The design methodology was developed to illustrate the multifunctional (fluidic/particle transport, particle separation, and droplet generation) functions of the microdevice. The details are briefly described below.

#### 3.1. Design Computational Model

Design simulations based on finite element analysis was carried out for geometric models shown in

Figure 1b. The microdevice design simulation for fluidic transport requires solving the Navier–Stokes equations related to conservation of mass, and momentum. The standard governing equations for the laminar flow are described as

where

$\overrightarrow{V}$ is the velocity vector,

P is the pressure,

ρ is the fluid density,

B is the body force, and

μ is its dynamic viscosity. The above equations were solved numerically on a fluid domain with moving walls to obtain the time-dependent flow field. A general-purpose computational fluid dynamics solver FLUENT software (ANSYS/FLUENT Inc., Canonsburg, PA, USA/Pittsburgh, PA, USA) [

23] with the finite volume method was used to carry out the simulations, and the transient solution was implemented with implicit marching techniques. The moving mesh approach updates the actuating walls with a new discretized computational domain at every time step. The convergence criteria used is based on the number of iterations to achieve 10

^{−5} for residuals of mass and momentum equations. To reduce the iteration error, the second-order accurate scheme was selected for spatial discretization. The SIMPLE algorithm was used for solving the pressure–velocity coupling, and this procedure is repeated at every time step until a converged solution for instantaneous flow field is obtained.

The movement of the microdevice actuation units to create a unit movement of periodic volume expanding and contracting is given by the following expression:

where

$s\left(x,t\right)$ is the displacement of the wall in vertical direction, and

ω is the vibrating frequency of the microdevice chamber. Due to the unique sequence of operations involved in the actuation events of the microdevice, the expected operating mode of unit vibration actuation can change the flow direction as well as cause the net fluid to be “pumped” from one side to another side of the microdevice.

The particles movement in the flow field can be simulated by the equation of the particles motion [

24], which is described by the following equations:

In the above equations,

$\overrightarrow{{V}_{p}}$ and

$\overrightarrow{V}$ are the particle velocity vector and local fluid velocity vector, respectively.

$\overrightarrow{{X}_{p}}$ is the particle trajectory obtained by integrating the kinematic and dynamic equations.

$f\left(\overrightarrow{V}-\overrightarrow{{V}_{p}}\right)/{\tau}_{p}$ is the drag force on the particle, where τ

_{p} =

ρ_{p}·

d_{p}^{2}/18µ is the characteristic time required for particles to respond to changes in the flow field. The drag factor

f, which represents the ratio of the drag coefficient to Stokes drag, is based on the expression of Morsi and Alexander [

24].

where

a_{i} coefficients are available for multiple particle Reynolds number ranges expected for the particles of interest.

For simulating the droplet generator aspect of the microdevice, the two-phase flow field (liquid phase in the microdevice and gas phase in the spray region) was solved using computational fluid dynamics with moving mesh technique by tracking the volume fraction of each of the fluids throughout the computational domain. For simulating the flow field in both the device and spray domains, the Navier–Stokes equations were solved under laminar, isothermal, and incompressible conditions. The continuum surface force (CSF) model proposed by Brackbill et al. [

25] was adopted to address surface tension at the interface of the gas and liquid. Additional details of the computational methods, and the relative validation and calculation procedures used in the design simulations can be found in Su et al. [

20].

#### 3.2. Prototyping and Testing

In order to illustrate the microdevice design concept for fluid pumping/transport, a prototype of the three-nozzle/diffuser microdevice was fabricated using polydimethylsiloxane (PDMS) material using standard rapid prototyping and CAD models as shown in

Figure 2. Accura60 resin (3D Systems, Inc., Atlanta, USA) was used in preparing the microdevice mold and fabricated using SLA prototyping. The PDMS material was prepared and poured into the mold, and the chemical remover and cleaner was utilized to finish the mold using standard Denature Alcohol. The details of the microdevice fabrication can be found in Cartin et al. [

26]. Due to difficulties involved in simulating and testing side actuation, testing was performed with top actuation. The specified actuation was achieved by using a reciprocal motor actuator that is accurately controlled with an externally supplied voltage. Water with a density of 998.2 kg/m

^{3} and viscosity of 0.001003 kg/m·s was used as the working fluid in the microdevice. A pressure difference of 0 Pa was set for the boundary condition at the inlet and the outlet of the microdevice. No-slip boundary condition was applied at an interface between microdevice walls and the working fluid. The performance of the device with respect to the flow rate and optimum pumping frequency was evaluated by testing various fluids with different viscosities.