The effect of weak shear thinning on the stability of the Taylor-Couette flow is explored for a Carreau-Bird fluid in the narrow-gap limit. The Galerkin projection method is used to derive a low-order dynamical system from the conservation of mass and momentum equations. In comparison with the Newtonian system, the present equations include additional nonlinear coupling in the velocity components through the viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of the base (Couette) flow, becomes lower as the shear-thinning effect increases. That is, shear thinning tends to precipitate the onset of Taylor vortex flow. Similar to Newtonian fluids, there is an exchange of stability between the Couette and Taylor vortex flows, which coincides with the onset of a supercritical bifurcation. However, unlike the Newtonian model, the Taylor vortex cellular structure loses its stability in turn as the Taylor number reaches a critical value. At this point, a Hopf bifurcation emerges, which exists only for shear-thinning fluids.
The nonlinear stability of the one-dimensional plane Couette flow is examined for a Johnson–Segalman fluid. The velocity and stress are represented by symmetric and antisymmetric Chandrasekhar functions in space. The flow field is obtained from the conservation and constitutive equations using the Galerkin projection method. Both inertia and normal stress effects are included. For given Reynolds number and viscosity ratio, two critical Weissenberg numbers are found at which an exchange of stability occurs between the Couette and other steady flows. The critical points coincide with the two extrema of the stress/rate-of-strain curve. At low (high) Reynolds number, the flow decays monotonically (oscillatorily) toward the steady-state solution. The number and stability of the nontrivial branches around the critical points are examined using the method of multiple scales. Comparison between the approximate and the numerical branches leads to excellent agreement in the vicinity of the critical points. The influence of the higher-order modes is assessed, showing low-order convergence and good accuracy when the flow profiles are compared against existing finite-element results.
The nonlinear stability and bifurcation of the one-dimensional plane–Poiseuille flow is examined for a Johnson–Segalman fluid. The methodology used is closely related to that of Ashrafi and Khayat [Phys. Fluids 12, 345 (2000)] for plane–Couette flow. The velocity and stress are represented by orthonormal functions in the transverse direction to the flow. The flow field is obtained from the conservation and constitutive equations using the Galerkin projection method. Both inertia and normal stress effects are included. The stability picture is dramatically influenced by the viscosity ratio, ε. The range of shear rate or Weissenberg number for which the base flow is unstable increases (from zero) as the fluid deviates from the Newtonian limit (as ε decreases). Typically, two turning points are observed near the critical Weissenberg numbers. The transient response is heavily influenced by the level of inertia. It is found that the flow responds oscillatorily when the Reynolds number is small, and monotonically at large Reynolds number (when elastic effects are dominated by inertia).
In this work, a new extraction process using steam explosion at high temperature and pressure was developed, to drastically shorten the extraction time and improved extraction of the essential oil from citrus peels. In steam explosion process, the material is subjected to the high-pressure saturated steam following by substantially dropping the pressure through an angle valve to a vacuum tank. The optimum essential oil yield by the steam explosion was obtained at the 170 °C, 8 bar in 240 seconds duration time. The essential oil extraction of a certain amount of citrus peels by hydro-distillation took nearly eight times longer than explosion extraction process. The obtained citrus oil from hydro-distillation processes had 10 to 13 major components more than the steam explosion, as shown by gas chromatography (GC-MS). The maximum product yield of Limonene, a major favorable component, were 77% and 100% in hydro-distillation and steam explosion processes, respectively.
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