Numerical Simulation of Spontaneous Capillary PenetrationTony FickComprehensive ExamOct. 27, 2004Goal: Develop a first principle simulation to explore fluid uptake in capillariesh(r,t)r

Motivation

Project ObjectivesProposed research to identify geometric effects on capillary rate1) Compute equilibrium height/shape in cylindrical, conical, wedge shaped, elliptical cross sections, and periodic walled capillaries2) Numerical simulation of capillary penetration in cylindrical, conical, and wedge shaped capillaries from infinite reservoir3) Modeling kinetics of capillary penetration in cylindrical, conical, and wedge shaped capillaries from finite reservoir4) Repeat steps 2 and 3 for elliptical cross section capillaries5) Repeat step 2 for periodically corrugated capillaries

Literature Experimental ResultsRegion IRegion IIRegion IIIt*h*tI*tII*hI*hII*M. Stange, M. E. Dreyer, and H. J. Rath, Capillary driven flow in circular cylindrical tubes, Physics of Fluids 15, 2587 (2003)

System to Test AlgorithmInterface modeled as function h(r,t)Dynamic contact angle qNeed to transform system into simulation boxCo-ordinate TransformationUse cylindrical capillary:easy systemexperimental results

Developing The ModelGoverning equations for the transformed system:

Boundary ConditionsVelocityPressureUpdate height

Numerical MethodInitial values for h, P, U, and V

Preliminary Results Static case

- test geometric effect on meniscus- determine improvement of conical capillary Dynamic simulation of dodecane rise

- test model against earthbound experiment- match equilibrium height/shape Dynamic simulation of microgravity rise

- match early time-height behavior- test effect of exponent in contact line velocity

Dynamic Rise of DodecaneB. V. Zhmud, F. Tiberg, and K. Hallstensson, Dynamics of capillary rise, J. Colloid Interface Sci. 228, 263 (2000) Simulation shows behavior of all three regions

Dodecane EquilibriumEquilibrium shape calculated from static equationsSimulation end shape within 0.1% of equilibrium shapeSimulation matches dynamic and equilibrium behavior

Dynamic Simulation of Microgravity Use microgravity rise of Dow Corning Silicon fluid SF 0.65 to match initial height behavior Test effect of exponent in contact line equation

Dynamic Simulation of MicrogravityM. Stange, M. E. Dreyer, and H. J. Rath, Capillary driven flow in circular cylindrical tubes, Physics of Fluids 15, 2587 (2003)Simulations match experimental behavior

Static Case Test geometric effect Model reduces to solving single height equationTwo different capillaries: cylinder and cone

Static CaseIncreased height for cone, also increased curvature

Conclusions Static Case height increase for conical capillary over cylindrical Dynamic Dodecane Rise end results within 0.1% of equilibrium dynamic data within 97.5% confidence of experimentalDynamic Microgravity Rise simulation matched experimental results exponent in constitutive equation only effects behavior in Region II Model for capillary flow developed based on first principle equations Algorithm able to predict previous experimental results

Future WorkDynamic simulation for capillaries with different geometries to determine geometric effect on capillary penetration (conical, wedge, ellipsoidal, periodic corrugated walls)Experimental results for capillaries with different geometriesDevelop constitutive equation for contact line for multi phase systems (e.g. surfactants)

AcknowledgementsFundingPenn State Academic Computing FellowshipAcademicDr. Ali BorhanDr. Kit Yan ChanPersonalDr. Kimberly WainRory StineMichael Rogers

Expanded microgravity graph

Constitutive contact line velocityplotted against contact angleqaqr

Based on: Force balance and Data match