Introduction

In the last chapter, we used a dipole model to provide a physical interpretation for the forces and torques exerted upon small particles by an electric field. An effective moment methodology was advanced for calculation of the dipole and higher-order multipolar forces. We extended this method to heterogeneous particles, that is, concentrically layered spherical shells, and to particles with dielectric and/or ohmic losses. With this necessary modeling framework now at our disposal, we direct our attention to the phenomenology of dielectrophoresis. Dielectrophoresis (DEP) refers to the force exerted on the induced dipole moment of an uncharged dielectric and/or conductive particle by a nonuniform electric field. This book's early focus on DEP serves as acknowledgment that the dipole force term predominates over higher-order multipolar components in the electromechanics of particles except in the case of a particle located near a field null or in the strongly nonuniform electric field of another closely spaced particle. Dielectrophoresis is technologically important in its own right, as evidenced by the number of applications in such scientific and technical fields as biophysics, bioengineering, electrorheological fluids, and mineral separation.

Electromechanical forces are exerted upon magnetic particles in a nonuniform magnetic field as well. This phenomenon, called magnetophoresis (MAP), is to some extent analogous to dielectrophoresis; however, because of the nonlinearity exhibited by most magnetic materials and the effectively diamagnetic behavior of (i) conductive particles in AC magnetic fields and (ii) superconductive particles in DC magnetic fields, there are some important differences. For these reasons, we treat the subject of magnetophoresis separately in Section 3.5 and highlight certain limitations of the dielectric–magnetic analogy.

Introduction to chaining and review of previous work

Closely spaced particles subjected to an electric or magnetic field interact electromechanically through the agency of their induced dipole and higher-order moments. Depending on the relative alignment of the particles, the mutual forces of interaction can be attractive or repulsive. In general, similar particles attract each other when aligned parallel to an applied field and repel each other when in perpendicular alignment. At close spacings, these interaction forces can become quite strong. There are two complementary physical interpretations of such interparticle electromechanics: one approach considers dipole–dipole interactions, while the other focuses upon the distortion of the applied field in the vicinity of each particle. The dipole–dipole interaction model stems from the “action-at-a-distance” physical interpretation of electrodynamics. Figure 6.1a shows two similar particles oriented with their line of centers parallel to the applied field. The induced dipoles clearly attract each other, irrespective of the sign of the Clausius–Mossotti function K (defined in Table A. 1 in Appendix A), just as do two permanent magnets when similarly aligned. On the other hand, when the particles are aligned perpendicular, as depicted in Figure 6.1b, they repel each other, again just as two permanent magnets aligned side by side would do.

The other interpretation of field-induced particle interactions focuses on the localized field disturbance caused by dielectric, conductive, or magnetic particles. For K > 0, the field is intensified near the poles and reduced near the equator. The reverse occurs when K < 0. Thus, the predicted particle interactions are consistent with those derived from consideration of dipole-dipole interactions.

Introduction

As early as 1892, Arno reported that small particles can be made to spin when placed in a rotating electric field. This rotation is not synchronous; the angular velocity of the particle depends on the electric field magnitude squared. In recognition of significant later contributions made by Born (1920) and Lertes (1920, 1921), this phenomenon has become known as the Born–Lertes effect. Shortly after Arno's work, Weiler (1893) discovered the related phenomenon that small solid particles suspended in liquids can rotate in a static electric field. Though Weiler published first, this effect has come to be known as Quincke rotation (Quincke, 1896). Unlike the Born–Lertes effect, Quincke rotation is a threshold phenomenon; spontaneous rotation occurs once the field strength is increased above some critical value. The rotational axis is always perpendicular to the imposed electric field for both effects. Pickard (1961) reviewed and clarified these phenomena, emphasizing the close relationship of the two effects. This chapter illuminates this relationship, relying on the effective moment method, viz. Equation (2.6), for calculation of the torque of electrical origin.

Electrically induced particle rotation provides one explanation for the observed disruption that sometimes occurs during the initial chain formation step of electrofusion procedures (Holzapfel et al., 1982). If the linearly polarized AC electric field is within certain limited frequency ranges, linear chains of cells deform into irregular corkscrew configurations that interfere with electrofusion protocols. In some cases, the cells from disrupted chains spin steadily in the presence of the electric field. Zimmermann and Vienken (1982) hypothesized that this field-induced rotation, evident only when cells are proximate to one another, is responsible for the frequency-dependent disruption of chains.

As a consequence of their electrical and/or magnetic properties, all particles experience forces and torques when subjected to electric and/or magnetic fields. Furthermore, when they are electrically charged, polarized, or magnetized, closely spaced particles often exhibit strong mutual interactions. In this book, I focus on these particle–field interactions, referred to collectively as particle electromechanics, by delineating common phenomenology and by developing simple yet general models useful in predicting electrically and magnetically coupled mechanics. The objective is to bring together diverse examples of field–particle interactions from many technologies and to provide a common framework for understanding the relevant electromechanical phenomena. It may disappoint some readers to learn that, despite the rather general definition offered for particle electromechanics, I restrict attention to particles in the size range from approximately 1 micron (10−6 m) to 1 millimeter (10−3 m). Though many of the ideas developed here indeed carry over into the domain of ultrafine particles, the lower limit recognizes that other phenomena, such as van der Waals forces and thermal (Brownian) motion, become important below one micron. The upper limit is consistent with a reasonable definition for a classical particle.

Chapter 1 introduces the subject, provides a definition for particle electromechanics, and adds some caveats to inform the reader of the book's limitations. Chapter 2 unveils the fundamental effective moment concept employed throughout the book in the calculation of electromechanical forces and torques. It also uses multipolar expansion methods to solve for the induced moments for a particle experiencing a strongly nonuniform field and exploits the analogy between electrostatic and magnetostatic problems to reveal how the results for a dielectric particle can be applied to a magnetizable particle.

Introduction

The definition of particle electromechanics offered in Chapter 1, Section 1.2, is very broad, precluding any possibility of definitive treatment in a single volume. Accordingly the scope of this book is restricted primarily to field–particle interactions involving (i) uncharged, lossy, dielectric and electrically conductive particles with AC and DC electric fields and (ii) magnetizable, electrically conductive particles with AC and DC magnetic fields. The particle electromechanics of interest here are a consequence of either the field-induced polarization of dielectric particles or the field-induced magnetization of magnetic particles. The forces and torques governing particle behavior result from the interaction of the dipole and higher-order moments with the field.

Electromechanics of particles

Two distinct types of electromechanical interactions may be identified: imposed field and mutual particle interactions. Imposed field interactions reign when a single particle, or an ensemble of noninteracting particles, is influenced by an externally imposed field. Examples include the dielectrophoretic force or the alignment torque exerted on an isolated particle. Here, it is customary to assume that the particle does not influence the field, though such an assumption is not always justified. Mutual particle interactions occur where particles are so closely spaced that the local field of a particle influences its neighbors. For particles in close mechanical contact, mutual interactions can be very strong, leading to significant changes in the equilibrium structure of particle ensembles (e.g., chain formation and cooperative electrorotation), as well as strong cohesive forces.

For the purpose of convenience in presentation, this monograph is organized into sections on imposed field interactions (Chapters 2 through 5) and mutual interactions (Chapters 6 and 7).

The earlier chapters of this book discussed the design and use of a simulator for use in the development of digital electronic systems. The discussion has been widened to include some aspects of testing and design for testability, since application of good practice in these areas leads to better use of costly resources in what is probably the largest part of the design procedure. It is now of value to review the extent to which the aims of simulation can be achieved; to discuss several topics related to the use of simulator; to introduce some enhancements to simulators; and to attempt to look into the future.

Desirable features of a simulator

Some years ago the author wrote down a list of the features he would like to find in a simulator.

1. A simulator is required to give an accurate prediction of the behaviour of a good network.

2. A simulator is required to recognise and give warning of a faulty network.

3. The basic simulator should be independent of technology but recognise the distinctive features of known technologies. Thus devices of any technology might be simulated.

4. The simulator should be capable of handling modes at several levels of abstraction and in the same run (Harding 1989).

5. There is no point in simulating a design in 1 s if it takes a day to diagnose a fault, modify and recompile the network. Hence, associated with the simulator, there must be means to assist the user to find the source of ‘wrong’ results, correct them and recompile quickly. That is, the simulation cycle must be given serious attention (the detail is not within the scope of this book).

Introduction

A few years ago a well known company stated that the size of silicon chip that could be designed and built would be limited by ‘engineer blow-out’ – what a single engineer could hold in his mind without going crazy. To overcome that limitation, techniques for ‘managing complexity’ have been developed. These have included methods for manipulating data in different ways. The computer can handle large quantities of data without becoming crazed and without error, leaving only the interesting and intelligent work to the engineer.

Computer aids are not limited to chip design. It is not difficult today to produce a chip which works first time according to its specification. But was the specification correct? Thus there is no point in designing a 10 million gate chip which works perfectly to specification if the specification is wrong. In the late 1980s, estimates varied in the region 10% to 50% that the chip would work within its intended system (Harding 1989, Hodge 1990). This was clearly unsatisfactory, so there has been increasing emphasis on the need for system design rather than purely chip design.

One of the problems with building hardware is that, once built, it is not easily changed. In the case of designing on silicon, change is impossible. It is estimated that the relative cost of finding faults at design time, chip-test time, printed circuit board construction time, or in the finished machine in the field is 1:10:100:1000 (Section 3.1.1).