Theory of detachment of colloidal particles from flat surfaces exposed to flow

Abstract Theoretical models are presented for the detachment of colloidal particles from solid surfaces exposed to shear flow. The models are most relevant to cases of hard, spherical particles, which are small enough to display Brownian motion. It is concluded that the component of hydrodynamic force acting parallel to a sheared wall is usually much larger than the lifting force. Thus, in most cases, one can expect the downstream component of force to govern the critical or rate-determining step in the process of entrainment. Alternative limiting modes of incipient motion, e.g., rolling, sliding, and lifting, can be distinguished, based on the dependency of the shear stress required for detachment on the size of particles. Rate laws for detachment and the dependency of rates on the applied shear stress permit one to discriminate between processes limited by viscous flow, Brownian motion, and fluctuations in hydrodynamic forces. Finally, it is proposed that separate geometric models of sphere-wall interaction be employed in computing long-and short-range forces.

[1]  T. Dąbroś,et al.  Kinetics of coating by colloidal particles , 1982 .

[2]  Helmut Eckelmann,et al.  The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow , 1974, Journal of Fluid Mechanics.

[3]  F. Bretherton.  The motion of rigid particles in a shear flow at low Reynolds number , 1962, Journal of Fluid Mechanics.

[4]  Thomas J. Hanratty,et al.  A study of turbulence at a wall using an electrochemical wall shear-stress meter , 1966, Journal of Fluid Mechanics.

[5]  B. Dahneke,et al.  Resuspension of particles: The range of validity of the quasi-stationary theories , 1976 .

[6]  R. G. Cox,et al.  Slow viscous motion of a sphere parallel to a plane wall—I Motion through a quiescent fluid , 1967 .

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

[8]  B. Yates,et al.  Mechanism of detachment of colloidal particles from a flat substrate in a turbulent flow , 1973 .

[9]  H. Eckelmann,et al.  Some properties of truncated turbulence signals in bounded shear flows , 1974, Journal of Fluid Mechanics.

[10]  M. E. O'neill,et al.  On the hydrodynamic resistance to a particle of a dilute suspension when in the neighbourhood of a large obstacle , 1971 .

[11]  C. Radke,et al.  Thermodynamics of the effects of adsorption on interparticle forces , 1973 .

[12]  E. Matijević,et al.  Particle adhesion and removal in model systems: III. Monodispersed ferric oxide on steel , 1980 .

[13]  P. G. Howe,et al.  LONDON – VAN DER WAALS ATTRACTIVE FORCES BETWEEN GLASS SURFACES , 1955 .

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

[15]  Ron F. Blackwelder,et al.  On the wall structure of the turbulent boundary layer , 1976, Journal of Fluid Mechanics.

[16]  H. Swinney,et al.  Dynamical instabilities and the transition to chaotic Taylor vortex flow , 1979, Journal of Fluid Mechanics.

[17]  M. E. O'Neill,et al.  A sphere in contact with a plane wall in a slow linear shear flow , 1968 .

[18]  G. Comte-Bellot,et al.  Intermittency of coherent structures in the core region of fully developed turbulent pipe flow , 1976, Journal of Fluid Mechanics.

[19]  B. Derjaguin,et al.  On two methods of calculation of the force of sticking of an elastic sphere to a rigid plane , 1983 .

[20]  T. J. Hanratty,et al.  Identification of turbulent wall eddies through the phase relation of the components of the fluctuating velocity gradient , 1974, Journal of Fluid Mechanics.

[21]  E. Clayfield,et al.  Detachment of adhered colloidal particles by non-aqueous surfactant solutions , 1966 .

[22]  Kenneth A. Smith,et al.  The velocity and eddy viscosity distribution in the wall region of turbulent pipe flow , 1968 .

[23]  J. Visser.  Measurement of the force of adhesion between submicron carbon-black particles and a cellulose film in aqueous solution , 1970 .

[24]  J. Pearson,et al.  Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder , 1957, Journal of Fluid Mechanics.

[25]  A. Maude.  End effects in a falling-sphere viscometer , 1961 .

[26]  J. Visser.  The adhesion of colloidal polystyrene particles to cellophane as a function of pH and ionic strength , 1976 .

[27]  S. Chandrasekhar.  Stochastic problems in Physics and Astronomy , 1943 .

[28]  E. Matijević,et al.  Particle adhesion and removal in model systems. Part 2.—Monodispersed chromium hydroxide on steel , 1979 .

[29]  F. R. Mobbs,et al.  Marginal instability in Taylor–Couette flows at a very high Taylor number , 1979, Journal of Fluid Mechanics.

[30]  H. Kramers.  Brownian motion in a field of force and the diffusion model of chemical reactions , 1940 .

[31]  P. S. Klebanoff,et al.  Probability distributions and correlations in a turbulent boundary layer , 1973 .

[32]  B. Dahneke.  Kinetic theory of the escape of particles from surfaces , 1975 .

[33]  B. Derjaguin,et al.  General theoretical consideration of the influence of surface forces on contact deformations and the reciprocal adhesion of elastic spherical particles , 1983 .

[34]  B. Dahneke.  Resuspension of particles , 1975 .

[35]  B. Py.  Étude tridimensionnelle de la sous-couche visqueuse dans une veine rectangulaire par des mesures de transfert de matière en paroi , 1973 .

[36]  D. Tabor.  Surface Forces and Surface Interactions , 1977 .

[37]  S. K. Hsu,et al.  The lateral migration of solid particles in a laminar flow near a plane , 1977 .

[38]  W. Willmarth,et al.  Structure of Turbulence in Boundary Layers , 1975 .

[39]  D. J. Montgomery,et al.  Adhesion of Small Metal Spheres to Plane Metal Substrates , 1971 .

[40]  E. Clayfield,et al.  Adhesion and detachment of solid colloidal particles in aqueous ionogenic surfactant media , 1970 .

[41]  E. Ruckenstein.  Reversible rate of adsorption or coagulation of brownian particles—effect of the shape of the interaction potential , 1978 .

[42]  Helmut Eckelmann,et al.  Behavior of the three fluctuating velocity components in the wall region of a turbulent channel flow , 1979 .