Fluid Mechanics of MEMS zDevices having a characteristic length of less than 1 mm but more than 1 micron. 10 -16 10 -14 10 -12 10 -10 10 -8 10 -6 10 -4 10 -2 10 0 10 2 Dia. Of ProtonH-Atom Diameter Human HairMan NEMSMEMS
FLUID MODELLING zConventional Navier Stokes with no-slip boundary conditions cannot be used. zPressure Gradient is non-constant along a microduct and flowrate greater than predicted. zSurface to volume ratio is high of the order of 10 6 m -1 for a characteristic length of 1 micron. zOther factors like thermal creep, rarefaction, viscous dissipation, compressibility etc.
zEither as a collection of molecules or as a continuum. zMean Free path, zCharacteristic Length, zKnudsen Number,
zLocal value of Knudsen Number determines the degree of rarefaction and the degree of validity of the continuum model. Kn=0.00010.0010.010.1110100 Continuum Flow (Ordinary Density Levels) Slip-Flow Regime (Slightly Rarefied) Transition Regime (Moderately Rarefied) Free-Molecule Flow (Highly rarefied)
CONTINUUM MODEL zLocal Properties such as Density and Velocity are averages over elements large compared with the microscopic structure of the fluid but small enough to permit the use of differential calculus. zConservation of Mass: zConservation of Momentum:
zConversation of Energy: zClosure:
zEuler’s Equation: yFluid is invisicid and non-conducting,
Compressibility zDENSITY CHANGES DUE TO TEMPERATURE yStrong wall Heating or cooling may cause density change. zDENSITY CHANGES DUE TO PRESSURE yPressure changes due to viscous effects even for Ma<0.3. zContinuity Equation:
zFor Adiabatic Walls;
zFor Isothermal Wall;
Boundary Conditions zAt the Fluid- Solid Interface zNo-slip and no-temperature jump is based on no discontinuities of velocity/temperature. zContinuum applicable for Kn<0.001 zTangential Slip velocity at wall, zFor Real gases,
zSlip velocity & Temperature Jump, ywhere
MOLECULAR BASED MODELS zGoal is to determine the position, velocity and state of all particles at all times. zDETERMINISTIC MODEL: zParticle described in the form of two body potential energy and time evolution of the molecular positions by integrating Newton’s Law of motion. zShortcomings: yNeed to choose a proper and convenient potential for a fluid & solid combination. yVast computer resources.
zSTATISTICAL MODEL: zBased on probability of finding a molecule at a particular position and state. zSix-dimensional phase space. zAssumption, for dilute gases with binary collision with no degrees of freedom. zLiouville equation, conservation of N-particle distribution function in 6N-dimensional space, zBoltzmann equation for monatomic gases with binary collision,
zNon-linear collision integral, describes the net effect of populating and depopulating collisions on the distribution.
LIQUID FLOWS zThe Average distance between the molecules approaches the molecular diameter. zMolecules are always in collision state. zDifficult to predict. zNon-Newtonian behaviour commences, zContradictory results in experimental data and modelling. zMD seems to be the best option available. zBased on MD, the degree of slip increases as the relative wall density increases or the strength of the wall-fluid coupling decreases.
SURFACE PHENOMENA zSurface to Volume ratio for 1 micron is 10 6 m -1. zHigh Radiative and Convective Heat transfer. zIncreased importance to surface forces and waning importance of body forces. zSignificant cohesive intermolecular forces between surface, stiction independent of device mass. zAdsorbed layer. zSurface tension and nonlinear volumetric intermolecular forces.
Fluid Mechanics for NEMS zNanofluids - thermal conductivity fluids. zPossibility of applying Continuum Model for low Knudsen number.(?) zModel applicability to Dense and rare gas. zPossible treatment of Liquids as dense gas at Nano scale.(?) zImportance of Quantum Mechanics. zImportance of Surface Phenomenon's.
TASKSAHEAD zModeling using the Continuum model for the Slip Flow Regime Knudsen Numbers. zUnderstanding the mechanics of Nano-scaled Domains. zArriving at a suitable modeling technique comparable with the experimental data (if available.)