MT-0.6081 Microfluidics and BioMEMS Microfluidics 2 Surface tension, contact angle, capillary flow 28.1.2017 Ville Jokinen
Surface tension & Surface energy Work required to create new surface = surface energy x area created δw = γ δa = γ Lδx Fundamental definition of surface energy: γ = δw / δa [ J / m 2 ] Hunter: Introduction to Modern Colloid Science, p.134 Surface energy is also known as surface tension: γ = δf / δx [ N / m] Concept applicable to all surfaces and interfaces: solid-solid, solid-liquid, liquid-liquid, solid-gas, liquid-gas Interfaces Surfaces
Molecular basis of surface energy The surface layer lacks some of the bonds in bulk phase This increased potential energy compared to the bulk is called surface energy!
Surface tension measurement: Drop weight method: Gravity = perimeter x surface tension mg = 2πr x γ Empirical correction factor needed force tensiometry Wilhelmy plate method: Force tensiometry: The force a liquid exerts on a plate is measured F = 2 L γ No correction factor needed Good method also in practice
Temperature dependence: water: 68 mj/m 2 at 50 o C, 59 mj/m 2 at 100 o C Water has a very high surface energy because of strong intermolecular bonds.
Scaling: surface forces vs body forces Surface area to volume ratio scales as d -1 Microsystems often dominated by surface effects An example: h Reservoir droplet Flow channel Case 1: The flow channel is a microchannel: 100 μm x 100 μm x 100 mm, Volume 1 μl Volume: Hydrostatic pressure from reservoir 10 Pa Area: Capillary pressure from channel 3000 Pa Surface dominated! Case 2: The flow channel is a garden hose: 1 cm x 1 cm x 10 m, Volume 1 liter Volume: Hydrostatic pressure from reservoir 1000 Pa Area: Capillary pressure from channel 30 Pa Volume dominated!
Bond number: Does gravity matter? Dimensionless number that characterizes the ratio of surface forces to body forces Capillary pressure= γ /L, Hydrostatic pressure= ρal a = acceleration (for gravity, 9.81m/s 2 ) L = characteristic length scale γ = surface tension ρ = density Bo = ρal 2 γ If Bo < 1 the system is dominated by surface forces (opposed to body forces) For water, Bo = 1 at around 1 mm range. Microfluidic channels are usually smaller than this so gravity typically does not matter in microfluidics. Example from previous page, water in a channel with 100 µm and 1 cm dimensions: Bo 1.4 * 10-3 (for 100 µm) Bo 14 (for 1 cm)
Surface tension measurement: optical tensiometry Drop shape analysis: Optical tensiometry: Surface tension measured from the shape of a hanging droplet Shape determined by the balance of gravity (hydrostatic pressure) and surface tension (laplace pressure). Image from biolin scientific.
Capillary number Dimensionless number that characterizes the ratio of viscous forces to surface forces Viscous shear pressure = µv/l, Capillary pressure= γ /L µ = dynamic viscosity (in multiphase systems, opt for the higher viscosity) γ = surface tension v = velocity Ca = µv γ Viscous forces and surface forces are both significant at microscale. Capillary numbers can be high or low. Illustration: a droplet of liquid is immobilized in a channel where an immiscible liquid flows. Will it stay as a sphere held together by surface tension or be elongated due to shear forces? Lower Ca (more influence of surface tension) Higher Ca (less influence of surface tension)
Surface energy, cohesion, adhesion Surface energy is linked to adhesion between materials and intra material cohesion. Work of cohesion, W 11 : Before separation: γ 11 =0 After separation: 2γ 1 Material 1 Material 1 γ 11 Material 1 Material 1 γ 1 γ 1 W 11 = 2γ 1-0 = 2γ 1 Work of adhesion, W 12 : Before separation: γ 12 After separation: γ 1 + γ 2 W 12 = γ 1 + γ 2 - γ 12 Material 2 Material 1 γ 12 Material 2 Material 1 γ 2 γ 1
Contact angle, experimental A liquid droplet makes a certain angle of contact with a solid surface The angle is called the apparent contact angle θ Property of a solid-liquid-fluid three phase system For a fixed liquid and fluid, contact angle is characteristic parameter of a surface/material
Contact angle, theoretical Young s equation: γ LG cos(θ) = γ SG - γ SL θ Thermodynamical, or Young s, contact angle γ LG Liquid-vapor surface energy ( liquid surface tension ) (often also γ l, γ lv ) γ SG Solid-vapor surface energy ( solid surface energy ) (often also γ s, γ sv ) γ SL Solid-liquid surface energy ( solid-liquid interface energy ) The thermodynamical contact angle does not necessarily equal the experimental contact angle on real surfaces because of hysteresis.
Contact angle hysteresis On real surfaces: θ rec < θ eq < θ adv Hysteresis θ adv θ rec θ rec = Receding contact angle θ eq = Equilibrium/static contact angle θ adv = Advancing contact angle Reasons for contact angle hysteresis: Adsorption of molecules from the solution Desorption of molecules from the surface Chemical inhomogenities Physical surface topography Which experimental contact angle is the one appearing in Young s equation? Unresolved, but some suggestions that have been made in the literature: 1. θ adv 2. (θ adv + θ rec ) /2 3. acos ((cos θ adv + cosθ rec )/2) 4. the most stable θ (e.g. after vibrations or other source of energy)
Contact angle measurement Same tools and methods as for surface tension: Force tensiometry, often Wilhelmy plate Optical goniometry of a sessile droplet Optical goniometry Wilhelmy plate method
Measuring solid-vapor surface energies With some assumptions, γ sv can be estimated by contact angle measurements Zisman method: Surface energy of a solid is the surface energy of the highest surface tension liquid exhibiting complete wetting. (= critical surface tension) Other (better) methods: Owens-Wendt Good-vanOss Important point: Solid liquid and solid-vapour surface tensions are difficult to measure. Liquid-vapour surface tensions and the contact angle are easy to measure.
Hydrophilic/ Hydrophobic terminology For water: hydrophilic/hydrophobic For oils: oleophilic/oleophobic For liquids in general: hygrophilic/hygrophobic, omniphilic/omniphobic θ = 0 Completely wetting θ 5 Superhydrophilic 0 < θ < 90 Hydrophilic Wetting 90 < θ < 150 Hydrophobic Nonwetting 150 < θ < 180 Superhydrophobic Ultrahydrophobic SiO 2 Clean metals roughness+chemistry SU-8, Si PDMS, Teflon roughness+chemistry
Contact angle on structured surfaces On the lowest surface energy planar surfaces, contact angles only go up to 120 for water and 75 for oils. Beyond that, topography can be used to enhance contact angle Cassie state: Possible on intrinsically hydrophobic surfaces Results in increased hydrophobicity cos(θ c ) = f cos(θ) -1 +f f = air fraction Wenzel state: Possible on any surface Results in enhanced intrinsic contact angle cos(θ w ) = r cos(θ) r = roughness factor Note! The contact angle is enhanced but the chemical nature of the surface remains the same The enhanced contact angles are relevant for fluidics, but not directly in e.g. adsorption
Superhydrophobicity Micro/nanostructures combined to hydrophobic surface properties can result in superhydrophobic surfaces. Properties: θ > 150, water repellent, water deposited on top stays as intact droplets and moves easily low sliding angles, self cleaning Silicon nanopillars (black silicon) Left: oxidized silicon surface θ 0 Right: fluoropolymer coating θ 170 Jokinen, Sainiemi, Franssila: Advanced Materials 2008
Young s equation and adhesion, number of independent parameters: Adhesion = γ γ cosθ = γ lv sv lv + γ γ sl sv γ sl On first sight, these two equations contain 4 parameters each. However, since the solid surface is unable to deform, γ sv + γ sl = constant. In wetting phenomena, we are only interested in changes, which is why the 2 solid surface energy terms only ever appear in the term (γ sv - γ sl ) and not independently. So in reality, both wetting related equations have only 3 independent terms. This is good news since both γ lv and cos(θ) are easily measurable, and measuring 2/3 of independent parameters is enough to know everything about the system. Inserting Young s equation into the work of adhesion equation we get: AAAAAAAAAAAAAAA = γ llll + γ llll cos θ = γ llll (1 + cos θ ) This is called the Young-Dupré equation, and it relates the work of adhesion to the surface tension and contact angle. You can test what happens to adhesion when θ=0, 90 or 180 degrees. Compare the results to the equation for the work of cohesion.
Laplace pressure There is a pressure difference across a curved liquid surface. Young-Laplace equation Calculating radius of curvature For a spherical droplet or bubble: 1 μl spherical water droplet in air, P 140 Pa Pressure is higher inside a spherical 1 μl spherical air bubble in water, P -140 Pa bubble or a droplet!
Capillary pressure and contact angle Liquid makes a contact angle of θ with a capillary with radius r. 1. What is the curvature of the meniscus? 2. What is the Capillary pressure? 1. From the triangle in the figure we get: r/r= cos(θ) so R=r/cos(θ) Curvature of the sphere was defined as -2/R (bubble) so Curvature = -2 cos(θ) / r 2. Capillary pressure is the corresponding Laplace pressure: P cap = γ * Curvature = -2 γ cos(θ) / r θ R θ r
Capillary rise and depression Hydrostatic pressure ρgδh = -4γcos(θ)/d Capillary pressure Note that θ is the only material parameter of the capillary that is needed, not eg. γ SG or γ SL
Capillary filling of microfluidic channels Main differences to classical capillary rise: Horizontal vs vertical Capillary filling continues until the channel network is full Geometry usually non circular and nonuniform materials Hydrophilic walls contribute to filling, hydrophobic oppose it θ t h θ l θ r θ b w P cosθt + cosθb = γ ( h + cosθl + cosθr ) w (is still just a form of Laplace pressure): The capillary pressure is calculated at the filling front (and possibly the de-wetting front), already filled areas still contribute to flow resistance.
Droplet microfluidics Microfluidics does not always mean continuous flow in a channel. Droplet microfluidics and digital microfluidics increasingly common Discrete droplets, either 2 immiscible liquid phases or liquid droplets and air. Each droplet can be viewed as a single experiment.
Droplet generation Two immiscible phases, typically water and oil/fluorinated oil. The walls of the system are wetting toward the continuous phase and anti-wetting toward the dispersed phase Droplet production is dependent on: capillary number, geometry, and ratio of the flows of the dispersed and the continuous phases. Shear forces attempt to divide the dispersed phase while surface tension tries to keep the dispersed phase together. Ca typically 0.001-10 Droplet generation rate can be in the range of 10kHz T junction Flow focusing Lab Chip, 2010, 10, 2032 2045
Digital microfluidics, electrowetting Droplets on hydrophobic surfaces, surface tension holds the droplets together (no spreading) Electrowetting used to move the droplets. Either one open surface or more commonly between 2 hydrophobic plates. V = applied voltage C = capacitance γ s =solid surface energy γ w = water surface energy γ 0 ws = water solid interfacial energy with no electric field.
CD microfluidics Actuating force by centrifugation. Capillary valves and hydrophobic valves to control flow.
Review The importance of surfaces in microfluidics/bio-mems Surface energy, Laplace pressure Contact angle, theoretical and experimental aspects Capillary rise and capillary filling of microfluidic channels Shear and surface tension effects for microfluidics Reading material For lecture 2, the reading material is: Chapter 5, surface tension, from a book Physics of Continuous matter by B. Lautrup. Pages 69-83 Available from link: http://www.cns.gatech.edu/~predrag/courses/phys- 4421-13/Lautrup/surface.pdf