Dimensional analysis and similitude in microsystem design and assembly

The effects miniaturization has on microsystems and related fields are the central subject of this work. Physical phenomena we are used to in our conventionally sized world seldom work at smaller scales. Before attempting to design a microsystem or try to perform any operation on or with it, the outcome of size reduction has to be considered. When well-known phenomena are involved it remains relatively simple to predict the outcome as a function of size. Unfortunately the behavior of microsystems is, in many cases, governed by phenomena that have been systematically and correctly neglected. In consequence our knowledge about them is limited to the point that we can't establish a relation between them and the size of the system. Dimensional analysis and theory of similitude are two engineering tools that have been long used to solve problems where analytical solutions were not available. While the first one gives us the possibility of obtaining prediction equations for our phenomena based on our initial hypothesis, the second allows us to test the validity of our findings through the use of models of convenient size. Combined they allow information and data obtained from the study of different cases where similar phenomena are involved to be extrapolated to the case under consideration. Ship engineering has benefited from those tools: the flow around a ship's hull is difficult to describe analytically and full-sized models are uneconomical to build for testing purposes alone. Since microsystems find themselves in a similar situation (some effects can't be described analytically and full-size models are difficult to work with) the use of dimensional analysis and similitude to solve different problems encountered in this domain is proposed. The subject of forces at the microsystem level is treated in detail to show how dimensional analysis can be used both qualitatively and quantitatively to help understand how forces behave at this scale.