121 Figure 5.34: Time trace of the vertical velocity of the 500 µm suspension interface. of particles in a suspended liquid with a viscosity of 2.05 cP. The central velocity for all cases was at.
SUSPENSION
These systems often exhibit many interesting phenomena that are not seen in the flow of a Newtonian fluid. The macroscopic flow behavior of a suspension depends on the dynamics at the microstructural level.
SUSPENSION VISCOSITY
In the biological systems such as living cells, blood, it is an even more exciting problem for practical application. The difficulty arises even more in the analysis of flow behavior of suspensions where the suspending fluids are not a simple fluid like water and air (Newtonian fluids).
SOME FLOW PHENOMENA IN SUSPENSIONS
Shear-induced particle migration
Hampton et al., 1997) particles migrate from high shear regions (near walls) to low shear regions (centerline). 1994) observed little or no particle migration in a rotating parallel-plate flow while Chow et al. 1995) observed migration that is radically outward from the apex of the cone in rotating cone-plate flow.
Axial segregation of particles
It was observed that the entire suspension separates into regions of high and low particle concentration along the length of the cylinder. 2000) performed similar experiments but in a different geometry (horizontal rotating cylinder) which was partially filled with the similar suspension and rotated about the horizontal axis. Following these experiments, Breu et al. 2003) studied the flow of non-neutral liquid suspension of mono-dispersed particles in a completely filled cylinder.
Surface corrugation 7
In the open channel flow, our aim was to measure the amplitude and velocity of the free surface motion. It was also desired to measure the variation in the height of the interface to quantify the free-surface deformation.
THESIS OUTLINE
They have also observed the contribution of wall slip to the volumetric flow rate in capillary flow. It was observed that increasing the surface roughness (increasing the value of κ1) prevented the wall sliding of the concentrated suspension.
PIV AND ITS APPLICATIONS
For example, during silo flow (as a result of wall friction between the granulated and transparent wall), the stresses on the surface can differ from those in the material. The instantaneous measurements of the free surface velocity and bulk velocity field for different suspensions are performed via PIV technique.
SURFACE CORRUGATION AND INTERFACE
For example, interface motion is associated with the free surface deformation or surface wave in suspension flow. 1998) measured free surface motion near the air-water interface of a submerged jet aircraft.
AXIAL SEGREGATION IN ROTATING CYLINDER
However, their measurements can be affected by lateral migration of particles initiated by the presence of the wall and non-uniform velocity gradients. Power spectral densities were calculated from the intensities of the refracted light from the free surface.
EXPERIMENTAL FACILITIES AND PROCEDURES 34
Channel and flow apparatus
The two ends of the reservoir were connected to the screw pump via circular tubes of inner diameter 2 cm which circulated the suspension in the channel. The speed of the pump as well as the slope of the channel could be adjusted to get the desired flow.
Particle image velocimetry
With the lens operating at 0.7 magnification, the captured image of the flow field was 15.5 mm x 11.5 mm. Thus, the size of the interrogation window was approximately 2.9 mm x 2.9 mm and the distance between two adjacent interrogation windows was approximately 729 meters.
PREPARATION OF SUSPENSION
To achieve density matching with PMMA particles of density 1.18 g/cc, the suspending liquid was prepared by mixing 74% glycerol and 26% water (v/v%). The suspension of 500 µm polystyrene particles in 98 cP Ucon oil was prepared by direct mixing as its density was almost equal to the polystyrene density 1.05 g/cc. For the rheological characterization of the suspension liquid mixture, the HAKKE RS1 rheometer was used.
R is the ratio of the radius of the inner cylinder to the radius of the outer cylinder.
RESULTS AND DISCUSSION
Free surface velocity profile for suspending fluid
Free surface velocity profile for concentrated suspension
Therefore, all velocity measurements were performed at the axial location of 27.3 cm from the duct entrance. In many situations, shear-induced migration will cause particles to migrate from the wall to the center of the channel. The shear velocity () at the wall achieved in most of our experiments was ~1s-1 and the average velocity in the channel was ~1 cm s-1.
The velocity measurements used in the analysis of wall sliding were performed 27 cm downstream of the channel.
Wall slip coefficients
To study the effect of suspending fluid viscosity alone on the wall slip, we took suspensions of 500 µm particles dispersed in different fluids with viscosity 2.05 cP, 98 cP and 204 cP. It can be observed that the wall slip velocity increases as the suspension fluid viscosity is lowered. In Fig.3.25a we have shown the sliding velocity scaled by the center line velocity plotted against the shear rate for the suspension of liquid with viscosity of 80 µm, 250 µm and 500 µm particles in 2.05 cP suspension liquid at 24°C.
The wall slip is greater in the suspension with 2.05 cP of suspended liquid compared to 98 cP and 204 cP (at 24 °C) of suspended liquid.
CONCLUSION
Even at low Reynolds number, the free surface flow of concentrated suspensions of non-colloidal particles exhibits surface ripple. Whether the presence of wall slip causes the free surface to exhibit deformation (as when a stretched membrane is suddenly relaxed) in the form of surface ripple was the motivation behind studying the effect of wall slip on surface waviness. The perturbations at the free surface were observed to span a wide range of frequency and wavelength.
The surface images were taken by placing the camera above the surface and illuminating the free surface using a cold light source (Thorlab).
CHARECTERIZATION OF FREE SURFACE
Power spectral densities of image intensity for both temporal and spatial directions provide indirect estimation of surface ripple since the exact relationship between surface curvature and intensity of the image is not known (Loimer et al., 2002; Timberlake and Morris, 2005). The recent studies on free surface flow of concentrated suspension (Loimer et al., 2002; critical fraction is reached, after which the autocorrelation functions decay slowly. Faster decay of autocorrelation with spatial dimension indicates greater fluctuation at the free surface.
Power spectral densities of image intensity for temporal and spatial directions provide an indirect estimate of surface wrinkling, as the exact relationship between surface curvature and image intensity is unknown (Loimer et al., 2002; Timberlake and Morris, 2005).
RESULTS AND DISCUSSION
There is no clear difference in the spectral distribution for all particle sizes and the viscosity of the suspension liquid. However, it is desirable to study the waviness in the velocity-vorticity plane (perpendicular to the plane of the free surface) to quantify the waviness and its dependence on the particle size and viscosity of the suspending fluid. The comparable graphs for different suspensions of 500 µm particles in different suspending liquids are shown in Figure 4.15 to Figure 4.18.
The results are similar for all suspensions, regardless of the size and viscosity of the suspended liquid.
CONCLUSION
Therefore, it is important to determine the location of the interface and study the disturbance of the air-suspension interface in the free surface flow of a concentrated suspension. Du et al. (2007) found that interface velocity is proportional to interface stiffness, mobility, and curvature. In a free surface flow of a suspension, the oscillation of particles near the surface causes deformation of the interface.
In this work, we reported the quantitative study of the interface in the velocity-vortex plane during the free surface flow of concentrated suspension.
EXPERIMENTAL DETAILS
Channel and flow apparatus
The fluctuation and perturbation of the interface is calculated in terms of the root-mean-square fluctuation and the root-mean-square vertical velocity at the interface.
Optics for interface location and PIV images
Preparation of suspensions
Suspender fluid density: 1.05 g/cm3 Suspender fluid viscosity: 2.05 cP Suspender fluid surface tension:. viscosity for 1.18 g/cm3 PMMA particles. Suspender fluid density: 1.18 g/cm3 Suspender fluid viscosity: 4000 cP Suspender fluid surface tension:. viscosity for 1.05 g/cm3 polystyrene particles.
RESULTS AND DISCUSSION
Interrogation of PIV images and bulk vertical velocity
The suspensions of different concentrations were prepared with 250 µm polystyrene particles in 2.05 cP of density-matched suspending fluid. The suspensions of different concentrations were prepared with 500 µm polystyrene particles in 2.05 cP of density-matched suspending fluid. The suspensions with different concentrations were prepared with 500 µm polystyrene particles in density adjusted suspending fluid with viscosity 98 cP.
The suspensions with different concentrations were prepared with 500 µm polystyrene particles in density adjusted suspending liquid with viscosity 204 cP.
Diffusive flux model for suspension flow
Time-averaged vertical velocity of the interface at different flow rates in the channel for different particle concentrations. Time-averaged vertical velocity of the interface at different flow rates in the channel for suspension of 200 µm particles. The number of bands was found to increase with the rotational speed of the cylinder.
Fig.6.12a shows that the number of bands at steady state (after band migration is complete) decreases with increasing cylinder rotation speed.
Determination of interface location, interface vertical
CONCLUSION
In some recent studies, it has been observed that a suspension of uniformly distributed neutral particles in a partially filled horizontally rotating cylinder separates into bands of particles that are separated by regions of clear liquid (Tirumkudulu et al., 1999; Tirumkudulu et al., 2000). To our knowledge, there are no reported studies on the suspension of non-neutrally dispersed particles in a rotating cylinder. The initial distribution of particles in the non-neutrally and neutrally buoyant double suspension present in a rotating cylinder is shown in Fig.6.1.
Despite their industrial importance, there are no reported studies of the size separation of bi-dispersed suspensions in horizontally rotating cylinder.
DETAILS OF EXPERIMENTAL SETUP
For a given fill fraction, the segregation rate increases with the angular speed of the rotating cylinder. 40 rpm, the particles' movement is restricted in the bottom of the cylinder without rising along the tube wall. It was found that the number of bands increases with the rotational speed of the cylinder (Fig.6.16).
The particles were redispersed in the suspending liquid as they fell with the downward movement of the cylinder wall.
