{"id":2271,"date":"2021-03-17T00:53:36","date_gmt":"2021-03-16T22:53:36","guid":{"rendered":"https:\/\/biophysical-tools.de\/?page_id=2271"},"modified":"2024-07-25T11:12:56","modified_gmt":"2024-07-25T09:12:56","slug":"pressure-driven-flow-control","status":"publish","type":"page","link":"https:\/\/biophysical-tools.de\/de\/pressure-driven-flow-control\/","title":{"rendered":"Str\u00f6mungskontrolle in der Mikrofluidik"},"content":{"rendered":"<div class=\"wpb-content-wrapper\"><div class=\"vc_row wpb_row vc_row-fluid\"><div class=\"wpb_column vc_column_container vc_col-sm-6\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p><a href=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Syring_Amplification_Velocity.png\"><img loading=\"lazy\" class=\"wp-image-2272 aligncenter\" src=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Syring_Amplification_Velocity.png\" alt=\"Syringe_amplification\" width=\"535\" height=\"336\" srcset=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Syring_Amplification_Velocity.png 658w, https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Syring_Amplification_Velocity-300x188.png 300w, https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Syring_Amplification_Velocity-100x63.png 100w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/a><\/p>\n\n\t\t<\/div>\n\t<\/div>\n\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p>Beitrag auf Englisch h\u00f6ren:<\/p>\n<!--[if lt IE 9]><script>document.createElement('audio');<\/script><![endif]-->\n<audio class=\"wp-audio-shortcode\" id=\"audio-2271-1\" preload=\"none\" style=\"width: 100%;\" controls=\"controls\"><source type=\"audio\/mpeg\" src=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/EN1_Pressure_and_volume_driven_flowcontrol.mp3?_=1\" \/><a href=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/EN1_Pressure_and_volume_driven_flowcontrol.mp3\">https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/EN1_Pressure_and_volume_driven_flowcontrol.mp3<\/a><\/audio>\n\n\t\t<\/div>\n\t<\/div>\n\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t\n\t\t<\/div>\n\t<\/div>\n\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p>Beitrag auf Deutsch h\u00f6ren:<\/p>\n<audio class=\"wp-audio-shortcode\" id=\"audio-2271-2\" preload=\"none\" style=\"width: 100%;\" controls=\"controls\"><source type=\"audio\/mpeg\" src=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/DE1_Druckbasierte_und_volumentbasierte_Stroemungskontrolle-18.04.21-20.19.mp3?_=2\" \/><a href=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/DE1_Druckbasierte_und_volumentbasierte_Stroemungskontrolle-18.04.21-20.19.mp3\">https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/DE1_Druckbasierte_und_volumentbasierte_Stroemungskontrolle-18.04.21-20.19.mp3<\/a><\/audio>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><div class=\"wpb_column vc_column_container vc_col-sm-6\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p><strong>Druckbasierte und volumenbasierte Str\u00f6mungskontrolle in der Mikrofluidik<\/strong><\/p>\n<p>Spritzen- und Peristaltikpumpen geh\u00f6ren seit Jahrzehnten in die biologischen und chemischen Labore. So war es nachvollziehbar, dass diese f\u00fcr den Einsatz in mikrofluidischen Setups bevorzugt wurden. Die beiden Pumpen basieren auf der volumengesteuerten Str\u00f6mungskontrolle und haben aus hydrodynamischer Sicht eine Reihe von Nachteilen, wodurch deren Einsatz f\u00fcr Mikrosysteme eher ung\u00fcnstig wird.<span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<p>So weisen<span class=\"Apple-converted-space\">\u00a0 <\/span><b>Spritzenpumpen<\/b> erhebliche Limitationen in puncto des verf\u00fcgbaren Fl\u00fcssigkeitsvolumens auf. Wird eine Spritze mit einer Querschnittsfl\u00e4che von A = 1 cm2 an einen typischen Mikrokanal von 10\u00d7100\u03bcm=0,00001xA angeschlossen, ergibt sich eine 100.000-fache Erh\u00f6hung der Str\u00f6mungsgeschwindigkeit im Mikrokanal. Zwar kann ggf. dieser Nachteil durch den Einsatz von kommerziell verf\u00fcgbaren hochpr\u00e4zisen Spritzenpumpen \u00fcberwunden werden, es bleiben jedoch weitere Schwierigkeiten, beispielsweise das Nachf\u00fcllen der Spritze w\u00e4hrend des Experiments, das gezwungenerma\u00dfen hierzu unterbrochen werden muss.<div class=\"su-accordion su-u-trim\"><\/div><div class=\"su-spoiler su-spoiler-style-fancy su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\" data-anchor-in-url=\"no\"><div class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Weitere Infos<\/div><div class=\"su-spoiler-content su-u-clearfix su-u-trim\"><\/p>\n<p class=\" translation-block\">In der <b>Peristaltikpumpe<\/b> erfolgt die Verdr\u00e4ngung des Volumens durch Zusammendr\u00fccken des Schlauchs.<span class=\"Apple-converted-space\"> <\/span>Das genaue Perfusionsvolumen l\u00e4sst sich dadurch nur schwer bestimmen, da es vom Schlauchmaterial abh\u00e4ngt, das wiederum in Abh\u00e4ngigkeit von Temperatur und Verschlei\u00df variiert. Auf der Mikroskala f\u00fchrt dieser Ansatz<span class=\"Apple-converted-space\"> <\/span>zu einigen Nachteilen. Zudem ist die Str\u00f6mung pulsierend und Zellen oder andere zu beobachtende Objekte k\u00f6nnen w\u00e4hrend des Quetschvorgangs besch\u00e4digt werden.<\/p>\n<p>Ein anderer Zugang zur Str\u00f6mungskontrolle<span class=\"Apple-converted-space\">\u00a0 <\/span>im mikrofluidischen Kanal basiert auf dem <b>Druck<\/b>. Am einfachsten erreicht man dies durch die Ausnutzung des hydrostatischen Drucks, wobei 100 mbar 1m Wassers\u00e4ule entsprechen. Nachteilig ist es jedoch dabei, dass kleinste Luftschwankungen bzw. \u00c4nderungen des atmosph\u00e4rischen Drucks oder Vibrationen das Experiment beeinflussen k\u00f6nnen.<span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<p>Seit 2004 werden in der Mikrofluidik <b>druckbasierte Str\u00f6mungsregler<\/b> verwendet.  Sie erm\u00f6glichen eine ultraschnelle, sanfte, pr\u00e4zise und vibrationsunempfindliche Str\u00f6mungskontrolle im Mikrokanal. Zudem k\u00f6nnen Fl\u00fcssigkeiten nachgef\u00fcllt werden, ohne dass das Experiment dabei unterbrochen werden muss. F\u00fcr diesen Ansatz ist es notwendig, in Druck und nicht in Volumen zu denken, um die Str\u00f6mung im Mikrokanal zu kontrollieren. Falls erforderlich, kann die Flussrate mit Durchflusssensoren gemessen, berechnet oder kalibriert werden, z. B. durch Abwiegung.<\/p>\n<p><\/div><\/div>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><\/div><div class=\"vc_row wpb_row vc_row-fluid\"><div class=\"wpb_column vc_column_container vc_col-sm-6\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p><strong>Durchflusssensoren und druckbasierte Str\u00f6mungskontrolle in der Mikrofluidik<\/strong><\/p>\n<p>Beim Einsatz der druckbasierten Str\u00f6mungskontrolle in der Mikrofluidik arbeitet man mit Druck, nicht mit volumetrischen Durchflussraten. In einigen F\u00e4llen ist es jedoch notwendig oder von Vorteil, die volumetrische Flussrate im Mikrokanal zu kennen. Beispielsweise bei der Realisierung eines vorgegebenen Protokolls f\u00fcr die Zellkultur, St\u00f6chiometrie im Mikrokanal oder einfach zur \u00dcberwachung des Verbrauchs von wertvollen Reagenzien. In solchen Situationen kann die Flussrate im Kanal auf unterschiedlichen Wegen bestimmt werden. In der Regel kann man sie berechnen, indem man die Tr\u00f6pfchen bei bestimmten Druckwerten wiegt und so das System kalibriert. Dies ist die genaueste Methode, sie ist aber auch etwas umst\u00e4ndlich. Eine gute Alternative hierzu sind kommerziell verf\u00fcgbare Durchflusssensoren.<\/p>\n<p>The available flow meters in the market are usually integrated upstream of the microchannel. However, the measured flow rate is not precisely equivalent to the actual volumetric flow rate, since the method is indirect, e.g. based on the temperature or Coriolis force. It makes the calibration before use mandatory. [\/text_output][text_output]<div class=\"su-accordion su-u-trim\"><\/div><div class=\"su-spoiler su-spoiler-style-fancy su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\" data-anchor-in-url=\"no\"><div class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Weitere Infos<\/div><div class=\"su-spoiler-content su-u-clearfix su-u-trim\"><\/p>\n<p>Furthermore,<span class=\"Apple-converted-space\">\u00a0 <\/span>besteht die Notwendigkeit, die Pr\u00e4zision der derzeit angebotenen Sensoren im \u00b5l-Bereich um einiges zu optimieren, um zuverl\u00e4ssige Ergebnisse bei der Messung zu erzielen.<span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<p>Die Durchflusssensoren f\u00fcr die Mikrofluidik basieren auf unterschiedlichen Ans\u00e4tzen. Die bekanntesten verwenden zwei Prinzipien:<\/p>\n<ul>\n<li>temperaturbasierte Durchflussmessung<\/li>\n<li>Durchflussmessung basierend auf der Corioliskraft<\/li>\n<\/ul>\n<p>Bei der temperaturbasierten Messung wird der Fl\u00fcssigkeit eine winzige W\u00e4rmemenge zugef\u00fchrt. Die Temperaturdifferenzen, die von vor- und nachgeschalteten Sensoren \u00fcberwacht werden, geben Auskunft \u00fcber den tats\u00e4chlichen Durchfluss. Dennoch m\u00fcssen in diesem Fall die physikalischen Eigenschaften der verwendeten Fl\u00fcssigkeit ber\u00fccksichtigt werden,<span class=\"Apple-converted-space\">\u00a0 <\/span>etwa spezifische W\u00e4rmekapazit\u00e4t der Fl\u00fcssigkeit.<span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<p>Coriolis-Durchflusssensoren, die in industriellen Anwendungen oft eingesetzt werden,  sind auch f\u00fcr die Messung des Massenstroms in der Mikrofluidik verf\u00fcgbar. Sie basieren in der Regel auf u-f\u00f6rmigen Rohren. Das Prinzip dieser Durchflussmesser basiert auf der Messung der Phasenverschiebung der stetigen Schwingung an verschiedenen Stellen entlang des Rohres, die durch die einstr\u00f6mende Fl\u00fcssigkeit in das System entsteht. F\u00fcr Fl\u00fcssigkeiten mit konstanter Dichte kann der Volumenstrom direkt aus dem gemessenen Massenstrom bestimmt werden. Bei Fl\u00fcssigkeiten mit variabler Dichte, z. B. im Falle der Kompressibilit\u00e4t, Tr\u00f6pfchen, Blasen, ist dieser Ansatz mit Schwierigkeiten verbunden. Dieses Verfahren ist zudem generell anf\u00e4llig gegen externe Vibrationen oder Bewegungen.<\/p>\n<p><\/div><\/div>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><div class=\"wpb_column vc_column_container vc_col-sm-6\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p style=\"text-align: center;\"><a href=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Durchflusssensor_Aufbau_bearbeitet.png\"><img loading=\"lazy\" class=\"wp-image-2275 aligncenter\" src=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Durchflusssensor_Aufbau_bearbeitet.png\" alt=\"Flow Meter\" width=\"653\" height=\"253\" srcset=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Durchflusssensor_Aufbau_bearbeitet.png 936w, https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Durchflusssensor_Aufbau_bearbeitet-300x116.png 300w, https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Durchflusssensor_Aufbau_bearbeitet-768x298.png 768w, https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Durchflusssensor_Aufbau_bearbeitet-100x39.png 100w, https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Durchflusssensor_Aufbau_bearbeitet-865x335.png 865w\" sizes=\"(max-width: 653px) 100vw, 653px\" \/><\/a><\/p>\n\n\t\t<\/div>\n\t<\/div>\n\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p>Beitrag auf Englisch h\u00f6ren:<\/p>\n<audio class=\"wp-audio-shortcode\" id=\"audio-2271-3\" preload=\"none\" style=\"width: 100%;\" controls=\"controls\"><source type=\"audio\/mpeg\" src=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/EN2_Flow_Meters_a_flow_control.mp3?_=3\" \/><a href=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/EN2_Flow_Meters_a_flow_control.mp3\">https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/EN2_Flow_Meters_a_flow_control.mp3<\/a><\/audio>\n<p>Beitrag auf Deutsch h\u00f6ren:<\/p>\n<audio class=\"wp-audio-shortcode\" id=\"audio-2271-4\" preload=\"none\" style=\"width: 100%;\" controls=\"controls\"><source type=\"audio\/mpeg\" src=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/DE2_Durchflussensoren_u_druckbasierte_Stroemungskontrolle-18.04.21-20.28.mp3?_=4\" \/><a href=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/DE2_Durchflussensoren_u_druckbasierte_Stroemungskontrolle-18.04.21-20.28.mp3\">https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/DE2_Durchflussensoren_u_druckbasierte_Stroemungskontrolle-18.04.21-20.28.mp3<\/a><\/audio>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><\/div><div class=\"vc_row wpb_row vc_row-fluid\"><div class=\"wpb_column vc_column_container vc_col-sm-6\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p><a href=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Spritze_in_der_Spritzenpumpe.png\"><img loading=\"lazy\" class=\"wp-image-2293 aligncenter\" src=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Spritze_in_der_Spritzenpumpe.png\" alt=\"\" width=\"573\" height=\"268\" srcset=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Spritze_in_der_Spritzenpumpe.png 1500w, https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Spritze_in_der_Spritzenpumpe-300x140.png 300w, https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Spritze_in_der_Spritzenpumpe-1024x479.png 1024w, https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Spritze_in_der_Spritzenpumpe-768x359.png 768w, https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Spritze_in_der_Spritzenpumpe-100x47.png 100w, https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Spritze_in_der_Spritzenpumpe-865x405.png 865w, https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/03\/Spritze_in_der_Spritzenpumpe-1184x554.png 1184w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/a><\/p>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><div class=\"wpb_column vc_column_container vc_col-sm-6\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p><strong>Methods of Flow Control<\/strong><\/p>\n<p>Pressure and flow rate are the main physical parameters which describe flow in microfluidic channels and devices. They are not independent from each other, but related through the flow resistance depending on the channel design and fluid properties quite similar to voltage and current in electrical circuits.<span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<p>Pressure is defined as force per area and we distinguish hydraulic and pneumatic pressure. These quantities are studied in the fields of Hydraulics and Pneumatics and all together in Hydrodynamics. Hydraulic pressure describes the exerted pressure transmitted by an incompressible medium as a liquid onto an immersed object or a boundary, e. g. water on biological cells or oil phase droplets in multi-phase fluids.<div class=\"su-accordion su-u-trim\"><\/div><div class=\"su-spoiler su-spoiler-style-fancy su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\" data-anchor-in-url=\"no\"><div class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Weitere Infos<\/div><div class=\"su-spoiler-content su-u-clearfix su-u-trim\"><\/p>\n<p>Pneumatic pressure, on the other hand, exerts force by means of a <i>compressible<\/i> medium, e. g. air, on an object or a boundary. Compressible media act like a spring and can store energy. This energy can be recuperated later allowing for smoothing out unwanted pressure pulses.<span class=\"Apple-converted-space\">\u00a0 <\/span>Pneumatic pressure can be transformed into hydraulic pressure by using a free water-air interface in a closed vessel carrying over the energy storage property to the liquid.<\/p>\n<p>Displacement of liquids and gases can be realised by essentially two approaches: volume-driven or pressure driven flow. They rely on the properties of the conjugated quantities \u201cpressure\u201d and \u201cvolume\u201d as known from thermodynamics. Both methods have very different characteristics &#8211; especially scaling &#8211; and one can choose one of them to control fluids.<\/p>\n<p><b><i>Volume-driven control<\/i><\/b> relies on the volume as a means of fluid movement control, requiring a closed and leakage-free system. They are best realised with liquids, since liquids essentially keep their volume mostly independent of pressure (incompressible). In microfluidics water and oil are the most common representatives. Pressure is generated by piston displacement in a syringe and exerted onto a downstream channel system which has to be tightly closed with exception of the waste outlet, of course. Here, pressure is not controlled and often not monitored. The scaling of this approach is poor, e. g. a minute piston displacement can result in a very large (up to 6 orders)<span class=\"Apple-converted-space\">\u00a0 <\/span>increase in hydraulic pressure in an attached microfluidic device. Further elasticity in the tubing and materials, leaks or air bubbles may reduce considerably responsiveness degrading device reliability and safety. In larger hydraulic systems sudden changes in volume flow may result in large pressure shocks (\u201chydraulic surge\u201d or \u201cwater hammer\u201d) or create strong shear forces damaging sensitive parts of devices, such as valves and small microfluidic structures or embedded objects like\u00a0biological cells.<\/p>\n<p><b><i>Pressure-driven control<\/i><\/b>, on the other hand, is best realised with compressible gasses, such as air or inert gasses as nitrogen. Pneumatic pressure is typically generated by a pressure and\/or vacuum control system fuelling a pressure storage recipient. The pressurised gas can subsequently drive liquid flow in microfluidic devices by connecting them to the liquid in the storage recipient. Sudden changes in flow rates will not cause pressure spikes, even if the gas source delivers pulsating pressure, since gas absorbs excessive forces and pulses by means of it\u2019s compressibility. As the liquid in the recipient is in contact to gas atmosphere, the system is not anymore closed as beforehand. Therefore pressure driven systems are usually \u201copen systems\u201d. The displaced volume is not controlled and often not monitored. As pneumatic-driven systems do not get in direct contact with the handling fluid any kind of contamination<span class=\"Apple-converted-space\">\u00a0 <\/span>is prevented and subsequent cleaning of the device is unnecessary. It is advantageous that back pressure is absorbed by gas compression and quickly eliminated by pressure stabilisation. By design, pressure-driven systems hence are more reliable, safer and require minimal maintenance. Thus, pneumatic pressure-driven systems are ideal for microfluidic channels and devices.<\/p>\n<p><\/div><\/div>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><\/div><div class=\"vc_row wpb_row vc_row-fluid\"><div class=\"wpb_column vc_column_container vc_col-sm-6\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p><strong>Pneumatischer und hydrostatischer Druck<\/strong><\/p>\n<p>Unsere Atmosph\u00e4re \u00fcbt Druck auf alle Oberfl\u00e4chen aus. Fl\u00fcssigkeiten k\u00f6nnen dies ebenfalls tun. Im Falle der Atmosph\u00e4re dr\u00fcckt das Gewicht des gesamten Gases oben aufgrund der Schwerkraft nach unten und erzeugt einen isotropen Druck, der auf Meeresh\u00f6he eine ziemlich beeindruckende Gr\u00f6\u00dfenordnung erreichen kann, die ungef\u00e4hr dem Druck einer Masse von 1 kg auf 1 cm<sup>2<\/sup>entspricht. Fl\u00fcssigkeiten haben jedoch eine viel h\u00f6here Dichte als Luft, etwa das 1000-fache, und mit der Tiefe steigt der Druck viel schneller an. Der Druck einer Fl\u00fcssigkeit in Abh\u00e4ngigkeit von deren Gewicht wird als <i>hydrostatischer Druck bezeichnet<\/i>.<\/p>\n<p>Veranschaulichen wir das Ganze anhand eines Zylinders (oder einer anderen Form) auf einer ebenen Fl\u00e4che <i>Z<\/i>. Der Zylinder mit einer bestimmten Masse und Gravitationskraft <i>F<\/i> \u00fcbt einen Druck p auf die untere Grenzfl\u00e4che mit gegebener Fl\u00e4che aus: p=F \/ A. Dies gilt f\u00fcr feste, fl\u00fcssige und gasf\u00f6rmige Stoffe gleicherma\u00dfen. Ersetzt man den Kraftterm mit den Materialeigenschaften einer Fl\u00fcssigkeit, z. B. Wasser, und den geometrischen Eigenschaften des hypothetischen Zylinders, so ergibt sich ein hydrostatischer Druck von p = h \u00b7\u03c1 \u00b7 g,<i>, <\/i>wobei <i>h<\/i> H\u00f6he der Fl\u00fcssigkeitss\u00e4ule ist, \u00a0\u03c1\u00a0(\u201c<i>rho\u201d)<\/i> the liquid density and g the gravitational acceleration. Thus, the hydrostatic pressure does not depend on the size of the cross-sectional area of the liquid column, but only on the height of the liquid column and the density of the liquid. In fact, the hydrostatic pressure is also indifferent to the shape of the hypothetical column.<div class=\"su-accordion su-u-trim\"><\/div><div class=\"su-spoiler su-spoiler-style-fancy su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\" data-anchor-in-url=\"no\"><div class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Weitere Infos<\/div><div class=\"su-spoiler-content su-u-clearfix su-u-trim\"><\/p>\n<p>When working with pressure-driven microfluidic systems, the hydrostatic pressure should always be considered, no matter how small the liquid quantities are. For instance, a one-meter-high water column is already generating a hydrostatic pressure of approx. 10 kPa, or 100 mbars, being quite significant in Microfluidics. Thus, when driving fluids through microfluidic devices, the liquid levels in microfluidic devices can vary considerably in height which is often neglected. Liquid reservoirs of tall and narrow shape appear to be especially prone to systematic pressure deviations. Other common sources of experiment errors are long microfluidic tubings transferring fluids upwards and downwards and even worse if still being partially filled with air. Here, the applied pressure at the source may deviate strongly from the received pressure at the microfluidic device. Once all tubings are filled with liquid and the micro-channel is placed approx. at the same height as the reservoirs and tubings are reduced to minimum, this phenomenon reduces strongly. How to explain this?<\/p>\n<p>Responsible for this is the \u201c<i>hydrostatic drift<\/i>\u201d. It can be understood and calculated as follows:<span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<p>The flow rate <i>Q<\/i>\u00a0is proportional to the applied pressure (<i>P<\/i>) difference plus the hydrostatic pressure (<i>p<\/i>) difference:<span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<p style=\"text-align: center;\">Q \u223c \u0394 P = P<sub>inlet<\/sub> &#8211; P<sub>outlet<\/sub> + p<sub>inlet<\/sub> &#8211; p<sub>outlet<\/sub><\/p>\n<p>The flow resistance<i>\u00a0R<\/i>\u00a0determines the resulting flow rate:<span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<p style=\"text-align: center;\">Q = 1\/R \u00b7 \u0394 P<\/p>\n<p>Flowing liquid changes the liquid levels in the outlet-reservoir with liquid volume V<sub>outlet<\/sub>(t):<span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<p style=\"text-align: center;\">dV<sub>outlet<\/sub>(t) \u2044\u00a0dt = Q(t)<\/p>\n<p>With constant reservoir cross section <em>Z<\/em>, note that V<sub>inlet<\/sub>(t) + V<sub>outlet<\/sub>(t)\u00a0, h<sub>inlet<\/sub>(t) + h<sub>outlet<\/sub>(t) and also p<sub>inlet<\/sub>(t) + p<sub>outlet<\/sub>(t) remain constant, if the total amount of liquid remains unchanged during this experiment.<span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<p>Hence, the level in the reservoirs changes with volume V<sub>outlet<\/sub>(t) = A \u00b7h<sub>outlet<\/sub>(t) accordingly:<\/p>\n<p style=\"text-align: center;\">dV<sub>outlet<\/sub>(t) \u2044\u00a0dt = A \u00b7 (dh<sub>outlet<\/sub>(t)\/dt) = 1\/R \u00b7 \u0394 P(t) = 1\/R (P<sub>inlet<\/sub> &#8211; P<sub>outlet<\/sub>) + 1\/R (p<sub>inlet<\/sub>(t) &#8211; p<sub>outlet<\/sub>(t))<\/p>\n<p>Hence: <span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<p style=\"text-align: center;\">A \/ (\u03c1 \u00b7 g) \u00b7 (dp<sub>outlet<\/sub>(t)\/dt) = 1\/R (P<sub>inlet<\/sub>-P<sub>outlet<\/sub>) + 1\/R (p<sub>inlet<\/sub>(t)-2p<sub>outlet<\/sub>(t))<\/p>\n<p>which is an inhomogeneous ordinary differential equation of 1<sup>st<\/sup> order with an exponential solution rising or decaying with the time scale (A \u00b7 R) \/ (2\u03c1 \u00b7 g).<span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<p><b>We conclude that less tall reservoirs of larger cross section, or higher hydrodynamic flow-channel resistances reduce the hydrostatic drift.<\/b><span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<p>If the flow rate should remain constant over a long period of time, hydrostatic drift compensation is recommended: The applied pressures have to be conducted such that the right side of the differential equation remains constant. The P<sup>2<\/sup>CS has a build-in function to accomplish this compensation automatically, with the function-setup:<span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<p style=\"text-align: center;\">set:hystatic_pressure<span class=\"Apple-converted-space\">\u00a0<\/span><\/p>\n<p style=\"text-align: center;\">set:hystatic_pressure:timescale<\/p>\n<p>On the other hand, the hydrostatic pressure can also be useful as an excellent source of (quasi-)static pressure for experimental setups. As illustrated, a one-meter large water column can generate significant pressures at the lower end. When doing experiments which require constant pressures with minimal liquid transfer (such that the liquid level of the column will not significantly decrease), water columns present an excellent and inexpensive tool for microfluidic and mesofluidic applications.<\/p>\n<p><i>Authors: F\u00fctterer, C., Kubitschke, H., Prasol, K.<\/i><\/p>\n<p><\/div><\/div>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><div class=\"wpb_column vc_column_container vc_col-sm-6\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p><a href=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/Hydrostatic_pneumatic_pressure.png\"><img loading=\"lazy\" class=\"wp-image-2324 aligncenter\" src=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/Hydrostatic_pneumatic_pressure.png\" alt=\"\" width=\"543\" height=\"385\" srcset=\"https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/Hydrostatic_pneumatic_pressure.png 1200w, https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/Hydrostatic_pneumatic_pressure-300x213.png 300w, https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/Hydrostatic_pneumatic_pressure-1024x726.png 1024w, https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/Hydrostatic_pneumatic_pressure-768x545.png 768w, https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/Hydrostatic_pneumatic_pressure-100x71.png 100w, https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/Hydrostatic_pneumatic_pressure-865x613.png 865w, https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/Hydrostatic_pneumatic_pressure-1184x840.png 1184w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/a><\/p>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><\/div><div class=\"vc_row wpb_row vc_row-fluid\"><div class=\"wpb_column vc_column_container vc_col-sm-6\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_text_column wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<p>[text_output]<strong>Melden Sie sich zu unserem Newsletter an! <\/strong><\/p>\n<p>We regularly update this page with new technical and application notes as well as background information on Microfluidics, Hydrodynamics and more. If you want to stay updated, please subscribe.[\/text_output]<\/p>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><div class=\"wpb_column vc_column_container vc_col-sm-6\"><div class=\"vc_column-inner\"><div class=\"wpb_wrapper\">\n\t<div class=\"wpb_raw_code wpb_raw_html wpb_content_element\" >\n\t\t<div class=\"wpb_wrapper\">\n\t\t\t<div class=\"tnp tnp-subscription\">\n<form method=\"post\" action=\"https:\/\/biophysical-tools.de\/de\/?na=s\" data-trp-original-action=\"https:\/\/biophysical-tools.de\/de\/?na=s\">\n\n<input type=\"hidden\" name=\"nlang\" value=\"\"><div class=\"tnp-field tnp-field-email\"><label for=\"tnp-1\">Email<\/label>\n<input class=\"tnp-email\" type=\"email\" name=\"ne\" id=\"tnp-1\" value=\"\" required><\/div>\n<div class=\"tnp-field tnp-field-button\"><input class=\"tnp-submit\" type=\"submit\" value=\"Anmelden\" >\n<\/div>\n<input type=\"hidden\" name=\"trp-form-language\" value=\"de\"\/><\/form>\n<\/div>\n\n\t\t<\/div>\n\t<\/div>\n<\/div><\/div><\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"Listen to the article in English: https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/EN1_Pressure_and_volume_driven_flowcontrol.mp3 Listen to the article in German: https:\/\/biophysical-tools.de\/wp-content\/uploads\/2021\/04\/DE1_Druckbasierte_und_volumentbasierte_Stroemungskontrolle-18.04.21-20.19.mp3 Pressure-driven and Volume-driven Flow Control in Microfluidics Since decades syringe and peristaltic pumps belong to biological and chemical laboratories. Thus, it was comprehensible that they were the first choice for the use with microfluidic devices, i.e. at a microscale. 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