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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.


Two electrical equivalent circuits occurring during droplet ejection (a) a pending droplet is connected to the electronic system by capacitive coupling; (b) a droplet after tear-off acts as dielectric body.
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f2-sensors-12-10550: Two electrical equivalent circuits occurring during droplet ejection (a) a pending droplet is connected to the electronic system by capacitive coupling; (b) a droplet after tear-off acts as dielectric body.

Mentions: A dispensing process comprises two distinct phases which are the droplet's growth until its tear-off from the dispenser nozzle and the free flight of the droplet after it has detached from the nozzle. It turns out that these two situations result in different boundary conditions for the electrical problem of the charged capacitor. Both situations can be described by two different electrical equivalent circuits like follows: in first consideration, a growing droplet is connected to the liquid inside the nozzle, which stays in contact to the aluminum housing of the used dispenser unit via the dispensing piston, like described in detail in [9]. The housing is electrically connected to the ground potential (GND = 0 V) of the electric read out circuit due to guarding reasons, to avoid the induction of external stray fields, caused by the dispenser actuation [8]. Though, the liquid is guided through a non-conductive polyimide tube, it still has to be supposed that the electrical potential of the liquid inside the nozzle is coupled to the housing potential via a capacitive network. This network can be considered to consist of a capacitor series connection given by Cliquid, CWall and CSolid as depicted in Figure 2. This effect is referred to in the following as “capacitive coupling” and it is essential for the specific signal characteristics. The signal recording starts when the dispenser is triggered and subsequently a growing droplet, which is still connected to the nozzle, is established. The charge on the positive electrode (U+ = 10 V) is compensated by negative free charge carriers, distributed on the measurement capacitor's negative electrode as well as on the increasing surface of the growing droplet. The increasing surface of the growing droplet leads to a shift from charge carriers from the negative electrode to the droplet surface and thus to an overall decrease of the charge on the negative electrode. Finally, this leads to a decrease of the capacity and explains the negative peak at the beginning of the signal characteristics like mentioned above. The appearing charge separation on the droplet's surface can be explained by the existence of free charge carriers, which are found even in de-ionized water based on the auto ionization of liquid water [10]. In principle this means, that beside the orientation polarization of the liquid molecule dipoles (considering water) initiated by the electric field, also a charge separation occurs, which compensates the applied electric field partly with regard to the GND potential. After the droplet's tear off from the nozzle the situation changes. The detached droplet is disconnected from the GND potential and acts as dielectric body only. A dielectric material changes the capacitance of a capacitor, according to its size and relative permittivity, and leads to an increase of the charge on the measurement electrode entailing a positive signal peak. As a conclusion the point of inflexion of the negative signal drop, see Figure 1, represents the point of droplet tear off from the dispenser nozzle, which could be used as a measure to evaluate e.g., the reproducibility of the droplet ejection process.


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)

Two electrical equivalent circuits occurring during droplet ejection (a) a pending droplet is connected to the electronic system by capacitive coupling; (b) a droplet after tear-off acts as dielectric body.
© Copyright Policy
Related In: Results  -  Collection

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

f2-sensors-12-10550: Two electrical equivalent circuits occurring during droplet ejection (a) a pending droplet is connected to the electronic system by capacitive coupling; (b) a droplet after tear-off acts as dielectric body.
Mentions: A dispensing process comprises two distinct phases which are the droplet's growth until its tear-off from the dispenser nozzle and the free flight of the droplet after it has detached from the nozzle. It turns out that these two situations result in different boundary conditions for the electrical problem of the charged capacitor. Both situations can be described by two different electrical equivalent circuits like follows: in first consideration, a growing droplet is connected to the liquid inside the nozzle, which stays in contact to the aluminum housing of the used dispenser unit via the dispensing piston, like described in detail in [9]. The housing is electrically connected to the ground potential (GND = 0 V) of the electric read out circuit due to guarding reasons, to avoid the induction of external stray fields, caused by the dispenser actuation [8]. Though, the liquid is guided through a non-conductive polyimide tube, it still has to be supposed that the electrical potential of the liquid inside the nozzle is coupled to the housing potential via a capacitive network. This network can be considered to consist of a capacitor series connection given by Cliquid, CWall and CSolid as depicted in Figure 2. This effect is referred to in the following as “capacitive coupling” and it is essential for the specific signal characteristics. The signal recording starts when the dispenser is triggered and subsequently a growing droplet, which is still connected to the nozzle, is established. The charge on the positive electrode (U+ = 10 V) is compensated by negative free charge carriers, distributed on the measurement capacitor's negative electrode as well as on the increasing surface of the growing droplet. The increasing surface of the growing droplet leads to a shift from charge carriers from the negative electrode to the droplet surface and thus to an overall decrease of the charge on the negative electrode. Finally, this leads to a decrease of the capacity and explains the negative peak at the beginning of the signal characteristics like mentioned above. The appearing charge separation on the droplet's surface can be explained by the existence of free charge carriers, which are found even in de-ionized water based on the auto ionization of liquid water [10]. In principle this means, that beside the orientation polarization of the liquid molecule dipoles (considering water) initiated by the electric field, also a charge separation occurs, which compensates the applied electric field partly with regard to the GND potential. After the droplet's tear off from the nozzle the situation changes. The detached droplet is disconnected from the GND potential and acts as dielectric body only. A dielectric material changes the capacitance of a capacitor, according to its size and relative permittivity, and leads to an increase of the charge on the measurement electrode entailing a positive signal peak. As a conclusion the point of inflexion of the negative signal drop, see Figure 1, represents the point of droplet tear off from the dispenser nozzle, which could be used as a measure to evaluate e.g., the reproducibility of the droplet ejection process.

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.