In chemical engineering, problems frequently arise in scaling up chemical processes. Research is normally conducted in glassware on the millilitre scale, whereas cubic-metre capacities are required for production. The main scale-up problems are associated with heat and mass transport, and can result in increased formation of by-products and lower yields. In the worst cases, shortcomings can lead to runaway, in which the rate of heat generation exceeds the rate of cooling available, and other hazardous situations. Some of the scaling laws described here were developed between the 1880s and the 1930s in the growing field of engineering. The aim was to provide a framework for engineers to establish how material would behave on different length scales, allowing them to optimize output and minimize the risk of runaway and other hazards. In the pre-computer era, these laws proved to be simple and useful tools, particularly when the engineering mathematics required to model a chemical process became complicated.During the past 20 years, microfluidics, micrometre-scale total analysis systems (ΞΌTAS) or so-called 'lab-on-a-chip' devices have revived interest in these scaling laws and dimensionless groups for downscaling purposes 1 . Such devices have a range of practical benefits (see page 368).Here, we aim to review some of the important principles that contribute to the design of novel Β΅TAS and to propose future research activity, to inform the reader, who might ultimately use such devices for research, and even to inspire the reader to take on the challenge of designing new Β΅TAS.For simplicity, we use three miniaturized devices as the main examples for discussion: an open-tubular chromatographic system that is used to separate molecules from mixtures (Fig. ); a microwell plate as an example of a device in which chemical interactions must be optimized; and a gas-phase detection device that uses a glow-discharge plasma (Fig. ).The scaling laws considered here are generally not valid on the nanometre scale, so 200 years' experience in chemistry cannot be applied in this case. We are not yet convinced that practical applications of nanofluidics are feasible; however, there seems to be tremendous potential for basic research on the subject. We consider the absolute limits of the principles described here for the scaling down of chemical processes.