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Gas-Sparged Ultrafiltration: Recent Trends, Applications and Future Challenges 673
since these involve significant modifications to the membrane module and some cases are very
energy intensive. Concentration polarization can also be controlled by solid–liquid two-phase
flow (25–27). However, the added solids can damage the membrane and more importantly
these need to be removed from the retentate stream. Gas sparging, i.e., injecting gas (e.g. air,
nitrogen) in the form of bubbles into the feed stream has proved to be an effective, simple and
cost-effective technique for controlling concentration polarization (1, 12–13). Gas sparging
works by formation of bubble induced secondary flow, physical displacement of the mass
transfer boundary layer, scouring of the membrane surface and pressure pulsing caused by gas
slugs (28). The contributions of these mechanisms in controlling concentration polarization
depend of the type of membrane module and their mode of operation. The basic and applied
aspects of gas-sparged ultrafiltration particularly the use of gas bubbles for permeate flux
enhancement are discussed in detail in the subsequent sections.
3. FUNDAMENTALS OF GAS–LIQUID TWO-PHASE FLOW
In order to use gas sparging in an effective manner it is necessary to understand gas–liquid
two-phase flow behaviour. This section provides a brief overview of gas–liquid two-phase flow.
3.1. Bubbles
When gas is injected into a stationary liquid, gas bubbles are formed and these move
upward due to buoyancy. The size of the bubbles depends on the way the gas is introduced
and on the gas flow rate. The bubble motion generates a secondary flow behind the bubble,
i.e., the wake region. The strength and extent of wake region depends on the shape and size of
the bubble. Based on their shape, bubbles in stationary liquids are classified into spherical,
ellipsoidal and spherical-cap bubbles. The shape of the bubbles can be anticipated empirically,
as shown in Fig. 16.1 (29). As the bubble size increases, the shape of the bubble
changes from spherical to ellipsoidal and eventually to spherical-cap.
Spherical bubbles are small and their size is usually less than 1 mm. Since there is no
boundary layer separation around such bubbles, there is no wake. Ellipsoidal bubbles are
typically of 1.5–15 mm size. There is boundary layer separation around such bubbles and
hence these are followed by helical vortex wakes. Spherical-cap bubbles are usually big
bubbles (>15 mm) and their primary wake is about 4.5 times the bubble volume (30). These
big bubbles can generate strong secondary flow effect.
The terminal rise velocity of spherical bubbles can be approximated by Stokes law (Re < 1),
Ub ¼ d2 egðr1 18m1 rgÞ : (1Þ
Ellipsoidal bubbles do not obey Stokes law and their rise velocity in water is approximately
0.24 m/s (31). This rise velocity decreases as viscosity of the liquid increases. The rise
velocity of spherical-cap bubbles can be approximated by,
Ub ¼ 0:71ðgdeÞ 0:5 : (2Þ