Equilibrium flow tests

Basic Protocol 2 Measuring Viscosity with Equilibrium Flow Tests HI. 2.6... 

Basic Protocol 2 is for time-dependent non-Newtonian fluids. This type of test is typically only compatible with rheometers that have steady-state conditions built into the control software. This test is known as an equilibrium flow test and may be performed as a function of shear rate or shear stress. If controlled shear stress is used, the zero-shear viscosity may be seen as a clear plateau in the data. If controlled shear rate is used, this zone may not be clearly delineated. Logarithmic plots of viscosity versus shear rate are typically presented, and the Cross or Carreau-Yasuda models are used to fit the data. If a partial flow curve is generated, then subset models such as the Williamson, Sisko, or Power Law models are used (unithi.i). 

For most samples, a step maximum time of 5 to 25 min should be set, so as to interrupt the step if steady state is unlikely to be achieved. All of the acceptance parameters can. be considered as a sliding scale. A fast equilibrium flow test can be not much better than, a continuous ramp. If the sample is time dependent with slow rebuild kinetics, then the times should be pushed to their longest limits. Sample stability is an issue, so if the sample is likely to dry or gel at the temperature of interest, the analysis should be carried out quickly (i.e., with shorter step maximum times). 

The equilibrium flow test in Basic Protocol 2 is very useful for measurement of time-dependent samples. The nonequilibrium tests in Basic Protocol 1 are much quicker, but can give results that are hard to reproduce if the sample is time dependent. The equilibrium flow test is far longer but may only need to be performed once. 

A good diagnostic for creep and stress relaxation tests is to plot them on the same scales as a function of either compliance (J) or modulus (G), respectively. If the curves superimpose, then all the data collected is in the linear region. As the sample is overtaxed, the curves will no longer superimpose and some flow is said to have occurred. These data can still be useful as a part of equilibrium flow. The viscosity data from the steady-state part of the response are calculated and used to build the complete flow curve (see equilibrium flow test in unit hi.2). 

Repeated shear cycles on the test sample will enable one to determine whether the sample exhibits time-dependent flow behaviour such as thixotropy. If the up and down curves for the first and successive cycles coincide, the sample is undergoing steady-state shear. However, if hysteresis loops between the up and down curves are observed for each successive cycle, the sample is exhibiting time-dependent flow behaviour. In such cases, it is advisable to repeat the experiment with the speed (or torque) held constant until the torque (or speed) attains a steady value before changing the speed (or torque) to the next value. This will yield an equilibrium flow curve in which the up and down curves coincide. 

As can be seen above, the equilibrium technique, gives a single line of data points in contrast to the hysteresis loops from traditional ramping techniques. While equilibrium flow may take a long time, it is certainly better to get the data in a usable form than to repeat ramp tests and try to estimate the steady state data. 

The concentration of the test atmosphere must be reasonably uniform throughout the chamber and should increase and decrease at a rate close to theoretical at the start or end of the exposure. Silver (1946) showed that the time taken for a chamber to reach a point of equilibrium was proportional to the flow rate of atmosphere passing through the chamber and the chamber volume. From this, the concentration-time relationship dining the run-up and run-down phase could be expressed by the equation... 

After determining a concentration of test compound which elicits no visually detectable response or effect in the aquatic species over a period of 48 hours (Step 1), fresh animals are placed in the chamber, exposed to known concentrations of test chemical (usually 14C-labelled), and the uptake rate and major metabolites determined (Step 2). Depuration rate from the dosed animals also can be estimated at this point by transfer to untreated water. Fresh animals also can be exposed to a constant flow of test solution until an absorption-excretion equilibrium (steady state) has been established, dosed briefly with labelled compound, and release (turnover) rate determined (Step 3). 

When developing a liquid phase adsorptive separation process, a laboratory pulse test is typically used as a tool to search for a suitable adsorbent and desorbent combination for a particular separation. The properties of the suitable adsorbent, such as type of zeolite, exchange cation and adsorbent water content, are a critical part of the study. The desorbent, temperature and liquid flow circulation are also critical parameters that can be obtained from the pulse test. The pulse test is not only a critical tool for developing the equilibrium-selective adsorption process it is also an essential tool for other separation process developments such as rate-selective adsorption, shape-selective adsorption, ion exchange and reactive adsorption. 

Figures 2 and 3 show typical test results for flux decline in laminar flow where the pressure and temperature are varied and the Reynolds number is held fixed. Similar behaviors are found with variations in Reynolds number and for turbulent flow. The important feature of the data is that the flux decline is exponential with time and an asymptotic equilibrium value is reached. Each solid curve drawn through the experimental points is a least-square fit exponential curve defined by Eq. (19). It is interesting to note that Merten et al ( ) in 1966 had observed an exponential flux decay in their reverse osmosis experiments. However, Thomas and his co-workers in their later experiments reported an algebraic flux decay with time (4,5).

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