Diffusion-induced bias in near-wall velocimetry

The Brownian fluctuations of the colloidal tracers often used in microscale velocimetry are typically isotropic in the bulk. In the near-wall region, however, these fluctuations are strongly affected by the hydrodynamic interaction with the wall and by the no-flux condition imposed by the wall. These wall effects can, under appropriate conditions, bias measurements based on colloidal tracers, potentially leading to significant overestimation of near-wall velocities. We use a Fokker–Planck description to generate probability density functions of the distances from a single wall sampled by the matched particles that are present in the same window at both the start and end of a time interval. The importance of the resulting bias for experimental parameters is then quantified in terms of the size of the imaged region and measurement interval. We conclude with a brief discussion of the implications for near-wall velocimetry measurements.

[1]  R. Sadr,et al.  Multilayer nano-particle image velocimetry , 2005 .

[2]  L. Goddard.  Linear Differential Operators , 1962, Nature.

[3]  Christel Hohenegger.  Small Scale Stochastic Dynamics For Particle Image Velocimetry Applications , 2006 .

[4]  M. Bawendi,et al.  Single quantum dot (QD) imaging of fluid flow near surfaces , 2005 .

[5]  Apparent slip due to the motion of suspended particles in flows of electrolyte solutions. , 2004, Langmuir : the ACS journal of surfaces and colloids.

[6]  C. Meinhart,et al.  Apparent fluid slip at hydrophobic microchannel walls , 2002 .

[7]  A. Conlisk,et al.  An experimental study of electro-osmotic flow in rectangular microchannels , 2004, Journal of Fluid Mechanics.

[8]  K. Breuer,et al.  APPARENT SLIP FLOWS IN HYDROPHILIC AND HYDROPHOBIC MICROCHANNELS , 2003 .

[9]  D. Ermak,et al.  Brownian dynamics with hydrodynamic interactions , 1978 .

[10]  Moti Lal,et al.  Dynamics of colloidal particles in the vicinity of an interacting surface , 1987 .

[11]  S. Granick,et al.  Rate-dependent slip of Newtonian liquid at smooth surfaces. , 2001, Physical review letters.

[12]  V. D. Sobolev,et al.  Slippage of liquids over lyophobic solid surfaces , 1984 .

[13]  D. Maynes,et al.  Velocity profile characterization in sub-millimeter diameter tubes using molecular tagging velocimetry , 2002 .

[14]  S. Troian,et al.  A general boundary condition for liquid flow at solid surfaces , 1997, Nature.

[15]  J. Rädler,et al.  Flow profile near a wall measured by double-focus fluorescence cross-correlation. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Jean-Louis Barrat,et al.  Influence of wetting properties on hydrodynamic boundary conditions at a fluid/solid interface , 1998 .

[17]  D. Williams,et al.  Shear-dependent boundary slip in an aqueous Newtonian liquid. , 2001, Physical review letters.

[18]  Patrick Tabeling,et al.  Direct measurement of the apparent slip length. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  P. Saffman.  The effect of wind shear on horizontal spread from an instantaneous ground source , 1962 .

[20]  Derek Thompson,et al.  Ceramics: Tough cookery , 1997, Nature.

[21]  D. Prieve,et al.  Hindered diffusion of colloidal particles very near to a wall: Revisited , 2000 .

[22]  Desmond J. Higham,et al.  An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations , 2001, SIAM Rev..

[23]  L. Léger,et al.  Direct experimental evidence of slip in hexadecane: solid interfaces , 2000, Physical review letters.

[24]  R. G. Cox,et al.  Slow viscous motion of a sphere parallel to a plane wall , 1967 .

[25]  Hiroshi Udagawa,et al.  Drag reduction of Newtonian fluid in a circular pipe with a highly water-repellent wall , 1999, Journal of Fluid Mechanics.

[26]  H. Brenner.  The slow motion of a sphere through a viscous fluid towards a plane surface , 1961 .

[27]  Phil Attard,et al.  Molecular dynamics study of the effect of atomic roughness on the slip length at the fluid-solid boundary during shear flow. , 2004, Langmuir : the ACS journal of surfaces and colloids.

[28]  A. Einstein.  Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen [AdP 17, 549 (1905)] , 2005, Annalen der Physik.

[29]  Steve Granick,et al.  No-slip boundary condition switches to partial slip when fluid contains surfactant , 2002 .

[30]  Joel Koplik,et al.  Molecular dynamics of fluid flow at solid surfaces , 1989 .

[31]  R. Sadr,et al.  Impact of hindered Brownian diffusion on the accuracy of particle-image velocimetry using evanescent-wave illumination , 2005 .