Deterministic Lateral Displacement (DLD) is a passive particle separation technique. It was first introduced in 2004 by Huang et al. and his colleagues for separation of microspheres and for DNA separation.
For a simple explanation, the separation of particles occurs inside a pillar array. The sample, consisting of a heterogeneous population, is loaded into an array of obstacles. Those particles pass through the pillar array in different paths depending on their sizes. Small particles move straight, following the flow while the big particles are displaced in relationship to the flow direction, and huge particles are trapped in the entrance of the array. The trajectory of each particle is a 5 function of its effective size. The effective size, in turn, is determined by a combination of size, shape and orientation of the particle in a certain position.
Before introducing DLD theory and the factors that influence particle behaviors, a brief review of fluid flow in microfluidics is necessary. In microfluidics, continuum fluid dynamics is described by the NavierStokes equation:
where ▽p is the gradient of the pressure, ƞ is the dynamic viscosity, u is the velocity of the fluid. This equation is simplified from Newton’s second law when the inertial term is negligible, which is the case for very low Reynolds numbers (Re≤10-3 ). The Reynolds number is the ratio between inertial and viscous effects. For a fluid with density ρ, viscosity η, average velocity u and characteristic dimension D, the Reynolds number is calculated using the following equation
Due to the small channels in microfluidics (with a diameter ranging from 100nm to 100µm), the Reynolds number is small and usually less than 500 where the flow is completely laminar and no turbulence occurs, but the mass transfer Péclet number (competition between convection and diffusion) is often large.
In laminar flow (or streamline flow), the motion of particles is confined to streamlines. Thus, in a straight channel, particles move parallel to each other although their velocities can vary according to their positions. Furthermore, if a particle can be switched to another streamline when moving, it can be sorted out in the end from the initial mixture. Relying on the property of laminar flow, various methods apply an external force to push the targeted particles away from one streamline to another and consequently achieve separation (active sorting techniques). As a passive sorting technique, DLD array also changes the streamlines of targeted particles, but it does this through interactions between the particles and the pillar array, and not through externally applied fields. The separation performance of each DLD device is based on its critical size (DC). Davis et al. gave 6 an empirical formula describing the critical size based on experiments with a parabolic flow profile and rigid spherical particle
where DC is the critical diameter, G is the gap between two posts, and N is the period of the array. This equation can be expressed in some practical parameters as shown in Figure 2-4. Note that N=λ/Δλ.
The critical size is an important parameter for the sorting characteristics of a DLD device. All particles smaller than a critical size move in zig-zag mode with the flow while bigger ones are displaced in relation to the flow direction. Gap size and the depth of a device are other device parameters that need to be considered carefully for particle sorting due to trapping or clogging. Particles bigger than device depth or gap size may be trapped in the reservoirs or in the entrance of array.
In general, when discussing the performance of sorting devices, the important parameters are purity, capture rate, resolution, and throughput. For biological samples or cells, cell viability, and cell recovery can be added to this list. Overall, the sorting efficiency is evaluated based on which combination of these parameters is most important in each separate case (high purity, high throughput or cell recovery, etc.).
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