fluid properties at nano-, meso scale. a numerical treatment, 2008, p.234

[...]... behaviour The mathematical solution of these equations throughout a fluid domain is known as computational fluid dynamics (CFD) The governing equations describe the mathematical representation of a physical model that is derived from experimental flow measurements and observations These representative equations are then replaced with an equivalent numerical description, which is solved using numerical. .. between two parallel plates separated by distance H The top plate moves with constant velocity U and the bottom plate is at rest The fluid in between them adheres to both plates, so that the fluid layers at each of the plates has the same velocity at the plate The velocity of the fluid changes linearly in this case, so the velocity at any point between the plates can P1: PIC c01 JWBK251-Ransing June 20,... elements allows complex geometries to be simulated, and smaller elements can be used to refine the solution in areas of high gradients or where a greater accuracy is needed By approximating the fluid as a continuum and ignoring the underlying molecular behaviour, a great deal of computational effort is saved and accuracy has been proved to be sufficient in many applications The molecular information can be approximated... simulation techniques and their advantages/disadvantages when applied to fluid systems at meso scales r Chapter 3 A meso scale simulation method is developed based on a ‘bottom- up’ approach This chapter shows the implementation of the molecular model and the upscaling of information to characterize the bulk properties of the fluid system Aim The reader should understand how fluid modelling at the meso scale.. . following notation will be used unless otherwise stated a a ahyd A A Ah AH Am B c co cw Cb d deff D D Bo Deff Dm Dmon Ds Dw e E E KE E PE E f Acceleration (m/s2 ) Particle radius (m) Hydrodynamic particle radius (m) Area (m2 ) Baseline (counts/s) Area of a hexagon (m2 ) Hamaker constant (J) Area of membrane surface (m2 ) Instrument factor ≤ 1 Solute concentration (kg/m3 ) Feed concentration at the inlet... performance with large numbers of molecules Aim The reader should understand the computational performance issues faced by molecular physics models at these scales r Chapter 7 A discussion of various experimental measurements and techniques that depend on fluid flow and properties at the nano /meso scale is presented These measurements range from macro scale measurements, such as rates of membrane filtration,... nano scale measurements performed using the atomic force microscope (AFM) Comparison between simulation and experiment is shown for several cases Aim By the end of this chapter the reader should be aware of and understand experimental techniques that can be used to study fluid systems at different scales and should also be aware of how events at the nano /meso scale can affect experimental results at. .. approximated at these scales, as the molecular motion cancels out, yielding only bulk properties at this scale Continuum simulations also have the flexibility to prescribe a wide variety of boundary conditions capable of replicating almost any system, while still maintaining global conservation laws 1.2.3.4 Limitations Continuum mechanics, however, has its drawbacks It is dependent on the generation of... the flow domain into elemental control volumes surrounding a node Flow parameters are then treated as fluxes between control volumes, and conservation is maintained in each element This allows for better treatment of flows with discontinuities such as shock waves 1.2.3.3 Advantages Continuum simulations are able to provide an accurate model for fluid behaviour in a wide range of applications and systems... relationship between the stress and strain rate and the heat flux and temperature gradient The thermodynamic equilibrium condition also states that there are sufficient interactions or collisions to smooth out any statistical variations occurring from the molecular scale (Figure 1.5) Molecular Property Property Continuum x x Figure 1.5 Statistical variations in properties arising from a finite number of molecules . advanced data analysis and optimization strategies for industry. Dr Rajesh S. Ransing Specialist Subjects: Data Analysis, Machine Learning, Optimization Techniques, Computer Simulation and Mathematical. advantages/disadvantages when ap- plied to fluid systems at meso scales. r Chapter 3. A meso scale simulation method is developed based on a ‘bottom- up’ approach. This chapter shows the implementation. class="bi x0 y0 w0 h0" alt="" P1 : ABC/ABC/SPH P2 : ABC fm JWBK251-Ransing June 20, 2008 21:20 Printer Name: Yet to Come Fluid Properties at Nano /Meso Scale Fluid Properties at Nano /Meso Scale: