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Numerical investigations on electric field characteristics with respect to capacitive detection of free-flying droplets.

Ernst A, Mutschler K, Tanguy L, Paust N, Zengerle R, Koltay P - Sensors (Basel) (2012)

Bottom Line: The simulations were realised using the computational fluid dynamic (CFD) software CFD ACE+.The sensitivity of the focused capacitor geometry was evaluated to be S(i) = 0.3 fC/nL.The simulation results are validated by experiments which exhibit good agreement.

View Article: PubMed Central - PubMed

Affiliation: Laboratory for MEMS Applications, Department of Microsystems Engineering (IMTEK), University of Freiburg, 79110 Freiburg, Germany. andreas.ernst@imtek.de

ABSTRACT
In this paper a multi-disciplinary simulation of a capacitive droplet sensor based on an open plate capacitor as transducing element is presented. The numerical simulations are based on the finite volume method (FVM), including calculations of an electric field which changes according to the presence of a liquid droplet. The volume of fluid (VOF) method is applied for the simulation of the ejection process of a liquid droplet out of a dispenser nozzle. The simulations were realised using the computational fluid dynamic (CFD) software CFD ACE+. The investigated capacitive sensing principle enables to determine the volume of a micro droplet passing the sensor capacitor due to the induced change in capacity. It could be found that single droplets in the considered volume range of 5 nL < V(drop) < 100 nL lead to a linear change of the capacity up to ΔQ < 30 fC. The sensitivity of the focused capacitor geometry was evaluated to be S(i) = 0.3 fC/nL. The simulation results are validated by experiments which exhibit good agreement.

No MeSH data available.


Results of the accomplished grid study to evaluate the accuracy of the used computational grid.
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f5-sensors-12-10550: Results of the accomplished grid study to evaluate the accuracy of the used computational grid.

Mentions: The applied solution technique follows the finite volume method, like described in Section 3.2, to solve the partial differential equations in the computational domain. The whole domain consists of 540,000 cells, whereas the area along the flight path of the droplet consists of a grid of smaller cells in comparison to the surrounding cells (cell size∼3:1). The planar geometry of the considered setup enabled to set a symmetry condition, which allowed for the calculation of only half of the real geometry, to save computation time. The simulation required transient conditions at a defined time step of Δt = 1 μs and a convergence criteria of 0.0001. To evaluate the accuracy of the numerical calculations, a brief grid refinement study was accomplished to investigate the influence of the cell size. To estimate the discretisation error the side length of all cells was decreased in all dimensions by a factor 2 and 4, as well as increased by a factor 2 respectively. Simulations were performed with the different grids by stationary simulation of an empty capacitor as well as for a capacitor with a droplet introduced in the middle of the electrodes at identical conditions like described above for the dynamic simulation model. The value of interest here was the change of the charge on the measurement electrode for the empty capacitor compared to the droplet filled one. The results are given in Figure 5 for the various grids.


Numerical investigations on electric field characteristics with respect to capacitive detection of free-flying droplets.

Ernst A, Mutschler K, Tanguy L, Paust N, Zengerle R, Koltay P - Sensors (Basel) (2012)

Results of the accomplished grid study to evaluate the accuracy of the used computational grid.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3472843&req=5

f5-sensors-12-10550: Results of the accomplished grid study to evaluate the accuracy of the used computational grid.
Mentions: The applied solution technique follows the finite volume method, like described in Section 3.2, to solve the partial differential equations in the computational domain. The whole domain consists of 540,000 cells, whereas the area along the flight path of the droplet consists of a grid of smaller cells in comparison to the surrounding cells (cell size∼3:1). The planar geometry of the considered setup enabled to set a symmetry condition, which allowed for the calculation of only half of the real geometry, to save computation time. The simulation required transient conditions at a defined time step of Δt = 1 μs and a convergence criteria of 0.0001. To evaluate the accuracy of the numerical calculations, a brief grid refinement study was accomplished to investigate the influence of the cell size. To estimate the discretisation error the side length of all cells was decreased in all dimensions by a factor 2 and 4, as well as increased by a factor 2 respectively. Simulations were performed with the different grids by stationary simulation of an empty capacitor as well as for a capacitor with a droplet introduced in the middle of the electrodes at identical conditions like described above for the dynamic simulation model. The value of interest here was the change of the charge on the measurement electrode for the empty capacitor compared to the droplet filled one. The results are given in Figure 5 for the various grids.

Bottom Line: The simulations were realised using the computational fluid dynamic (CFD) software CFD ACE+.The sensitivity of the focused capacitor geometry was evaluated to be S(i) = 0.3 fC/nL.The simulation results are validated by experiments which exhibit good agreement.

View Article: PubMed Central - PubMed

Affiliation: Laboratory for MEMS Applications, Department of Microsystems Engineering (IMTEK), University of Freiburg, 79110 Freiburg, Germany. andreas.ernst@imtek.de

ABSTRACT
In this paper a multi-disciplinary simulation of a capacitive droplet sensor based on an open plate capacitor as transducing element is presented. The numerical simulations are based on the finite volume method (FVM), including calculations of an electric field which changes according to the presence of a liquid droplet. The volume of fluid (VOF) method is applied for the simulation of the ejection process of a liquid droplet out of a dispenser nozzle. The simulations were realised using the computational fluid dynamic (CFD) software CFD ACE+. The investigated capacitive sensing principle enables to determine the volume of a micro droplet passing the sensor capacitor due to the induced change in capacity. It could be found that single droplets in the considered volume range of 5 nL < V(drop) < 100 nL lead to a linear change of the capacity up to ΔQ < 30 fC. The sensitivity of the focused capacitor geometry was evaluated to be S(i) = 0.3 fC/nL. The simulation results are validated by experiments which exhibit good agreement.

No MeSH data available.