Pinched Flow Fractionation

Pinched flow fractionation (PFF) is a purely hydrodynamic method of separating particles by size or mass, using a microfluidic device. The separation of particles is critical in many biomedical applications (Ref. 1). One of the popular areas of interest is the separation of cells from whole blood such as red blood cells, white blood cells, and platelets. A clear blood plasma is also utilized in cancer detection.

This is a tutorial model of a microfluidic device with two inlets. Inlet 1 delivers a sample of fluid containing particles to separate while inlet 2 delivers pure fluid with no particles at a significantly higher flow rate than the first. When the two inlets converge at a narrow microchannel, the stream carrying the sample is pinched into a narrow region near the wall opposite the high-velocity flow. The smaller particles are pushed closer to the wall. After entering the microchannel, the wall-induced lift force pushes the particles toward the center of the channel. Under the combination of lift and drag forces, the particles become sorted by size, with larger particles migrating closer to the center of the channel.. The sample then enters a wider section that branches into many outlets. The particles exit through different branches based on their lateral position when exiting the microchannel, effectively sorting the particles by size.

The outlet at the end close to inlet 2 is called the drain. When the drain is shorter and/or broader than the other outlets, then the method is called asymmetrical pinched flow fractionation (AsPFF) (Ref. 2). AsPFF has lesser resistance to the flow in the drain and hence allows more liquid to flow. This in turn allows the wider spread of streamlines along the outlets and hence the separation utilizes more of the outlet branches and the range of sizes of particles collected by each outlet becomes smaller. Thus AsPFF allows better fractionation of particles compared to PFF. The model used in this example can be used to simulate both PFF and AsPFF by simply changing the value of ratio of drain length to branch length in the geometry.

Model Definition

The geometry consists of two inlets each of width 0.1 mm and length 0.5 mm fused with each other at an angle of 45°. The inlets converge to a microchannel of width 20 μm and length 120 μm. The microchannel opens to a wider opening which is divided into twelve outlets and one drain. The distance of each outlet from the midpoint of opening of microchannel is 1 mm while the distance to the drain outlet is 0.5 mm. The dimensions of inlets, microchannel, outlets, and drain and the number of outlets can be changed by editing appropriate parameters of the geometry.

Figure 1: Model geometry of asymmetric pinched flow fractionation device. Fluid enters through two inlets on the left and exits through the 13 numbered outlets.

Figure 2: The mesh is refined around the entrance of microchannel and near corners.

The sample used here is water containing spherical particles of density 1300 kg/m3, with diameters uniformly distributed between 1.5 μm and 11 μm. The inlet in the upper left corner of Figure 1 delivers the sample at the rate of 25 μl/hr. The inlet in the lower left corner delivers pure water at the rate of 1200 μl/hr. The outlet branches are numbered from 0 to 12 in a clockwise direction, with 12 being the drain in Figure 1. The microchannel should be meshed at higher resolution relative to the rest of the geometry. When the particle enters the microchannel there is sudden change in the velocity, thus the entrance is manually meshed to finer sizes as shown in Figure 2.

The geometry is divided into three domains; the first domain consists of inlets, second domain is the microchannel, and the third domain includes the outlets. The lift force is most significant in the microchannel where the particles will be in very close proximity to the channel walls. Thus the lift force is applied only in the second domain using the feature. The drag force is applied in all domains using the feature.

Notes on COMSOL Implementation

The model is solved in two steps. First, the fluid velocity and pressure are solved using the Laminar Flow interface and study step. Then the particle trajectories is created using the Particle Tracing for Fluid Flow interface and study step.

A total of 100 particles are released, one at every 5 ms. The released particles have random diameter between 1.5 μm and 11 μm and random position along the boundary. The particles cannot be released very close to the walls of inlet because the wall induced lift force gives nonphysical values if distance between wall and particle is less than the particle radius, so only the middle 80% of the inlet boundary is used to generate the particles. To release particles with random diameters, needs to be chosen from the options in the setting of the Particle Tracing for Fluid Flow interface.

The asymmetric flow of fluid in the drain outlet is easily captured using an feature in the Laminar Flow interface. A boundary condition of zero gauge pressure is applied to each outlet. The pressure drop along the drain channel is faster because of its smaller length which results in a higher flow rate compared to the other branches.

For the smallest particles in this model, the relaxation time is approximately 0.16 μs, which is about three million times smaller than the maximum output time. However, the default time-dependent solver for most particle tracing models is a second-order implicit method that handles numerically stiff problems rather well, even when taking time steps that are larger than the relaxation time. Nevertheless, the smallest particles are still the main driver of the computational cost of transient inertial particle tracing simulations.

Results and Discussion

The velocity field and the streamlines are shown in Figure 3. The streamlines closer to the upper wall of the microchannel lead to the upper branches whereas those closer to the lower wall lead toward lower branches or into the drain. The effect of AsPFF is seen in the greater density of streamlines in the drain where the flow rate is higher due to its lower viscous losses compared to the other branches.

Figure 3: Velocity field and streamlines for the fluid flow

When the fluid from two inlets are squeezed through the microchannel, the particles are sorted based on their size as the lift force pushes the larger particle farther from the wall in perpendicular direction to the flow. When the particles exit the microchannel, they flow with the fluid toward different outlets based on their lateral position in the channel and their inertia (Figure 4).

When zooming in very close to the ends of the microchannel, most notably the right end, some particle trajectories may appear to pass through the channel walls instead of exiting through the end of the microchannel. This is just an artifact of the way that the lines in particle trajectory plots are displayed, with interpolation between a discrete number of output times. If the number of output times were significantly increased, the particles would appear to exit the channel normally, but the file size would be much larger.

Figure 4: Particle trajectories colored by particle size top of fluid velocity field. The background shows the fluid velocity magnitude on a logarithmic scale

Figure 5 is a histogram that shows the number of particles exiting from each outlet. In this simulation, the particles exit from first 5 outlet branches. In addition, Figure 6 is a 2D histogram that shows the particle sizes exiting from each outlet.

These two histograms give a clear quantitative picture of sorting of particles using the AsPFF method. Because the model is fully parameterized, a natural extension would be to use a or some optimization functionality to utilize a larger number of outlet branches, while simultaneously reducing the range of particle diameters that exit through any single branch.

Figure 5: Histogram of number of particles exiting through each outlet branch.

Figure 6: 2D histogram showing the range of particle size exiting through each outlet branch.

References

1. D.R. Gossett, W.M. Weaver, A.J. Mach, S.C. Hur, H.T.K. Tse, W. Lee, H. Amini, and D. Di Carlo, “Label-free cell separation and sorting in microfluidic systems,” Anal. Bioanal. Chem., vol. 397, p. 3249–3267, 2010.

2. J. Takagi, M. Yamada, M. Yasuda, and M. Seki, “Continuous particle separation in a microchannel having asymmetrically arranged multiple branches,” Lab Chip, vol. 5, p. 778–784, 2005.

Particle_Tracing_Module/Fluid_Flow/pinched_flow_fractionation

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
V1	25[ul/h]	6.9444E-12 m³/s	Flow rate in inlet 1
V2	1200[ul/h]	3.3333E-10 m³/s	Flow rate in inlet 2
rho_p	1300[kg/m^3]	1300 kg/m³	Particle density
d_min	1.5[um]	1.5E-6 m	Minimum particle diameter
d_max	11[um]	1.1E-5 m	Maximum particle diameter

Geometry 1

Insert the prepared geometry sequence from file. You can read the instructions for creating the geometry in the appendix.

In the toolbar, click and choose .

Browse to the model’s Application Libraries folder and double-click the file pinched_flow_fractionation_geom_sequence.mph.

In the toolbar, click

. The geometry should look like Figure 1.

Definitions

Variables 1

In the toolbar, click

and choose .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Unit	Description
dphi	pi[rad]/Nb	rad	Angle between adjacent branches
phi0	dphi/2	rad	Half of the angle
dx	x-Cr	m	Distance from center of rotation along x-axis
phi	atan2(dx,y)	rad	Angle with positive y-axis around center of rotation
exit	floor((phi-phi0)/dphi)+1		Branch index in clockwise direction