Acoustofluidics 3: Continuum mechanics for ultrasonic particle manipulation

Although ultrasonic particle manipulation is performed in fluids, the adjacent solid material and its modelling play an important part in the design of such devices, as the impedance difference between liquids and solids is not very large. The modelling of the solid is done in the framework of linear elastodynamics, which is described by the displacement field, the strain field and the stress field. These quantities are related by kinematical relations, local linear momentum conservation and constitutive laws. Also material damping is important and can be modelled in the framework of linear viscoelasticity. Because of the finite size of the devices, resonant modes are important to analyse. In addition some of the elements behave as mechanical structures obeying specific equations that take into account the structural boundaries. A practical example is given, which shows the full complexity of device modelling, which is preferably done using the Finite Element Method.