Simplex drawbacks

As mentioned in the previous section, a major drawback of the simplex atomizer is the poor atomization quality at the lowest flow rate due to too-low pressure differential if swirl ports are sized to allow the maximum flow rate at the maximum injection pressure. This problem may be resolved by using dual-orifice, duplex, or spill-return atomizers. Alternatively, the atomization processes at low injection pressures can be augmented via forced aerodynamic instabilities by using air or gas stream(s) or jet(s). This is based on the beneficial effect of flowing air in assisting the disintegration of a liquid j et or sheet, as recognized in the application of the shroud air in fan spray and pressure-swirl atomization. 

One way to include the less desirable variables of Table HI in the simplex optimization process would be to perform a simplex optimization for each of a limited number of user-selected combinations of the less suitable variables. The optimum results obtained for these selected combinations could then be compared, with the best overall result indicating which combination of fluid, modifier, stationary phase, etc. is best for that particular separation. A drawback of this approach, particularly if the individual optimization procedure is not automated, is its time-consuming, labor intensive nature. 

This type of experimental design still has one of the drawbacks of the initial simplex lattice design, since most of the responses used to determine the coefficients are obtained from mixtures formed of q components (q < q) and these experiments are situated at the limits of the domain (which is the major drawback),... 

Simplex optimization has become very popular and has been widely used in chromatography, but there are three major disadvantages (1) the relationship between the factor to be optimized and the parameters involved is seldomly revealed in detail, and the procedure therefore does not lead to a better understanding of the separation process, (2) a local optimum may be found and the optimization process stops there, and (3) a larger number of experiments are required. In order to overcome these drawbacks, recently a computer-assisted mixture design simplex method has been introduced by Wang and co-workers [18]. 

A drawback of the simplex and other analytical optimizers is the unavailability of numerical potentials. What is needed is a relatively small set of parameters, B , defining the entire parameter space. The limit is typically 4-6 independent parameters, because any additional dimension increases the need for computing resources tremendously. A typical choice for such parameters is a Lennard-Jones-like expansion " in Eq. [5]... 

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