V09 Electrokinetic I Electroosmosis WS 23 PDF

V9 V09 Electrokinetic I < Electroosmosis (EO) > Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 1 Contents V9 Contents 9.1 Introduction Electrokinetics 9.2 Solid-Liquid Interface  Electric Dou...

V9 V09 Electrokinetic I < Electroosmosis (EO) > Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 1 Contents V9 Contents 9.1 Introduction Electrokinetics 9.2 Solid-Liquid Interface  Electric Double Layer (EDL)  ζ- Potential  Debye length 9.3 Electroosmosis (EO)  Mechanism of Electroosmosis  Flow Profile in Micro Channel 9.4 Electroosmotic Pumps (EOP) 9.4.1 DC-EOP 9.4.2 AC-EOP 9.4.3 AC-EOP with Travelling Wave 9.5 AC Electroosmotic Mixer Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 2 Learning Targets V9 Learning Targets  Electrical double layer (EDL)  Helmholtz theory  Gouy-Chapman theory  Stern theory  ζ-Potential  Debye length  Electroosmosis  Electroosmotic pumps  Mechanisms  DC-EOP  Flow profile  AC-EOP  AC-EOP travelling wave Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 3 V9 9.1 Electrokinetics - Introduction Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 4 9.1 Introduction V9 5 Electrokinetics Fluid or particle transport through application of an electric field in a micro channel  Enables non-mechanical actuated liquid or particle transport / manipulation  3 Electrokinetic platforms  Electroosmosis (EO) → V09  Electrophoresis (EP) → V10  Dielectrophoresis (DEP) → V11 Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 9.1 Introduction V9 Electrokinetic Platforms Fluid or particle transport through application of electric fields Electroosmosis (EOF) Electrophoresis (EP) Dielectrophoresis (DEP) Transport of fluid Transport of fluid and separation of charged molecules Manipulation of polarizable particles Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 6 V9 9.2 Solid-Liquid Interface Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 7 9.2 Solid-Liquid Interface V9 Electrical Double Layer (EDL) Solid surfaces acquire a nonzero surface charge in aqueous solution  Channel wall surfaces can carry electrostatic charges  Surface charges are generated through, e.g.,  Dissociation of, e.g.,  Carboxylic acid groups COOH ↔ COO- + H+  Silanol groups  Ion adsorption  Acid-base reactions Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 SiOH ↔ SiO- + H+ 8 9.2 Solid-Liquid Interface V9 Electrical Double Layer (EDL)  When wall is charged, the charge at the wall is counteracted by a thin cloud of oppositely charged ions, called electrical double layer (EDL)  Electrical potential at the wall is different from that in the bulk  Bulk solution is electroneutral Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 9 Helmholtz-Theory (1878) Rigid Double Layer  One-to-one compensation of charge  Charges are fixed  No charges in the gap (no sources and sinks)  Linear change of potential      x 2  r 0 with ρ = 0 in gap    C1 x  C2 10 Distance x from surface 2 Poisson equation Electrolyte Electrode / Surface V9 www.daten.didaktikchemie.uni-bayreuth.de 9.2 Solid-Liquid Interface Ψ …… Electrical double layer potential ρ ……. Electrical double layer charge density εr ……. Relative dielectric constant ε0 …… Dielectric constant of vacuum C1,C2.. Integration constants Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 9.2 Solid-Liquid Interface V9 11 Two Helmholtz Layers  Dehydrated ions  Completely immobilized  Strongly bonded https://www.ufz.de/  Inner Helmholtz Layer Hermann von Helmholtz (1821 - 1894)  Outer Helmholtz Layer  Hydrated ions  Completely immobilized  Weakly bonded Helmholtz Theory does not include diffusion effects www.iee.tu-clausthal.de Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 9.2 Solid-Liquid Interface V9 Two Helmholtz Layers https://web.nmsu.edu/~snsm/classes/chem435/Lab14/double_layer.html Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 12 9.2 Solid-Liquid Interface V9 13 Areal Capacity CH of Helmholtz Layer CH   0 d Example: Width dHelmholtz = 0.2 nm (one monolayer)  Electric field strength E = 109 V/m ! Theory is only applicable for highly concentrated electrolytes CH... Capacity per area of Helmholtz layer ε…... Dielectric constant ε0.... Dielectric constant of vacuum d …. Distance electrode – outer place of dissolved ions directly covering the metallic surface Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 9.2 Solid-Liquid Interface V9 14 www.daten.didaktikchemie.uni-bayreuth.de Gouy-Chapman-Theory (1910) Solid-Liquid Interface is Described by Diffusion of Ions  Based on thermodynamics and Boltzmann statistics  Equilibrium exists when the probability that ions diffuse away from the interface (due to thermal energy) equals the probability that ions will be attracted to the surface (due to charge)  Exponential decay of potential  Diffusive layer is larger than thickness of one monolayer Distance from surface Theory only applicable for highly diluted electrolytes Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 9.2 Solid-Liquid Interface CGC 2   c  zF   zF   cosh   U DL  R T  2  R T  z … Number of ions F … Faraday constant ε … Dielectric constant c … Ion density at the electrode R.. Ideal gas constant T … Absolute temperature UDL Voltage drop at the double layer E. J. Bowen: Biogr. Mems Fell. R. Soc. 4 34-44 (1958) Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 15 https://de.wikipedia.org/ Areal Capacity CGC of Gouy-Chapman Layer V9 Louis Georges Gouy (1854 -1926) David Leonard Chapman (1869 -1958) 9.2 Solid-Liquid Interface V9 16 Helmholtz layer Stern Theory (1924) Gouy-Chapman layer Combination of Helmholtz double layer CH CGC www.lamp.tu-graz.ac.at and Gouy-Chapman double layer 1 1 1   C DL C H CGC C DL  C H  CGC C H  CGC  0 < x < δ : Helmholtz layer  δ < x < ∞: Gouy-Chapman layer Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 δ Distance from surface 9.2 Solid-Liquid Interface When the fluid is in motion, than the V9 17 ζ-Potential strongly bonded ions remain at the surface whereas the weakly bonded ions in the EDL will be sheared off Potential Between Surface and Solution ζ-Potential Dependent on  Surface charge + + + + + + + + + + +  Bounded ions  Electric properties of electrolyte Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 distance from the surface 9.2 Solid-Liquid Interface ζ-Potential  Describes the potential as well as the position of the slip plane at which no more ions are sheared off by the fluid flow along the wall  Slip plane  Interface between mobile and fixed charges  Position in neighborhood to Helmholtz layer (in some references, the position defined at V9 18 ζ-Potential + + + + + + + + + + + the transition point between linear and distance from the surface exponential decrease)  Fluid slips without adhesion along the wall Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 ζ can exceed |60 mV| 9.2 Solid-Liquid Interface V9 Helmholtz layer 19 Gouy-Chapman Layer  e  RT www.lamp.tu-graz.ac.at Debye length D  F 2 zi2ci  1/e-decay of potential  Defines the distance at which the potential in the solution is negligible  Defines the thickness of the EDL  Ions will not be attracted and bonded to the surface above λD Typical Debye lengths 0.1 nm < λD < 100 nm Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 Distance from surface δ λD εe … R… T … F… zi … ci … Permittivity of electrolyte Ideal gas constant Absolute temperature Faraday constant Charge of ion i Concentration of ions i 9.2 Solid-Liquid Interface D   e  RT F 2 zi2 ci Debye length can be varied by changing  Surface charge 20 www.nobelprize.org Debye length V9 Petrus Debye (1884-1966)  Ion concentration of the solution  pH value EDL occurs for pH > 2.5 Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 εe … Permittivity of electrolyte R … Ideal gas constant T … absolute temperature F … Faraday constant zi … Charge of ion i ci … Concentration of ions i 9.2 Solid-Liquid Interface Microfluidics V9 Nanofluidics https://doi.org/10.1007/s10404-012-1105-5 Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 21 V9 9.3 Electroosmosis* < EO > * Fist reported by F. F. Reuss: Mem. Soc. Imp. Nat. Moscou 2 327–337 (1809) Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 22 9.3 Electroosmosis V9 23 Mechanism of Electroosmosis  Capillary or microfluidic channel is needed  Application of an axial electric field (100 V - 1000 V) www.micromachine.standford.edu perpendicular to the EDL  Electric field acts as net force (Coulomb force) on mobile, means weakly bounded electric charges in EDL  Ion transport only in EDL (bulk fluid is electroneutral)  As a result of the viscous effect, the moving ions will drag their surrounding fluid molecules, forming electroosmotic flow in the pump channel → Electroosmotic flow Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 9.3 Electroosmosis Electroosmosis ! ! ! Appears only in microchannels ! ! ! In macrochannels the diameter is too large to drag the bulk volume (too small surface-to-volume ratio) C.-T. Kuo et al.: Lab Chip 8 725-733 (2008) Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 V9 24 9.3 Electroosmosis Analytical Description of Electroosmosis Assumptions  Straight and long channel  Constant diameter over length  EDL constant and uniform  Debye length small with respect to channel diameter  Homogeneous electric field E in x-direction perpendicular to EDL  One-phase laminar flow  Mechanical properties are constant  Constant temperature Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 V9 25 9.3 Electroosmosis V9 Analytical Description of Electroosmosis Matched Asymptotic Approach Outside the EDL Inside the EDL Fluid is electroneutral Fluid is charged by ions and irrotational Coulomb forces in EDL No Coulomb forces Motion of fluid by ions E ┴ EDL Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 26 9.3 Electroosmosis V9 Analytical Description of Electroosmosis Matched Asymptotic Approach Inside the EDL Fluid is charged by ions Coulomb forces in EDL Motion of fluid by ions E ┴ EDL Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 27 9.3 Electroosmosis NS equation V9 v   (v  ) v     p    2 v  f volume t     v 2   (v  ) v     p     v   e E t Coulomb force ρ … Density v … Velocity p … Pressure η … Viscosity ρe … Electrical charge density in EDL E … Externally applied electrical field strength (acting uniformly in the EDL) Course „Microfluidic Systems - Bio-MEMS“ - V09 Electroosmosis Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 28 9.3 Electroosmosis V9  Re