Apparent viscosity (ηapp ) as a function of shear rate. Shear thickening was measured for shear rates lower than 3000 s−1. The range of shear thickening ηapp > 1.1 × (ηapp ) γ =3000 is indicated by an arrow for each solution to compare the shear thickening in the rheometer with the friction change in the pipe flow [Fig. 8(a) ].
Schematics of SIS visualization. The top view was taken with a horizontal laser sheet in the y-z plane, and the frontal view with a vertical laser sheet in the x-y plane.
Shear-induced threadlike streaks of surfactant. (a) and (c) Top views of the quiescent state show uniform light scattering without threads using 500 ppm × 1 and 500 ppm × 10. (b) Top view of steady flow for the same 500 ppm × 1 solution as Fig. 3(a) . The Reynolds number was 3000. After the flow becomes steady, the additional induction time of about 8 s is necessary to develop the threadlike streak. The small arrows show the threadlike streaks. (d) Top view of steady flow for the same 500 ppm × 10 solution as Fig. 3(c) . The Reynolds number was 8000. After the flow becomes steady, it takes the additional induction time of about 0.6 s to develop the threadlike streak.
Impinging jet at the pipe exit. (a) A typical impinging jet at the pipe exit is composed of a stagnation flow and the following thin wall shear flow. The surrounding fluid is almost quiescent. (b) Vector map of impinging jet for water. Rew = 8000. (c) Vector map of a branched streak at the pipe exit. The solution of 500 ppm × 10, and Rew = 8000. The branched streak shows higher velocities than the surrounding fluid.
Trajectory of a PIV particle in the branching streak at the pipe exit. The solution of 500 ppm × 10, and Rew = 8000. (a) Tracked particle at t = 0 ms in the PIV image. (b) Particle trajectory traced at an interval of 3.3 ms. The particle velocity is 0.12 V near the exit and increases to 0.37 V over the impinging wall.
Elastic behavior of shear-induced threadlike streaks at the pipe exit. The solution of 500 ppm × 10, and Rew = 8000. A thread is stretched by radial flow on the impinging wall and is shifted into the surrounding quiescent fluid.
Frontal view of the dark threads spouting out of the pipe exit. The laser sheet in the x-y plane was radiated along the glass window. Solution of 500 ppm × 10, and Rew = 8000.
Pipe frictional coefficient and visualization of threadlike SISs. (a) The pipe frictional coefficient λ was obtained from pressure loss measurements in the same pipe as the visualization. (b)–(f) Frontal views of the pipe cross section were illuminated by a laser sheet. The Reynolds numbers were 1000, 2000, 3000, 5000, and 8000, respectively, for the solution 500 ppm × 10. The dark near-wall ring [Figs. 8(c)–8(f) ] corresponds to a dense distribution of threads, and the thickness of the ring increases with Rew. (g) Top view of the threadlike SISs for the 500 ppm × 10 solution. Rew = 20 000 and DR = 64%, where DR is a drag reduction rate from a Blasius formula. (h) Top view of the threadlike streaks in the 500 ppm × 1 solution. Rew = 8000 and DR = 44%. Drag reduction occurs when this thread structure is present as occurred with the threads shown in Fig. 8(g) . (i) Top view of 500 ppm × 1 solution for Rew = 20 000. At this Reynolds number, the thread structure breaks down and the drag reduction drops to zero [Fig. 8(a) ].
Lateral velocity of the threadlike SIS branched from the impinging jet. The 500 ppm × 10 solution, and Rew = 8000. The lateral shift and velocity of the thread were measured at an interval of 10 ms.
Drag reduction and surfactant threads in the pipe flow, and shear thickening in the rheometer. 500 ppm× 1. DR is a drag reduction rate in the pipe friction coefficient from a Basius formula. (ηapp ) γ =3000 = 1.72 mPa s. Shear thickening appears in the shear stress range of τ < 2.8 Pa.
Drag reduction and surfactant threads in the pipe flow and shear thickening in the rheometer. 500 ppm× 10. (ηapp ) γ =3000 = 1.37 mPa s. Shear thickening appears in the shear stress range of 0.22 Pa< τ< 3.2 Pa.
Streamwise length ℓ and spanwise spacing B of turbulent coherent structures in the past studies. Rew = 8000, kinematic viscosity νw = 1.5 × 10−6 m2/s, and pipe radius R = 5 mm. DR = 43% and frictional velocity uτ ( ) = 0.0387 m/s (500 ppm× 10).
Article metrics loading...
Full text loading...