Harbir Antil - Research

Modeling, Simulation and Shape Optimization of Surface Acoustic Wave Driven Microfluidic Biochips

microfludic biochip

Fig 1: Microfludic biochip with microchannels

and two hexagonal reservoirs, typical characteristic

length is O(mm).

microfludic biochip

Fig 2: A sharp jet is created by an interdigital transducer (IDT), placed on a piezoelectric substrate (lithium niobate in our case) and steers out surface acoustic waves (SAWs), which in turn makes the fluid to move (experimental setup).

microfludic biochip

Fig 3: A cartoon with further elaboration of the phenomenon explained in left figure (courtesy: D. Köster [2006]).

Modeling Equations

Model Validation

microfludic biochip

Fig 4: Experimentally obtained acoustic streaming pattern.

In order to validate our model we consider a square domain (0,1)² mm². The video on the left (Fig 5) shows a SAW entering the domain and Figure 6 on the right shows the stationary surface acoustic streaming pattern formed. Figure 4 shows the experimentally obtained stationary surface acoustic streaming pattern. Qualitatively and quantitatively our numerical results matches quite well the experiments.
Surface Acoustic Wave

Fig 5: A SAW entering entering in the domain using an IDT placed at the bottom left corner.

microfludic biochip

Fig 6: Stationary acoustic streaming pattern.


After validation of our model using the experiments, the next goal of this project is to ensure that the hexagonal reservoirs in biochip are filled with precise amount of fluid and vorticity is minimized (cf. Fig 7). This requires us to do shape optimization of capillary barriers marked in red in Figure 8. Hence we need to solve a PDE constrained optimization problem subject to microfluidic biochip equations (see Modeling Equations above) as constraints.
microfludic biochip

Fig 7: Experimental filling of hexagonal shaped reservoirs which are part of microfluidic biochip.

microfludic biochip

Fig 8: In order to ensure that the reservoirs are filled with precise amount of fluid we want to do shape optimization of the capillary barriers (marked in red) and since remaining part of the domain is large and fixed there we apply model reduction. As a result we have to solve a system of very small size as compared to a huge problem during optimization.



microfludic biochip

Fig 9: A finite element mesh generated for the microfluidic biochip using gmsh.

Related Publications

  • H. Antil, R.H.W. Hoppe, C. Linsenmann, and A. Wixforth.
    Reduced Order Modeling Based Shape Optimization of Surface Acoustic Wave Driven Microfluidic Biochips.
    Mathematics and Computers in Simulation (2010). link
  • H. Antil, R. Glowinski, R.H.W. Hoppe, and C. Linsenmann, T.-W. Pan, and A. Wixforth.
    Modeling, Simulation, and Optimization of Surface Acoustic Wave Driven Microfluidic Biochips .
    Journal of Computational Mathematics (2010), 28(2):149--169. link