan gelombang gempa tiga-komponen, adalah yang diusulkan pertama kali dalam makalah ini. Metode ini dikembangkan berdasarkan tiga-puluh satu gelombang gempa tiga-komponen yang tersebar di dunia. Indeks tersebut selanjutnya diikatkan dengan skala intensitas Mercalli termodifikasi untuk menunjukkan potensi kerusakannya. Hasil yang diperoleh menunjukkan bahwa karakterisasi gelombang kuat dapat dilakukan berdasar indeks intensitas komposit lebih baik daripada metode lain yang tersedia.
Kata kunci: Karakterisasi gelombang gempa, tiga komponen, indeks intensitas komposit, spektrum percepatan, durasi, kecepatan puncak, permukaan, skala MMI.

Engineering Characterization of Earthquake Ground Motions Based on Composite-intensity Index Spectrum

Abstract
This study introduces a new procedure for three-component spectral matching of seismic ground acceleration records. The procedure involves preserving the phase angle and varying the Fourier amplitudes to match the spectra of the recorded records with a provided target spectrum that represents the spectral values of ground motions in three orthogonal directions. Several three-component recorded records were matched against two target response spectra to test the method. An accurate convergence was achieved in the velocity and displacement records. In addition, the scales among the components’ magnitude were maintained, creating realistic three-component ground motions. Such ground motion inputs are important to qualify critical structures sensitive to three-component motions. Our proposed procedure is novel because the present practices are mostly created based on one-component ground motions.
Keywords: Spectral matching, three components, component scales, phase angle, critical structures.
Abstrak
Studi ini mengusulkan prosedur baru terkait penyesuaian spektra catatan percepatan gempa. Prosedur ini dilakukan dengan mempertahankan sudut phasa tetapi mengubah amplitudo Fourier catatan percepatan gempa demikian hingga spektrumnya sesuai dengan target. Target spektrum yang diinputkan mewakili tiga komponen gempa. Untuk mengujinya, beberapa catatan gempa tiga-komponen disesuaikan spektrumnya terhadap dua target spektra. Ketelitian yang cukup baik terlihat dari catatan kecepatan dan simpangan. Skala ketiga komponen juga dijaga sehingga dihasilkan percepatan gempa tiga-komponen yang realistis. Percepatan gempa sejenis ini diperlukan dalam proses kualifikasi struktur penting yang sensitif terhadap pengaruh gerakan tiga arah. Prosedur tersebut adalah baru karena teknik yang ada sekarang didasarkan pada penyesuain spektrum per-komponen.
Kata-kata Kunci: Penyesuaian spektra, tiga komponen, skala komponen, sudut phasa, struktur penting.
 

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S. Mangkoesoebroto

Papers

Analysis of Lubrication Theory for the Power Law Fluid

Engineering Characterization of Earthquake Ground Motions Based on Composite-intensity Index Spectrum

Spectral Matching of Three-Component Seismic Ground Accelerations for Critical Structures