@inproceedings{OberlaenderJildehKirchneretal.2015, author = {Oberl{\"a}nder, Jan and Jildeh, Zaid B. and Kirchner, Patrick and Wendeler, Luisa and Bromm, Alexander and Iken, Heiko and Wagner, Patrick and Keusgen, Michael and Sch{\"o}ning, Michael Josef}, title = {Experimental and numerical evaluation of interdigitated electrode array for monitoring gaseous sterilization processes}, series = {12. Dresdner Sensor-Symposium 2015}, booktitle = {12. Dresdner Sensor-Symposium 2015}, doi = {10.5162/12dss2015/P3.11}, pages = {163 -- 168}, year = {2015}, language = {en} } @article{WernerWagnerYoshinobuetal.2013, author = {Werner, Frederik and Wagner, Torsten and Yoshinobu, Tatsuo and Keusgen, Michael and Sch{\"o}ning, Michael Josef}, title = {Frequency behaviour of light-addressable potentiometric sensors}, series = {Physica Status Solidi (A)}, volume = {210}, journal = {Physica Status Solidi (A)}, number = {5}, publisher = {Wiley-VCH}, address = {Weinheim}, issn = {1521-396X ; 0031-8965}, doi = {10.1002/pssa.201200929}, pages = {884 -- 891}, year = {2013}, abstract = {Light-addressable potentiometric sensors (LAPS) are semiconductor-based potentiometric sensors, with the advantage to detect the concentration of a chemical species in a liquid solution above the sensor surface in a spatially resolved manner. The addressing is achieved by a modulated and focused light source illuminating the semiconductor and generating a concentration-depending photocurrent. This work introduces a LAPS set-up that is able to monitor the electrical impedance in addition to the photocurrent. The impedance spectra of a LAPS structure, with and without illumination, as well as the frequency behaviour of the LAPS measurement are investigated. The measurements are supported by electrical equivalent circuits to explain the impedance and the LAPS-frequency behaviour. The work investigates the influence of different parameters on the frequency behaviour of the LAPS. Furthermore, the phase shift of the photocurrent, the influence of the surface potential as well as the changes of the sensor impedance will be discussed.}, language = {en} } @article{SchoeningKirchnerNgetal.2010, author = {Sch{\"o}ning, Michael Josef and Kirchner, Patrick and Ng, Yue Ann and Spelthahn, Heiko and Schneider, Andreas and Henkel, Hartmut and Friedrich, Peter and Kolstad, Jens and Berger, J{\"o}rg and Keusgen, Michael}, title = {Gas sensor investigation based on a catalytically activated thin-film thermopile for H2O2 detection}, series = {Physica Status Solidi (A). 207 (2010), H. 4}, journal = {Physica Status Solidi (A). 207 (2010), H. 4}, isbn = {1862-6300}, pages = {787 -- 792}, year = {2010}, language = {en} } @article{TurekSchoeningKloocketal.2008, author = {Turek, Monika and Sch{\"o}ning, Michael Josef and Kloock, Joachim P. and Schubert, J{\"u}rgen and Zander, Willi and Kr{\"u}ger, Peter and Keusgen, Michael}, title = {Herstellung und Charakterisierung eines hybriden Sensorarrays auf Halbleiterbasis f{\"u}r die Umweltanalytik}, series = {Sensoren und Messsysteme 2008 : 14. Fachtagung Ludwigsburg, 11. und 12. M{\"a}rz 2008 / VDI/VDE-Gesellschaft Mess- und Automatisierungstechnik}, journal = {Sensoren und Messsysteme 2008 : 14. Fachtagung Ludwigsburg, 11. und 12. M{\"a}rz 2008 / VDI/VDE-Gesellschaft Mess- und Automatisierungstechnik}, publisher = {VDI-Verl.}, address = {D{\"u}sseldorf}, isbn = {978-3-18-092011-5}, pages = {803 -- 810}, year = {2008}, language = {de} } @inproceedings{OberlaenderArreolaHansenetal.2017, author = {Oberl{\"a}nder, Jan and Arreola, Julio and Hansen, Christina and Greeff, Anton and Mayer, Marlena and Keusgen, Michael and Sch{\"o}ning, Michael Josef}, title = {Impedimetric Biosensor to Enable Fast Evaluation of Gaseous Sterilization Processes}, series = {MDPI Proceedings}, volume = {1}, booktitle = {MDPI Proceedings}, number = {4}, doi = {10.3390/proceedings1040435}, pages = {4 Seiten}, year = {2017}, language = {en} } @article{JanusAchtsnichtTempeletal.2023, author = {Janus, Kevin Alexander and Achtsnicht, Stefan and Tempel, Laura and Drinic, Aleksaner and Kopp, Alexander and Keusgen, Michael and Sch{\"o}ning, Michael Josef}, title = {Influence of fibroin membrane composition and curing parameters on the performance of a biodegradable enzymatic biosensor manufactured from Silicon-Free Carbon}, series = {Physica status solidi : pss. A, Applications and materials science}, volume = {220}, journal = {Physica status solidi : pss. A, Applications and materials science}, number = {22}, publisher = {Wiley-VCH}, address = {Weinheim}, issn = {1862-6300 (Print)}, doi = {10.1002/pssa.202300081}, pages = {Artikel 2300081}, year = {2023}, abstract = {Herein, fibroin, polylactide (PLA), and carbon are investigated for their suitability as biocompatible and biodegradable materials for amperometric biosensors. For this purpose, screen-printed carbon electrodes on the biodegradable substrates fibroin and PLA are modified with a glucose oxidase membrane and then encapsulated with the biocompatible material Ecoflex. The influence of different curing parameters of the carbon electrodes on the resulting biosensor characteristics is studied. The morphology of the electrodes is investigated by scanning electron microscopy, and the biosensor performance is examined by amperometric measurements of glucose (0.5-10 mM) in phosphate buffer solution, pH 7.4, at an applied potential of 1.2 V versus a Ag/AgCl reference electrode. Instead of Ecoflex, fibroin, PLA, and wound adhesive are tested as alternative encapsulation compounds: a series of swelling tests with different fibroin compositions, PLA, and Ecoflex has been performed before characterizing the most promising candidates by chronoamperometry. Therefore, the carbon electrodes are completely covered with the particular encapsulation material. Chronoamperometric measurements with H2O2 concentrations between 0.5 and 10 mM enable studying the leakage current behavior.}, language = {en} } @inproceedings{WernerMansourRateikeetal.2011, author = {Werner, Frederik and Mansour, Ahmed and Rateike, Franz-Matthias and Schusser, Sebastian and Wagner, Torsten and Yoshinobu, Tatsuo and Keusgen, Michael and Sch{\"o}ning, Michael Josef}, title = {Kompakter Aufbau eines lichtadressierbaren potentiometrischen Sensors mit verfahrbarem Diodenlaser}, series = {10. Dresdner Sensor-Symposium : Dresden, 5. - 7. Dezember 2011 ; miniaturisierte analytische Verfahren, Hochtemperatur-Sensoren, Sensoren f{\"u}r Bioprozess- und Verfahrenstechnik, Sensoren f{\"u}r die Medizin, Chemische Verfahrenstechnik, Lebensmittelanalytik, innovative Sensorl{\"o}sungen, Sensoren f{\"u}r die Wasserqualit{\"a}t, Selbst{\"u}berwachung / Gerald Gerlach ... (Hg.) Dresdner Beitr{\"a}ge zur Sensorik. 43}, booktitle = {10. Dresdner Sensor-Symposium : Dresden, 5. - 7. Dezember 2011 ; miniaturisierte analytische Verfahren, Hochtemperatur-Sensoren, Sensoren f{\"u}r Bioprozess- und Verfahrenstechnik, Sensoren f{\"u}r die Medizin, Chemische Verfahrenstechnik, Lebensmittelanalytik, innovative Sensorl{\"o}sungen, Sensoren f{\"u}r die Wasserqualit{\"a}t, Selbst{\"u}berwachung / Gerald Gerlach ... (Hg.) Dresdner Beitr{\"a}ge zur Sensorik. 43}, editor = {Gerlach, Gerald}, publisher = {TUDpress}, address = {Dresden}, isbn = {978-3-942710-53-4}, pages = {277 -- 280}, year = {2011}, language = {de} } @article{BronderPoghossianKeusgenetal.2017, author = {Bronder, Thomas and Poghossian, Arshak and Keusgen, Michael and Sch{\"o}ning, Michael Josef}, title = {Label-free detection of double-stranded DNA molecules with polyelectrolyte-modified capacitive field-effect sensors}, series = {tm - Technisches Messen}, volume = {84}, journal = {tm - Technisches Messen}, number = {10}, publisher = {De Gruyter}, address = {Oldenbourg}, doi = {10.1515/teme-2017-0015}, pages = {628 -- 634}, year = {2017}, abstract = {In this study, polyelectrolyte-modified field-effect-based electrolyte-insulator-semiconductor (EIS) devices have been used for the label-free electrical detection of double-stranded deoxyribonucleic acid (dsDNA)molecules. The sensor-chip functionalization with a positively charged polyelectrolyte layer provides the possibility of direct adsorptive binding of negatively charged target DNA oligonucleotides onto theSiO2-chip surface.EIS sensors can be utilized as a tool to detect surface-charge changes; the electrostatic adsorption of oligonucleotides onto the polyelectrolyte layer leads to a measureable surface-potential change. Signals of 39mV have been recorded after the incubation with the oligonucleotide solution. Besides the electrochemical experiments, the successful adsorption of dsDNA onto the polyelectrolyte layer has been verified via fluorescence microscopy. The presented results demonstrate that the signal recording of EISchips, which are modified with a polyelectrolyte layer, canbe used as a favorable approach for a fast, cheap and simple detection method for dsDNA.}, language = {en} } @article{SchoeningBronderWuetal.2017, author = {Sch{\"o}ning, Michael Josef and Bronder, Thomas and Wu, Chunsheng and Scheja, Sabrina and Jessing, Max and Metzger-Boddien, Christoph and Keusgen, Michael and Poghossian, Arshak}, title = {Label-Free DNA Detection with Capacitive Field-Effect Devices—Challenges and Opportunities}, series = {Proceedings}, volume = {1}, journal = {Proceedings}, number = {8}, publisher = {MDPI}, address = {Basel}, issn = {2504-3900}, doi = {10.3390/proceedings1080719}, pages = {Artikel 719}, year = {2017}, abstract = {Field-effect EIS (electrolyte-insulator-semiconductor) sensors modified with a positively charged weak polyelectrolyte layer have been applied for the electrical detection of DNA (deoxyribonucleic acid) immobilization and hybridization by the intrinsic molecular charge. The EIS sensors are able to detect the existence of target DNA amplicons in PCR (polymerase chain reaction) samples and thus, can be used as tool for a quick verification of DNA amplification and the successful PCR process. Due to their miniaturized setup, compatibility with advanced micro- and nanotechnologies, and ability to detect biomolecules by their intrinsic molecular charge, those sensors can serve as possible platform for the development of label-free DNA chips. Possible application fields as well as challenges and limitations will be discussed.}, language = {en} } @article{WeldenJablonskiWegeetal.2021, author = {Welden, Rene and Jablonski, Melanie and Wege, Christina and Keusgen, Michael and Wagner, Patrick Hermann and Wagner, Torsten and Sch{\"o}ning, Michael Josef}, title = {Light-Addressable Actuator-Sensor Platform for Monitoring and Manipulation of pH Gradients in Microfluidics: A Case Study with the Enzyme Penicillinase}, series = {Biosensors}, volume = {11}, journal = {Biosensors}, number = {6}, publisher = {MDPI}, address = {Basel}, issn = {2079-6374}, doi = {10.3390/bios11060171}, pages = {Artikel 171}, year = {2021}, abstract = {The feasibility of light-addressed detection and manipulation of pH gradients inside an electrochemical microfluidic cell was studied. Local pH changes, induced by a light-addressable electrode (LAE), were detected using a light-addressable potentiometric sensor (LAPS) with different measurement modes representing an actuator-sensor system. Biosensor functionality was examined depending on locally induced pH gradients with the help of the model enzyme penicillinase, which had been immobilized in the microfluidic channel. The surface morphology of the LAE and enzyme-functionalized LAPS was studied by scanning electron microscopy. Furthermore, the penicillin sensitivity of the LAPS inside the microfluidic channel was determined with regard to the analyte's pH influence on the enzymatic reaction rate. In a final experiment, the LAE-controlled pH inhibition of the enzyme activity was monitored by the LAPS.}, language = {en} } @article{WagnerVornholtWerneretal.2016, author = {Wagner, Torsten and Vornholt, Wolfgang and Werner, Frederik and Yoshinobu, Tatsuo and Miyamoto, Ko-Ichiro and Keusgen, Michael and Sch{\"o}ning, Michael Josef}, title = {Light-addressable potentiometric sensor (LAPS) combined with magnetic beads for pharmaceutical screening}, series = {Physics in medicine}, volume = {2016}, journal = {Physics in medicine}, number = {1}, issn = {2352-4510}, doi = {10.1016/j.phmed.2016.03.001}, pages = {2 -- 7}, year = {2016}, abstract = {The light-addressable potentiometric sensor (LAPS) has the unique feature to address different regions of a sensor surface without the need of complex structures. Measurements at different locations on the sensor surface can be performed in a common analyte solution, which distinctly simplifies the fluidic set-up. However, the measurement in a single analyte chamber prevents the application of different drugs or different concentrations of a drug to each measurement spot at the same time as in the case of multi-reservoir-based set-ups. In this work, the authors designed a LAPS-based set-up for cell culture screening that utilises magnetic beads loaded with the endotoxin (lipopolysaccharides, LPS), to generate a spatially distributed gradient of analyte concentration. Different external magnetic fields can be adjusted to move the magnetic beads loaded with a specific drug within the measurement cell. By recording the metabolic activities of a cell layer cultured on top of the LAPS surface, this work shows the possibility to apply different concentrations of a sample along the LAPS measurement spots within a common analyte solution.}, language = {en} } @article{KirchnerOberlaenderFriedrichetal.2011, author = {Kirchner, Patrick and Oberl{\"a}nder, Jan and Friedrich, Peter and Berger, J{\"o}rg and Suso, Henri-Pierre and Kupyna, Andriy and Keusgen, Michael and Sch{\"o}ning, Michael Josef}, title = {Optimisation and fabrication of a calorimetric gas sensor built up on a polyimide substrate for H2O2 monitoring}, series = {Physica status solidi (a) : applications and material science. 208 (2011), H. 6}, journal = {Physica status solidi (a) : applications and material science. 208 (2011), H. 6}, publisher = {Wiley}, address = {Weinheim}, isbn = {1862-6319}, pages = {1235 -- 1240}, year = {2011}, language = {en} } @article{PilasYaziciSelmeretal.2017, author = {Pilas, Johanna and Yazici, Yasemen and Selmer, Thorsten and Keusgen, Michael and Sch{\"o}ning, Michael Josef}, title = {Optimization of an amperometric biosensor array for simultaneous measurement of ethanol, formate, d- and l-lactate}, series = {Electrochimica Acta}, volume = {251}, journal = {Electrochimica Acta}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0013-4686}, doi = {10.1016/j.electacta.2017.07.119}, pages = {256 -- 262}, year = {2017}, abstract = {The immobilization of NAD+-dependent dehydrogenases, in combination with a diaphorase, enables the facile development of multiparametric sensing devices. In this work, an amperometric biosensor array for simultaneous determination of ethanol, formate, d- and l-lactate is presented. Enzyme immobilization on platinum thin-film electrodes was realized by chemical cross-linking with glutaraldehyde. The optimization of the sensor performance was investigated with regard to enzyme loading, glutaraldehyde concentration, pH, cofactor concentration and temperature. Under optimal working conditions (potassium phosphate buffer with pH 7.5, 2.5 mmol L-1 NAD+, 2.0 mmol L-1 ferricyanide, 25 °C and 0.4\% glutaraldehyde) the linear working range and sensitivity of the four sensor elements was improved. Simultaneous and cross-talk free measurements of four different metabolic parameters were performed successfully. The reliable analytical performance of the biosensor array was demonstrated by application in a clarified sample of inoculum sludge. Thereby, a promising approach for on-site monitoring of fermentation processes is provided.}, language = {en} } @article{ArreolaMaetzkowDuranetal.2016, author = {Arreola, Julio and M{\"a}tzkow, Malte and Dur{\´a}n, Marlena Palomar and Greeff, Anton and Keusgen, Michael and Sch{\"o}ning, Michael Josef}, title = {Optimization of the immobilization of bacterial spores on glass substrates with organosilanes}, series = {Physica status solidi (A) : Applications and materials science}, volume = {213}, journal = {Physica status solidi (A) : Applications and materials science}, number = {6}, publisher = {Wiley-VCH}, address = {Weinheim}, issn = {1862-6319}, doi = {10.1002/pssa.201532914}, pages = {1463 -- 1470}, year = {2016}, abstract = {Spores can be immobilized on biosensors to function as sensitive recognition elements. However, the immobilization can affect the sensitivity and reproducibility of the sensor signal. In this work, three different immobilization strategies with organosilanes were optimized and characterized to immobilize Bacillus atrophaeus spores on glass substrates. Five different silanization parameters were investigated: nature of the solvent, concentration of the silane, silanization time, curing process, and silanization temperature. The resulting silane layers were resistant to a buffer solution (e.g., Ringer solution) with a polysorbate (e.g., Tween®80) and sonication.}, language = {en} } @article{KirchnerOberlaenderFriedrichetal.2012, author = {Kirchner, Patrick and Oberl{\"a}nder, Jan and Friedrich, Peter and Berger, J{\"o}rg and Rysstad, Gunnar and Sch{\"o}ning, Michael Josef and Keusgen, Michael}, title = {Realisation of a calorimetric gas sensor on polyimide foil for applications in aseptic food industry}, series = {Sensors and Actuators B: Chemical}, volume = {170}, journal = {Sensors and Actuators B: Chemical}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0925-4005}, doi = {10.1016/j.snb.2011.01.032}, pages = {60 -- 66}, year = {2012}, abstract = {A calorimetric gas sensor is presented for the monitoring of vapour-phase H2O2 at elevated temperature during sterilisation processes in aseptic food industry. The sensor was built up on a flexible polyimide foil (thickness: 25 μm) that has been chosen due to its thermal stability and low thermal conductivity. The sensor set-up consists of two temperature-sensitive platinum thin-film resistances passivated by a layer of SU-8 photo resist and catalytically activated by manganese(IV) oxide. Instead of an active heating structure, the calorimetric sensor utilises the elevated temperature of the evaporated H2O2 aerosol. In an experimental test rig, the sensor has shown a sensitivity of 4.78 °C/(\%, v/v) in a H2O2 concentration range of 0\%, v/v to 8\%, v/v. Furthermore, the sensor possesses the same, unchanged sensor signal even at varied medium temperatures between 210 °C and 270 °C of the gas stream. At flow rates of the gas stream from 8 m3/h to 12 m3/h, the sensor has shown only a slightly reduced sensitivity at a low flow rate of 8 m3/h. The sensor characterisation demonstrates the suitability of the calorimetric gas sensor for monitoring the efficiency of industrial sterilisation processes.}, language = {en} } @article{PilasSelmerKeusgenetal.2019, author = {Pilas, Johanna and Selmer, Thorsten and Keusgen, Michael and Sch{\"o}ning, Michael Josef}, title = {Screen-printed carbon electrodes modified with graphene oxide for the design of a reagent-free NAD+-dependent biosensor array}, series = {Analytical Chemistry}, volume = {91}, journal = {Analytical Chemistry}, number = {23}, publisher = {ACS Publications}, address = {Washington}, doi = {10.1021/acs.analchem.9b04481}, pages = {15293 -- 15299}, year = {2019}, language = {en} } @article{TurekHeidenGuoetal.2010, author = {Turek, Monik and Heiden, Wolfgang and Guo, Sharon and Riesen, Alfred and Schubert, J{\"u}rgen and Zander, Willi and Kr{\"u}ger, Peter and Keusgen, Michael and Sch{\"o}ning, Michael Josef}, title = {Simultaneous detection of cyanide and heavy metals for environmental analysis by means of µISEs}, series = {Physica Status Solidi (A). 207 (2010), H. 4}, journal = {Physica Status Solidi (A). 207 (2010), H. 4}, isbn = {1862-6300}, pages = {817 -- 823}, year = {2010}, language = {en} } @article{OberlaenderMayerGreeffetal.2018, author = {Oberl{\"a}nder, Jan and Mayer, Marlena and Greeff, Anton and Keusgen, Michael and Sch{\"o}ning, Michael Josef}, title = {Spore-based biosensor to monitor the microbicidal efficacy of gaseous hydrogen peroxide sterilization processes}, series = {Biosensors and Bioelectronics}, volume = {104}, journal = {Biosensors and Bioelectronics}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0956-5663}, doi = {10.1016/j.bios.2017.12.045}, pages = {87 -- 94}, year = {2018}, abstract = {In this work, a spore-based biosensor is evaluated to monitor the microbicidal efficacy of sterilization processes applying gaseous hydrogen peroxide (H2O2). The sensor is based on interdigitated electrode structures (IDEs) that have been fabricated by means of thin-film technologies. Impedimetric measurements are applied to study the effect of sterilization process on spores of Bacillus atrophaeus. This resilient microorganism is commonly used in industry to proof the sterilization efficiency. The sensor measurements are accompanied by conventional microbiological challenge tests, as well as morphological characterizations with scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The sensor measurements are correlated with the microbiological test routines. In both methods, namely the sensor-based and microbiological one, a tailing effect has been observed. The results are evaluated and discussed in a three-dimensional calibration plot demonstrating the sensor's suitability to enable a rapid process decision in terms of a successfully performed sterilization.}, language = {en} } @article{OberlaenderKirchnerKeusgenetal.2015, author = {Oberl{\"a}nder, Jan and Kirchner, Patrick and Keusgen, Michael and Sch{\"o}ning, Michael Josef}, title = {Strategies in developing thin-film sensors for monitoring aseptic food processes : Theoretical considerations and investigations of passivation materials}, series = {Electrochimica Acta}, volume = {183}, journal = {Electrochimica Acta}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0013-4686}, doi = {10.1016/j.electacta.2015.06.126}, pages = {130 -- 136}, year = {2015}, abstract = {The sterilization of packages in aseptic food processes is highly significant to maintain a consumer-safe product with extended shelf-life. Today, the sterilization of food packages is predominantly accomplished by gaseous hydrogen peroxide (H2O2) in combination with heat. In order to monitor this sterilization process, calorimetric gas sensors as differential set-up of two platinum temperature sensors representing a catalytically active (additionally deposition of MnO2) and a passive segment have been recently developed. The temperature rise of the exothermic decomposition serves as an indicator of the present H2O2 concentration. In the present work, a theoretical approach considering the sensor's thermochemistry and physical transport phenomena was formulated to evaluate the temperature rise based on the energy content of gaseous H2O2. In a further part of this work, three polymers have been analyzed with respect to their application as passivation materials. The examined polymers are photoresist SU-8, perfluoroalkoxy (PFA) and fluorinated ethylene propylene (FEP). Thermal analyses by means of differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) have been conducted to determine the operation limits of the polymers. The overall chemical resistance and stability of the polymers against the harsh environmental conditions during the sterilization process have been examined by attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR).}, language = {en} } @article{OberlaenderJildehKirchneretal.2015, author = {Oberl{\"a}nder, Jan and Jildeh, Zaid B. and Kirchner, Patrick and Wendeler, Luisa and Bromm, Alexander and Iken, Heiko and Wagner, Patrick and Keusgen, Michael and Sch{\"o}ning, Michael Josef}, title = {Study of Interdigitated Electrode Arrays Using Experiments and Finite Element Models for the Evaluation of Sterilization Processes}, series = {Sensors}, volume = {15}, journal = {Sensors}, number = {10}, publisher = {MDPI}, address = {Basel}, issn = {1424-8220}, doi = {10.3390/s151026115}, pages = {26115 -- 26127}, year = {2015}, abstract = {In this work, a sensor to evaluate sterilization processes with hydrogen peroxide vapor has been characterized. Experimental, analytical and numerical methods were applied to evaluate and study the sensor behavior. The sensor set-up is based on planar interdigitated electrodes. The interdigitated electrode structure consists of 614 electrode fingers spanning over a total sensing area of 20 mm2. Sensor measurements were conducted with and without microbiological spores as well as after an industrial sterilization protocol. The measurements were verified using an analytical expression based on a first-order elliptical integral. A model based on the finite element method with periodic boundary conditions in two dimensions was developed and utilized to validate the experimental findings.}, language = {en} }