FLOW CHARACTERISTICS OF MICROBUBBLE
4.3 Experimental Setup and Procedure
This gives the hydrodynamic drag coefficient as
L A U d a
U U
A d U C P
t sl l l
mb l l
mb l sl l
lw sl t l
t m fl l
m 3
3 3
0
) 1 ( 3
4
(4.25)
In Eq. (4.18), exceptl, all parameters are known. Using the experimental pressure drop, the corresponding values of l can be calculated from Eq. (4.18). Once the value of l is calculated, the drag coefficient of microbubble flow can be calculated from Eq. (4.25). From the definition ofl, one can calculate the friction factor, fl-mb in the straight pipe as
l l l mb l
f f
0 (4.26)
The average liquid-microbubble interfacial shear stress (τi) is expressed as
2 2 2 0
2)/ 0.5( )/
( 5 .
0 l sl l
l l l l
sl l mb l
i f U
U
f
(4.27)
If there is a slip at the interface, then Eq. (4.27) can be expressed as
2 2
/ ) (
2( 1
l is sl m mb l
i f U U
(4.28)
where Uis is slip velocity.
valves, a thermometer and a test section. Pressure drop was measured in straight horizontal pipes having diameters of 3 × 10-3, 6 × 10-3, 8 × 10-3, and 1 × 10-2 m, respectively.
Figure 4.1: Schematic representation of experimental setup for pressure drop. Legend: Ai: Air Inlet; CP: Pump; DL: Data logger unit; Li: Liquid inlet; MBG: Microbubble Generator; MS:
Microbubble suspension; P1-4: Pipes (i.d. 0.003 m, 0.006 m, 0.008 m and 0.010 m); R:
Rotameter; S: Self angle support; PT1-8: Pressure transducers; TS: Test section; Ts: Microbubble suspension tank with cooling jacket; Tm: Thermometer; V1-11: Flow control valve;
Wi: Water inlet; Wo: Water outlet.
The distance between the two pressure transducers was taken as 2.4 m for each pipe based on the condition L/d > 50 for fully developed ow. The test section was designed well to minimize losses due to contraction and expansion. The rotameter and pressure transducers were calibrated well to minimize the experimental error. Microbubbles were generated in a tank with a volume of 5 × 10-2 m3 by the microbubble generator. The volumetric ow rate of uid owing through the pipe was measured by the rotameter and controlled by a ow control valve. The test uid containing dispersed microbubbles was transported from the tank to the test section by a pump ( ow rate range of 0 6 × 10-4 (m3/s). The pressure transducer with a data logger
was used to measure the pressure drop along the length. Each experiment was performed repeatedly and allowed to run for 5 min to attain steady-state conditions.
4.3.2 Estimation of Gas Holdup
Gas holdup is defined as the volume fraction of the gas phase occupied by bubbles. The gas holdup in a microbubble column can be measured by the phase isolation method (Karamah et al., 2010; Kawahara et al., 2009). The gas holdup in microbubble-aided aeration systems can be measured by
w m
g
1 (4.29)
where εg is the gas holup, ρm and ρw are densities of the gas-liquid mixture and water respectively. In case of microbubble aided systems, the volume of liquid before and after bubbling does not change remarkably. Therefore the accuracy of the phase isolation method decreases as the bubble size and liquid volume under test is very less. In the present study, the gas holdup was measured by the electrical conductivity method. Maxwell (1892) reported that the effective conductivity of a dispersion (Kl-d) is related to the volume fraction (d) of a dispersed nonconductive phase by
d d l
d
l k
k
5 . 0 1
1 (4.30)
Gas holdup can be calculated based on this principle as
g l l
g l l
g k k
k k
5 .
0 (4.31)
where kl and kl-g are the electrical conductivities of the liquid and liquid-gas mixture respectively. The electrical conductivities of the liquid and liquid-gas mixture were measured
by digital conductivity meter (Model: VSI-04 ATC Deluxe, VSI Electronics Pvt. Ltd., Chandigarh, India). A schematic diagram of the apparatus used for gas holdup measurements is shown in Figure 4.2. The cell in the conductivity meter was an adaptation of a section of the
“ideal” cell consisting of two infinite and parallel plate electrodes (Kasper, 1940). The electrical conductance provided by the electrodes is described by the equation
e
l L
K A (4.32)
where Kl is the electrical conductance (inverse of resistance); is the electrical conductivity and A and Le are the area (m2) and separation (m) of the electrodes respectively. A/Le is referred to as the cell constant. Such a cell has been used to measure effective conductivities of dispersions (Achwal and Stepanek, 1975; Dhanuka and Stepanek, 1978; Marchese et al., 1992; Turner, 1976). Alternating current (ac) of sufficiently high frequency (about 1000 Hz) and low voltage (~1.5 V) was used to avoid polarization of the electrodes.
Figure 4.2: Schematic representation of gas holdup measurement.
4.3.3 Physical Properties of the System
In the present work, aqueous solutions of sodium dodecyl sulphate (SDS), cetyl trimethyl ammonium bromide (CTAB) and Tween-20 were used as liquid phase whereas air was used as gas phase. The densities of the solutions were measured with a specific gravity bottle. The surface tension was measured by tensiometer (model K9-MK1, Kruss GmbH, Hamburg, Germany). All the experiments in the present work were carried out at 25° C. Each test was replicated five times by repeating the above procedure and the average of them was taken as final reading. The physical properties of gas and liquid phase are shown in Table 2.1. Moreover, the viscosities of these fluids can increase or decrease due to changes in the rate of shear, which again is subject to the nature of the fluid. Unlike Newtonian fluids, non-Newtonian fluids are defined as materials that do not conform to a direct proportionality between shear stress and shear rate (Chhabra and Richardson, 1999). The effective viscosity of the liquid flowing through the pipe was calculated according to the equation
8 1
4 1
3
n
t sl n
e d
U n
K n
(4.33)
where µe is the effective viscosity of the suspension, n is flow behavior index, K is the flow consistency index, Usl is the velocity of the microbubble suspension and dt is diameter of the pipe.