3. Theory of surface forces

particulate fouling in microfluidic applications. Particulate fouling refers to that finely suspended solid particles accumulate onto solid surfaces. The diameters of particles are usually less than microns. Without other mechanisms having particles firmly attached onto solid surface, the deposit formed by particulate fouling is normally thin and easily removed.

Particulate fouling is caused by particle deposition onto the solid surfaces of collectors. This is a complex process affected by diffusion, convection, colloidal, and external interaction forces. To better understand the physical process of particle deposition, it can be conceptually divided

When particles are at large distances from the collector surface, the particles are transported from the bulk fluid to the collector by diffusion, flow convection, and migration due to external forces. Particle concentration gradients usually exist between the bulk fluids to the collector surfaces and drive the suspended particles approaching the collector surfaces. Flow convection, especially in turbulent flow, could give particles momentum to move across the bulk fluid toward the collector surface. Besides, particles would migrate to the collector when they are affected by external fields, such as gravity filed and electric field.

When particles get close to the collector within a distance comparable to the particle radius, the motion of the fluid between the particle surface and the collector surface becomes much more difficult compared to the scenario at large distances. It is because that the particles need to experience additional hydrodynamic drag caused by the presence of the collector surface. Thus, the reduction of particle mobility is commonly attributed to the

As particles approach the collector at even closer distances, typically less than 100 nm, the motion of the particles is influenced by colloidal forces besides the hydrodynamic interaction. Within such extremely short distance, the influences of the colloidal forces are overwhelmingly stronger than those of external forces. Thus, the particle adhesion onto the collector is mainly determined by the competition of the attractive and repulsive colloidal forces. The colloidal forces consist of the universal van der Waals (VDW) force and the electric double layer (EDL) force. These two interaction forces form the basis of the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of colloidal chemistry. The van der Waals force originates from spontaneous electrical and magnetic polarizations, which generate a fluctuating electromagnetic field within the particle and the collector as well as in the gap between them. Solid surfaces in aqueous media (electrolyte solution) are always charged because of the dissociation of ionisable surface sites or the adsorption of ionic surface active sites. As a result, electric double layers are formed in the vicinity of both the

2. Particle deposition

1. Particle transport/diffusion

2. Particle-wall hydrodynamic interaction

particle-wall hydrodynamic interaction.

into three steps [3]:

104 Microfluidics and Nanofluidics

3. Particle adhesion

The behaviours of particles in aqueous media are significantly influenced by the physicochemical characteristics of the interaction forces between particles and solid surfaces [4]. Thus, the interaction forces exerted on colloidal particles determine particulate fouling or particle deposition. In this section, the colloidal forces between particles and surfaces are briefly reviewed, including colloidal interaction forces, van der Waals attraction force and electrical double layer repulsion force. These two forces form the basis of the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, which were independently developed by Derjaguin and Landau [5] from Soviet/Russian and Verwey and Overbeek [6] from Netherlands. Besides the DLVO forces, non-DLVO forces are also involved in particle deposition and aggregation, such as polymer bridging, solvation forces, steric forces or hydrophobic forces.
