INTRODUCTION TO NANOTECHNOLOGY

INTRODUCTION TO NANOTECHNOLOGY An Overview of Fluid Mechanics for MEMS -Reni Raju MEMS (Applications) Accelerometers for airbags Micro heat exchangers Sensors Actuators Micropumps NEMS (Application) Nanostructured Catalysts Drug Delivery systems Molecular Assembler/Replicators Sensors Magnetic Storage Applications Reinforced Polymers Nanofluids Fluid Mechanics of MEMS  Devices 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 10-2 100 102 Dia. Of Proton H-Atom Diameter Human Hair Man NEMS MEMS FLUID MODELLING  Conventional Navier Stokes with no-slip boundary conditions cannot be used.  Pressure Gradient is non-constant along a microduct and flowrate greater than predicted.  Surface to volume ratio is high of the order of 106 m-1 for a characteristic length of 1 micron.  Other factors like thermal creep, rarefaction, viscous dissipation, compressibility etc. For Gases Fluid Modeling Molecular Modeling Continuum Models Deterministic MD DSMC Statistical Liouville Boltzmann Euler Navier Stokes Burnett  Either as a collection of molecules or as a continuum.  Mean Free path,  1 2n 2  Characteristic Length, L   y  Knudsen Number,   Ma  L 2 Re Kn  Kn=0.0001 0.001 0.01 0.1 1 10 100 Continuum Flow (Ordinary Density Levels) Transition Regime (Moderately Rarefied) Slip-Flow Regime (Slightly Rarefied) Free-Molecule Flow (Highly rarefied)  Local value of Knudsen Number determines the degree of rarefaction and the degree of validity of the continuum model. CONTINUUM MODEL  Local 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.  Conservation of Mass:   uk   0  t xk  Conservation of Momentum:  ui ui  uk xk  t   ki   g i  xk     Conversation of Energy:    Closure:  e e  uk xk  t  qk ui    ki  xk xk   ki   p ki      ui uk  xk xi   u j       x j     ki   qi   k T  Flux(radiation) xi de  cv dT p  RT  Euler’s Equation:  Fluid is invisicid and non-conducting,   uk   0  t xk    ui ui  uk xk  t  p   g i  xk  cv    T T  uk xk  t  u k   p  xk  Compressibility  DENSITY CHANGES DUE TO TEMPERATURE  Strong wall Heating or cooling may cause density change.  DENSITY CHANGES DUE TO PRESSURE  Pressure changes due to viscous effects even for Ma<0.3.  Continuity Equation: u D  k 0 Dt xk 1 D Dp DT    Dt Dt Dt  ( p, T )  1   p T  ( p, T )   1   T p  For Adiabatic Walls; T*  T  T0  u  Pr 0  c   p0  1 D * Dp * Pr B * DT *     0 Ma 2  *    * Dt * Dt * A Dt *   A   0  0c p 0T0 ; B   0T0  For Isothermal Wall; T  T0 ˆ T  Tw  T0 ˆ  T  T0  DT 1 D * Dp *    0 Ma2 *  B *  w  T  Dt *  * Dt * Dt * 0   Boundary Conditions  At the Fluid- Solid Interface  No-slip and no-temperature jump is based on no discontinuities of velocity/temperature.  Continuum applicable for Kn<0.001  Tangential Slip velocity at wall, u w  u gas  uwall   u y w  For Real gases, u w  u gas  uwall  2  v  u y v w  Slip velocity & Temperature Jump, u gas  u wall * * 2   v  u *  3 (  1) Kn 2 Re  T *      *    y  v Ec  x*  w  w 4    2   T  2  Kn  T *     T    1 Pr  y *  w     * T * gas  Twall   where v   i  r ,  i  w dEi  dEr dEi  dEw T  MOLECULAR BASED MODELS  Goal is to determine the position , velocity and state of all particles at all times.  DETERMINISTIC MODEL:  Particle described in the form of two body potential energy and time evolution of the molecular positions by integrating Newton’s Law of motion.  Shortcomings:  Need to choose a proper and convenient potential for a fluid & solid combination.  Vast computer resources.  STATISTICAL MODEL:  Based on probability of finding a molecule at a particular position and state.  Six-dimensional phase space.  Assumption, for dilute gases with binary collision with no degrees of freedom.  Liouville equation, conservation of N-particle distribution function in 6N-dimensional space, N N     k .   Fk . 0 t xk xk k 1 k 1  Boltzmann equation for monatomic gases with binary collision,  ( nf )  ( nf )  ( nf )  j  Fj  J ( f , f *) t x j x j j  1,2,3  Non-linear collision integral, describes the net effect of populating and depopulating collisions on the distribution.  4 J ( f , f *)   0  n 2 ( f * f1*  f f1 ) rd(d )1 LIQUID FLOWS     The Average distance between the molecules approaches the molecular diameter. Molecules are always in collision state. Difficult to predict. Non-Newtonian behaviour commences,    u  2 1 y  Contradictory results in experimental data and modelling.  MD seems to be the best option available.  Based on MD, the degree of slip increases as the relative wall density increases or the strength of the wall-fluid coupling decreases.  Slip length,     Ls  Lo 1    c   SURFACE PHENOMENA  Surface to Volume ratio for 1 micron is 106 m-1.  High Radiative and Convective Heat transfer.  Increased importance to surface forces and waning importance of body forces.  Significant cohesive intermolecular forces between surface, stiction independent of device mass.  Adsorbed layer.  Surface tension and nonlinear volumetric intermolecular forces. Fluid Mechanics for NEMS  Nanofluids - thermal conductivity fluids.  Possibility of applying Continuum Model for low Knudsen number.(?)  Model applicability to Dense and rare gas.  Possible treatment of Liquids as dense gas at Nano scale.(?)  Importance of Quantum Mechanics.  Importance of Surface Phenomenon's. TASKS AHEAD  Modeling using the Continuum model for the Slip Flow Regime Knudsen Numbers.  Understanding the mechanics of Nano-scaled Domains.  Arriving at a suitable modeling technique comparable with the experimental data (if available.)