Basics of fluid rheology
Fluid viscosity is defined as µ in the following equation (1), where the force (F) required to move the top plate with an area of A at a velocity, v, against the parallel static plate placed with a distance, y, is proportional to the fluid viscosity, µ. The original equation can be arranged against the shear stress, F/A, which is proportional to apparent fluid viscosity, µ. For pure water, µ is constant for a wide range of shear rate, v/y.
Fig. 1. Laminar shear of fluid between two plates. Friction between the fluid and the moving boundaries causes the fluid to shear. The force required for this action is a measure of the fluid’s viscosity. This type of flow is known as a Couette flow(Wikipedia).
However, the apparent viscosities of the fluids with solutes are often variable depending on shear rate and the time the fluids are exposed to the shear rate. Table 1 summarizes many different fluids in terms of rheological properties and Fig. 2 illustrate the various rheological behavior of fluids.
Biological sludge are known to show pseudoplastic behavior, where apparent viscosity is negatively correlated with the shear rate (Rosenberger, 2002; Mori, 2006). In addition, the viscosity of biological sludge decreases more or less with the time the sludge is exposed to the shear rate to some extent, which qualifies biological sludge as thixotropic (Honey, 2000).
An explanation for pseudoplastic and thixotropic behaviour can be found in the bioparticulate structure of activated sludge. The particles tend to flocculate in a large-scale network. With increasing shear rate, this network is disrupted and aligned that results in a decrease in viscosity (Kraume, 2004).
Table 1. Classification of fluid in terms of rheological property (modified from Wikipeida)
|Newtonian fluids||Viscosity is constant regardless of the shear||Pure water|
|Apparent viscosity increases with shear||Suspensions of corn starch* or sand in water|
|Pseudoplastic (shear thinning)||Apparent viscosity decreases with shear||Paper pulp in water, latex paint, ice, blood, syrup, molasses,shampoo, biological sludge|
|Bingham plastic||Minimum shear is required to flow||Toothpaste, margarine|
|Time-dependent||Rheopectic||Apparent viscosity increases with duration of shear||Some lubricants, whipped cream|
|Thixotropic||Apparent viscosity decreases with duration of shear||Some clays, some drilling mud, many paints, synovial fluid, cerebral spinal fluid|
* In the movie file linked, people can walk over the pool surface filled with corn starch solution. Apparently they walk fast enough so that viscosity of the fluid is high enough to support their body weight. If they moved slower, they might sink.
|a) As a function of shear rate b) As a function of time|
Fig. 2. Various rheological behavior of liquid.
Fig. 3 shows the viscosity change with time when mixed liquor is exposed to a constant shear rate of 1.83 sec-1. When MLSS is 10 g/L, the initial visocity of ~35 cP declines to below 20 cP within 300 seconds and continue to decline although the declining rate slows down.
Fig. 4 shows the relation between shear rate and apparent viscosity. It is noticeable that apparent viscosity of biological sludge can vary widely more than two orders of magnitude. The increase of viscosity at very high shear rate is a result of turbulent viscosity that can be explained by the Taylor numbers (Mori, 2006), but it is likely irrelevant for iMBR since the shear rates in iMBR are no more than a few hundreds/s. Fig. 5 shows similar graph from different literature. Although the absolute viscosities are different due to the different sludge origin and the different rheometer used, trends of the viscosity per shear rate agree each other well.
The shear thinning (or pseudoplastic) behavior of concentrated activated sludge has a strong impact on the operation of membrane bioreactors: viscosity increases by one or two orders of magnitude in areas with low convection. This is likely to form dead zones and thus decrease the effective volume of the activated sludge compartment. In addition, clogging, especially of the membrane modules, is difficult to remove without additional energy supply (Kraume, 2004).
Fig. 3. Thixotropy of mixed liquor at constant shear rate of 1.83 sec-1 (Civelekoglu, 2010).
Fig. 4. Shear thinning nature of biological mixed liquor (MLSS = 8 g/L, Brannock, 2010)
Fig. 5. Apparent viscosity as a function of shear rate for four different MLSS measured by TA rheometer type AR2000 with 1 mm gap (Ratkovich, 2013)
Civelekoglu, G.; Kalkan, F.C. (2010) Rheological characterization of biological treatment sludges in a municipal wastewater treatment plant, Wat. Env. Res., 82(9), 782-789.
Brannock, M.; Wang, Y.; Leslie, G. (2010) Mixing characterisation of full-scale membrane bioreactors: CFD modelling with experimental validation, Wat. Res., 44(10), 3181-3191.
Ratkovich, N.; Horn, W.; Helmus, F.P.; Rosenberger, S.; Naessens, W.; Nopens, I. (2013) Activated sludge rheology: A critical review on data collection and modelling, Water Res., 47, 463-482.
© Seong Hoon Yoon