(1995). There is again good qualitative agreement between the two measurements when we compare the plot of ( a s) against particle concentration in the Fig. 3.28b.
Figure 3.27: (a) Plot of slip velocity scaled with maximum centerline velocity against shear rate for the suspension of 500 m particles in suspending fluids of viscosity 2.05 cP, 98 cP, and 204 cP. (b) Plot of wall slip velocity against particle concentration.
Figure 3.28: (a) Plot of apparent wall slip coefficient (β) with particle concentration and (b) comparison of slip coefficient after taking account the viscosity of suspending fluid ηs (2.05 cP, 98 cP and 204 cP at 24°C. The particle size in all the cases of our measurement was 500 m.
particle size, volume fraction of particles and the viscosity of suspending fluids. The images were captured using a 1360 x 1024 pixel CCD camera (PixFly HiRes from PCO) in conjugation with a macro zoom lens. The camera was operated with frame rate of 19 frames/s and the duration between subsequent images was 52 ms. The captured images were used for the velocity profile measurement using the tool of Particle Image Velocimetry (PIV). To find out the accuracy of PIV measurements, we performed the comparison of experimentally determined mean y – velocity profile for both the channels (plane and serrated) with the analytical value (parabolic profile) for the Newtonian suspending fluids. To get the mean velocity profiles, an average of 100 velocity vectors was taken which were obtained by cross – correlation analysis of 100 consecutive pairs of images. All the velocity measurements were carried out at the axial location of fully developed from the channel entrance. It was observed that the scaled velocity profiles are similar at different flow rates. This is true for both plane and serrated channel. In the present experiments, no significant particle migration was expected. Moreover, the mixing of suspension in the screw pump and the small length of channel ensured that lateral migration of particles across the channel remained minimal. The wall slip coefficients (β) were determined. Linearity of slip velocity in shear rate was observed. The plot of slip velocity against particle concentration was also shown. As expected, the slip velocity increases with particle concentration and particle size but decreases with increase in the viscosity of suspending fluid. Comparative plot of dependence of apparent slip co-efficient on particle concentration with the experimental measurements of Jana et al. (1995) was presented. The results are in reasonably good agreement.
4
FREE SURFACE CORRUGATION IN OPEN CHANNEL FLOW
4.1 INTRODUCTION
Even at low Reynolds number, the free surface flow of concentrated suspensions of non- colloidal particles exhibits surface corrugation. It is also well known that non-colloidal concentrated suspensions have non-zero normal stress differences. Many polymeric fluids have large first normal stress difference. Under condition of no-slip polymeric fluids with negative (extensional) first normal stress difference will behave like a stretched membrane.
The non-colloidal suspensions are known to have positive (in the compression sense) first and second normal stress difference. Whether the presence of wall slip causes the free surface to exhibit shape (like when a stretched membrane is suddenly relaxed) in the form of surface corrugation was the motivation behind studying the effect of wall slip on surface corrugation.
The corrugation structure depends on a number of factors such as particle concentration, shear rate, particle size and surface tension of the suspending fluid. By analyzing the power density of the refracted light from the free-surface, the surface roughness was characterized.
Since the relative illumination intensity is associated with the local inclination of the surface, study of temporal and spatial intensity spectra provided valuable information about the wave amplitude and frequency of the surface deformation patterns. It was observed that the disturbances at the free surface span over wide range of frequency and wavelength. We have performed experiments to study whether wall slip affects the surface corrugation pattern or not. The surface images were taken by placing the camera above the surface and illuminating the free surface using cold light source (Thorlab). The light source was placed at an appropriate angle so that it reached the camera lens after refraction from the free surface. The corrugated surface refracted the light depending upon the local free surface orientation. Our objective is also to study the effect of plane walled and serrated walled channel. The setup
arrangement for plane walled channel is shown in Fig.4.1. Power spectral densities of image intensity for both temporal and spatial directions provide indirect estimate of surface corrugation since the exact relation between surface curvature and intensity of the image is not known (Loimer et al., 2002; Timberlake and Morris, 2005). The near surface particle fluctuation causes deformation of the interface. When the deformation relaxes, the energy contained within it is released back into the fluid. This may further affect the surface topography elsewhere. The experiments were studied towards the effect of suspended particle size, suspended particles fractions and suspending fluid viscosity. The power spectral density (PSD) of image intensity values was computed using fast Fourier transform similar to Singh et al. (2006). A total of 444 frames were taken to get the PSDs.
Figure 4.1: Photograph showing the experimental arrangements for capturing images of surface corrugation.
4.2 CHARECTERIZATION OF FREE SURFACE CORRUGATION