1994
DOI: 10.1002/pen.760342006
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The behavior of bubbles in Bueche model fluids

Abstract: The nonlinear oscillation of a spherical gas bubble in polymer solutions was theoretically analyzed. Using the rheological equation of Bueche model fluid, the equation of motion and the pressure equation for a bubble are derived. According to the numerical calculations, the effects of rheological properties and initial radius of the bubble on the bubble radius‐time history, pressure at the bubble wall, critical and equilibrium radii of the bubble, as well as pressure distribution in liquid are discussed.

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Cited by 5 publications
(4 citation statements)
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“…As R 0 decreases to 10 −2 mm, the maximum bubble wall pressure decreases to 6:07 ×10 3 and is then within an order of magnitude of the similar value in water (p max =p ∞ = 2:33 × 10 4 ). This ÿnding is in qualitative agreement with the predictions of several incompressible formulations derived by using di erent rheological models (Shima and Tsujino, 1981;Shima et al, 1983 andBrujan, 1994). It is possible that the substantial reduction of the maximum bubble wall pressure caused by the polymer additives in the case of very small bubbles may cause a corresponding reduction in cavitation damage.…”
Section: Numerical Results and Discussionsupporting
confidence: 87%
“…As R 0 decreases to 10 −2 mm, the maximum bubble wall pressure decreases to 6:07 ×10 3 and is then within an order of magnitude of the similar value in water (p max =p ∞ = 2:33 × 10 4 ). This ÿnding is in qualitative agreement with the predictions of several incompressible formulations derived by using di erent rheological models (Shima and Tsujino, 1981;Shima et al, 1983 andBrujan, 1994). It is possible that the substantial reduction of the maximum bubble wall pressure caused by the polymer additives in the case of very small bubbles may cause a corresponding reduction in cavitation damage.…”
Section: Numerical Results and Discussionsupporting
confidence: 87%
“…The dependence of zero‐shear viscosity ( η 0 ) on concentration ( c ) is usually used to distinguish the dilute and concentrated solution regions of polymer solution. The η 0 value is usually estimated from the Newtonian flow region at low shear rates or various models such as Bueche model, 43 Carreau model, 44 Cross model, 45 Ellis model, 46 and power‐law fluid model, 47 which are used to simulate the relationship between the apparent viscosity ( η a ) and shear rate. So far, no models have been found for simulation of shear‐thickening behavior of polymer solutions.…”
Section: Resultsmentioning
confidence: 99%
“…To prevent the solution concentration from changing resulted from solvent evaporation, the sample solution was covered with a thin layer of lowviscosity silicone oil. 5,42 The usually used viscosity models of Bueche model, 43 Carreau model, 44 Cross model, 45 Ellis model, 46 and power law model, 47 as well as the yield stress models of Bingham model, 48 Casson model, 49 Cox-Merz model, 50 and Herschel-Bulkley model 51 were used to simulate the steady shear rheological behaviors of polysaccharides.…”
Section: Steady-shear Viscosity Measurementmentioning
confidence: 99%
“…The power-law model was adopted by Yang and Yeh [21] and Shima and Tsujino [22] in their investigations. In addition, the Casson model [23], the Ellis model [24], Sisko model [25], the Carreau model [26], the Powell-Eyring model [27], the Shima model [28], the Williamson model [29,30], and the Bueche model [31] have been applied.…”
Section: Equations Of Motion For the Bubble Radiusmentioning
confidence: 99%