Being able to accurately predict the eluted volume of a substance with a known distribution ratio will depend on accurately knowing the retention volume of the stationary phase. Sample resolution depends on a number of factors that are not so easy to predict: the properties of the phase systems, the number of mixing and settling cycles per unit time, the rate of mass transfer during mixing, and the quality of mixing between the phase systems. The extent of mixing between the phases will, in turn, depend on the flow rate of the mobile phase and the ''g'' field acting across the stratified phases within the coiled tubing. A systematic study is made of how sample resolution changes with the key operating variables associated with scale-up: the mobile phase flow, the bore of the tubing, and the rotational speed. It shows how the commonly accepted characteristic, good 1475 resolution at low flow and poor resolution at high flow, slowly changes as tubing bore increases to one of poor resolution at low flow rising to optimum resolution at high flow and a slow decline in resolution at very high flow. Furthermore, it goes on to show that, as phase system physical properties change when moving from hydrophobic phase systems to more polar hydrophilic ones, the optimum resolution remains in a similar speed and flow range. It also shows that the key variable for scale-up, the throughput of sample in kg=hour, increases significantly as mobile phase flow increases, provided the rotational speeds are high enough. Optimum throughput has not yet been reached, which is extremely promising for realising process scale CCC.

Abstract. A relation algebra atom structure α is said to be strongly representable if all atomic relation algebras with that atom structure are representable. This is equivalent to saying that the complex algebra Cm α is a representable relation algebra. We show that the class of all strongly representable relation algebra atom structures is not closed under ultraproducts and is therefore not elementary. This answers a question of Maddux (1982).Our proof is based on the following construction. From an arbitrary undirected, loop-free graph Γ, we construct a relation algebra atom structure α(Γ) and prove, for infinite Γ, that α(Γ) is strongly representable if and only if the chromatic number of Γ is infinite. A construction of Erdös shows that there are graphs Γr (r < ω) with infinite chromatic number, with a non-principal ultraproduct D Γr whose chromatic number is just two. It follows that α(Γr) is strongly representable (each r < ω) but D (α(Γr )) is not.

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