5.1.4. Effect of external field on particle deposition

In the previous literature, transport of micron-size particles is normally simplified as a mass transfer process that is majorly affected by Brownian diffusivity. However, gravity or a constant body force exerted on the particles could have significant influence on the deposition process, even for such tiny colloidal particle size (less than 1 μm). Yiantsios and Karabelas [88] reported that gravity played a key role for the deposition rate of spherical Ballotini glass particles (diameter: 1.8 μm). Gravity could control the particle transport boundary layer in a horizontal narrow channel under laminar flow over a fairly wide range of flow rate. They [89] conducted further experiments on the effects of physicochemical and hydrodynamic conditions by using dilute microsized glass particle suspensions (diameter: 1.5 μm) in a parallel-plate channel. They concluded that gravity was a determining factor for deposition at low wall shear stresses. While the hydrodynamic wall shear stress was increased, particle deposition rates were noticeably decreased because of hydrodynamic lift or drag forces hindering transport or attachment.

temperature, the attraction energy (van der Waals force) between the particles and the solid surface is increased while the repulsive energy (electric double layer force) is decreased. Moreover, they further studied the hydrodynamic effects on particle deposition in microchannels at elevated temperatures, including steady flow and pulsatile flow [71, 72]. The dimensionless particle deposition rate (Sherwood number) was found to be reduced with the Reynolds number and changed insignificantly for the Reynolds number beyond 0.091 (0.5 mL/h) within the tested range with a given solution temperature (324.85 K) and an electrolyte concentration (5 <sup>10</sup><sup>4</sup> M). Under the pulsatile flow condition, the normalised particle deposition rate was found to be reduced significantly as the flow oscillation frequency was increased from 0 Hz to 1 Hz, while keeping the steady flow component and the amplitude of the flow oscillation

Particle Deposition in Microfluidic Devices at Elevated Temperatures

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Spielman and Friedlander [93] theoretically analysed the effect of the electrical double layer on particle deposition based on the equation of convective diffusion in an external force field. They reported that the deposition process of Brownian particles was equivalent to ordinary convective diffusion in the bulk with a first-order surface reaction at the collector. With respect to the net interaction potential, a formula can be derived for the surface reaction coefficient.

Another analytical model was developed by Adamczyk and Van De Ven [94] for particle deposition kinetics onto the surfaces of parallel-plate and cylindrical channels (Figure 12). As governing equation, the mass transport equation was formulated with consideration of electrical double layer force, van der Waals force, and external forces such as gravity. The 'perfect sink' boundary condition was applied to solve the mass transport equation. Different dimensionless parameters (Ad, Pe, Dl, and Gr) were proposed to account for dispersion, convection/

Studies on particle deposition onto permeable surfaces are practically meaningful for membrane filtration industry. Song and Elimelech [95, 96] theoretically studied this phenomenon in

unchanged.

5.2. Theoretical modelling/studies

diffusion, electrical double layer, and gravity, respectively.

Figure 12. Schematics of parallel-plate and cylindrical channels [94].

Stamm et al. [90] experimentally examined the initial stage of cluster growth in a particle-laden flow in a microchannel and investigated the parametric effects of a void fraction, flow shear strain rate and channel height to particle diameter ratio. Thereafter, Gudipaty et al. [91] studied the cluster formation of colloidal particles in a PDMS microchannel and found that the clusters were initiated by the attachment of individual flowing particle onto the bottom surface. However, they have not either addressed the physical mechanism of the initial particle attachment to the surface or observed the adherence process in the experiments.

Unni and Yang [92] experimentally investigated the dynamics of particle deposition in an electroosmotic flow using video microscope, and reported that the increased surface coverage at higher salt concentrations resulted from weakened EDL repulsion with particles being adsorbed onto the channel surface. Hydrodynamic blocking became relatively weaker with lower electric field strengths because the surface blocking was majorly caused by electrical interactions.
