Pulsatile flow of thixotropic fluids is investigated numerically in a partially-constricted tube assuming that the fluid obeys Moore's structural model as is constitutive equation. Assuming that the flow is laminar, incompressible, two-dimensional and axisymmetric, the equations of motion are simplified using lubrication theory. The simplified equations are then solved numerically using the finite difference method. A suitable coordinate transformation is used to immobilize the boundary of the tube. The effect of the structure breakdown/reformation parameters is investigated on the velocity field and wall shear stress distribution. The importance of the geometrical parameters of the constriction is also investigated on the flow characteristics.
In the present work, the collapse of a single non-spherical gas bubble situated above a rigid wall and surrounded by a viscoelastic liquid is studied numerically using the boundary element method (BEM). Assuming that the liquid obeys the “material” Maxwell model as its constitutive equation, the modified viscous potential theory developed by Lind and Phillips32) is used to investigate the role played by the buoyancy and Bjerkness forces on the bubble collapse. To simplify the analysis, the bubble is assumed to retain its axisymmetric shape during its collapse. Also, the non-condensible perfect gas inside the bubble is assumed to undergo an adiabatic process during the bubble's collapse. The numerical results show that at the latest stages of the collapse, an oscillating liquid jet is developed if the Bjerknes and buoyancy forces are more dominant than the viscous and elastic forces. However, if viscous and elastic effects are more dominant, there will be no liquid jet formed near the wall with the bubble preserving its nearly spherical shape all throughout its oscillatory motions.
We investigated the laminar and turbulent impinging jet for drag reducing surfactant solutions. The counterion was added at the molecular ratio to surfactant of 1:1 or 10:1. Although both solutions showed turbulent drag reduction in pipe flow, different flow was observed in the impinging wall flow depending on the counterion concentration. The solution with equimolar counterions showed the rheological behavior such as a Bingham plastic in an impinging jet, and the radial wall flow was blocked at some radial location by surrounding quiescent solution and turned perpendicular to wall. The radius of this wall flow was increased with the Reynolds number. When the impinging wall flow was turbulent, the shear flow and turbulence appeared in the thin wall layer between impinging wall and quiescent solution. By contrast, the surfactant solution with excess counterions developed laminar and turbulent boundary layer flow on the impinging wall similarly as water. These flow characteristics were consistent with the past study, which showed that the surfactant solution with excess counterions maintained the similar heat transfer as water.
A model estimating local particle dispersion/aggregation behaviors in a suspension has been developed for a non-uniform shear flow. In this model, the size distributions of particle clusters were calculated with taking a balance of Brownian and shear coagulations and shear breakup. A numerical simulation was performed for a two-dimensional backward-step flow as a non-uniform shear flow. A flow experiment using a micro-channel with a rib was also conducted for the verification of the present numerical analysis. The solid volume fraction of the suspension was set at 0.01 and the step height Reynolds number was kept constant at 1.5×10-4 both for numerical and for experimental studies. The numerical results obtained in this study were rather reasonable compared with the experimental data. From this, it was found that the present numerical model is promising for estimating particle dispersion/aggregation in a non-uniform shear flow.
Viscoelastic properties of symmetric poly(styrene-block-2-vinylpyridine)s in the ordered and disordered states under steady shear flow are examined for relatively low molecular weight samples at melt based on the temperature dependence of interaction parameter χ. Since both components have almost the same viscoelastic properties, data for block copolymers and components are directly compared. In the disordered state near the ODT, two constant values for shear viscosity η, η01 and η02 at lower and higher shear rates, γ, respectively are obtained for diblock samples and η01 coincided with the value obtained by dynamic flow measurements, which are higher than the values for components. The constant values of Je are obtained at γ range where η02 are obtained, which are also higher than those of components. It was concluded that higher η01 and lower η02 values are due to the fluctuation effects and their suppression by the flow with higher γ, respectively. It was also concluded that fluctuation effects on viscoelastic properties completely disappear at around χN < 2 - 3 for SPs. In the ordered state, well aligned state was only attained for the sample having lowest molecular weight. The values of η0 and Je obtained in well aligned state are consistent with those in disordered state, denoting that there is no discontinuity of data due to ODT.
Separation method of responses from large scale motions and polymer chain motions are investigated for viscoelastic properties of symmetric poly(styrene-b-2-vinylpyridine)s (SP) in the ordered state taking into account of the effects of flow history on the sample. Due to the almost same thermo-rheological properties of components, master curves of dynamic moduli for SP, G*SP are obtained and shown that the data well coincide with those of polystyrene homopolymers (hPS) at high frequency ω, while responses from large scale motions of lamellar structure, ΔG*grain are observed at low ω, which asymptote to ΔG*grain ∼ ω0.5. After the pre-shear, magnitude of ΔG*grain became lower at the lower ω region. When the magnitude of G*SP are appropriately higher than ΔG*grain extended to higher ω, ΔG*grain and the responses of polymer chains, ΔG*chain, having Rouse like modes, are successfully obtained by subtraction, ΔG*chain = G*SP - ΔG*grain, irrespective of pre-shear. By combining thus obtained ΔG*grain, ΔG*chain, and the data for hPS, G*hPS at higher ω region, G*SP data can be well approximated in a whole frequency range of the measurement.