Continuous Flow Microfluidics

Micro/Bio/Nano Fluidics

Continuous flow microfluidics is the manipulation of liquid flow through fabricated microchannels without breaking continuity. Fluid flow is established by external sources such as micropumps (e.g., peristaltic or syringe pumps) or internal mechanisms such as electric, magnetic or capillary forces. Continuous flow microfluidics finds applications in a variety of applications including micro- and nanoparticle separators, particle focusing, chemical separation as well as simple biochemical applications but they may not be the method of choice when a high degree of control is required.

Some of the processes or devices that fall in this category and have been successfully simulated using FLOW-3D are Joule heating, liquid gating, microfluidic circuits, electro-osmotic valves, particle focusing, sorting and separation, point-of-care (POC) capillary flow devices and patterned surface devices.

Electro-osmosis

Electro-osmosis refers to the fluid flow that occurs when an electric field is applied to the electrical double layer, an intrinsic property of a fluid-solid pair. This phenomenon has proven to have significant practical importance for microfluidic applications. FLOW-3D enables the modeling of combined pressure- and electro-osmotic-driven flows, with or without a free surface, in one- or two-fluid configurations.

Micro-pumps

By creating a series of deep slots in a microchannel, and then applying a potential across the channel, fluid flow can be controlled in a MEMS-scale pump. By adjusting the applied potential, the flow rate can be controlled. The video below demonstrates the application of electro-osmosis for use with micro-pumps.

As illustrated in the example above, FLOW-3D accurately represents the streamlines at any point in time for a complex and evolving flow field. The streamlines and particles in this animation show the inefficiencies in this pump design by capturing recirculation zones. These zones reduce efficiency when not all the flow is driven forward effectively.

A micro-pump should be able to raise the system pressure in order to drive the flow. The pump in the simulation is doing precisely this. The flow in the micro-pump is completely electrokinetically driven in that both inlet and outlets are at atmospheric pressure. So, there is no external pressure gradient across the pump. The pressure gradient is created over time due to electro-osmosis inside the pump. The gradient overcomes the drag forces within the channel driving flow.

Velocity Profile Evolution of an Electro-Osmotic Micro Pump

The simulation below shows the evolution of the flow direction velocity between the slots. Velocities drop to zero approaching the slot walls because of a no-slip condition. Between every slot pair, a plug-like velocity is established starting with approximately parabolic profiles at the start of the simulation. Over time, the profiles become constant and linear due to higher flow velocities and mixing of fluid.

At the right end of the plot in the simulation, distorted plug-like structure can be seen due to substantial mixing and trapping of particles in that zone. The circulation and trapping of particles can be seen in the first simulation. Fluid is moving under the influence of electric potential due to zeta-potential of -0.15V at the slot walls. Inlets and outlets are at zero potential. Flow is pulled in towards the center (in the slots area) due to their potential difference and continues to move on and out of the outlet due to inertia.

In the animation above, a non-uniform potential is created on the walls of a microchannel to induce a helical flow inside the channel. FLOW-3D clearly shows the mixing effect as the fluid stretches and folds, indicated by marker particles.

Joule Heating

Understanding both Joule heating and electrothermal effects is critical for the proper design of microdevices. FLOW-3D provides a useful and robust flow simulation tool to model these physical processes.

Simulation of a Conducting Di-electric Fluid placed over Electrodes

Simulating electric potential in a micro pump
Simulating electric potential with FLOW-3D

Joule heating occurs when an electric current passes through a conducting material, such as a fluid. At a microscopic level, Joule heating is caused by interactions between the moving charged particles. Additionally, if the fluid is di-electric, polarization will happen in the presence of an electric field causing fluid flow. FLOW-3D can capture all such effects, which is demonstrated by the simulation below that highlights FLOW-3D‘s ability to accurately capture electro-kinetics physics.

The image above shows the arrangement of electrodes from a cell culture chamber. Electrodes in blue are at a positive potential of 9V and the electrodes in pink are at an equal negative potential, i.e., -9V. A conducting fluid is placed over the electrodes. The fluid has been given a value of di-electric constant, which causes polarization. Over time, the polarized particles in the fluid follow the electric field, inducing velocity in the fluid (the electric field is shown in top left of the animation below).

This simulation shows a temperature rise of the fluid due to Joule heating. The temperature rises to 500° Celsius by the end of the simulation. FLOW-3D captures the fluid flow physics of a di-electric fluid inside an electric field as seen in the right half of the simulation. Streamlines have been plotted in order to visualize the fluid flow and are colored by electric field magnitude. Over time, clearly visible distinct circulation cells are formed in the fluid as the polarized particles are moved around by the electric field. The top left plot in the simulation shows the electric field magnitude contours.

Simulate Resistance Heating in Bubble Jet Printheads

Thermal bubble-driven printheads require some method of vaporizing a small volume of ink. The resulting vapor bubble pushes ink through a nozzle creating a tiny droplet which, along with millions of other droplets, creates a printed image. A common method of heating the ink is to pass an electrical current through a thin layer of metal to generate resistance, i.e., Joule heating.

This FLOW-3D simulation shows a thermal bubble opening, where the heating element is inside the base. The duration and the magnitude of the electrical pulse must be chosen carefully so that the right amount of heat is generated. Too little heat will fail to vaporize the ink. Too much heat will cause the droplet to be too large and risks possible damage to the printhead. FLOW-3D provides all the tools necessary to simulate the many complex and intertwined physical processes in thermal bubble jet printheads.

Lab-on-a-chip

Patterned Surfaces Using Varied Surface Tensions

Patterned surfaces in micro channels can be used to transport liquids from one reservoir to another along specified pathways, with multiple liquids flowing side-by-side without the need of actual physical walls between the liquids. Patterned surfaces are used to transport fluids in lab-on-a-chip, bioassays, microreactors and, chemical and biological sensing. In this case surface tension is used to manipulate fluid flows in micro channels to create patterned flows. Hydrophilic or hydrophobic behavior of a fluid on a solid surface is exploited to control the motion of multiple fluids through a microchannel. Fluid flow inside micro channels is laminar, meaning that multiple fluid streams (two in this case) can flow side-by-side without turbulent mixing. Because there are no physical walls on the sides of the fluid stream, the streams are confined by the so called virtual walls. These walls are basically the hydrophilic-hydrophobic boundaries between the two fluids.

Patterned surfaces in micro channels
Experimental results showing the three phases – A, B and C (left to right), Bin Zhao et al.

The figure above shows the microchannel in the experiment. The middle strip of the central horizontal channel is hydrophilic, whereas the remaining channel along with the upper and lower vertical channels, have different degrees of hydrophobicity. They differ in their hydrophobicity only by a few degrees of the contact angle. Upper channels have a contact angle of 118and the bottom channels have a contact angle of 112o. This small difference in contact angles however requires significantly different pressures for the fluid to flow into these regions.

Numerical Simulation

Initially all channels are filled with another fluid (transparent). When the pink fluid is pushed into the horizontal channel, it takes the hydrophilic path in the central region (Phase A). As the pressure is increased, the fluid breaks the bottom hydrophilic-hydrophobic barrier and starts flowing into the bottom hydrophobic region (Phase B). On increasing the pressure even further, the fluid finally breaks the upper hydrophilic-hydrophobic barrier as well and starts flowing in upper region too (Phase C).

Numerical results - patterned surfaces using varied surface tension
Numerical results showing the three phases – A, B and C.

The numerical results above show reasonable comparability with the overall idea of patterned surface study in the experiment, given that there were important differences between the two. The numerical results shown above are in the transient state (pressure is continuously increasing), and therefore the fluid boundaries are not exactly similar to the experimental results. Similarly, the fluid properties are not exactly similar to the one used in the experiments. Notwithstanding, Fluid 1 goes through phases A, B and C as the pressure increases, just as in the experiment. In phase B, the transparent fluid continues to flow through the upper channels, but only the pink fluid flows in the bottom region. This is consistent with the experiment. What is interesting to see is the bubble formation shown in phase C. Revelation and study of interesting physics like bubble formation in phase C could be crucial to the design and fabrication process of microfluidic devices.

FLOW-3D Results

The animation below shows the simulation results of FLOW-3D for the experiment shown above. Fluid 1 (light blue) is equivalent to the pink fluid in the experiment. Initially the whole domain is filled with Fluid 2 (transparent fluid). The pressure is increased in a stepwise manner and all the three phases can be seen as the simulation evolves.

Evolution of fluid flow with increasing pressure in patterned micro channels created by varying contact angles.

Ref: Bin Zhao, Jeffrey S. Moore, David J. Beebe,
Surface-Directed Liquid Flow Inside Microchannels, Science 291, 1023 (2001)

Magnetic Fields

In a uniform magnetic field, magnetic particles become magnetized and assemble into chain-like microstructures due to dipole-dipole interactions. The assembled chains tend to align with the direction of the external field. In this analysis using FLOW-3D, a uniform field is applied upward in the z-direction through a micro-channel that contains an initial random distribution of superparamagnetic beads and an array of spherical (gold colored) magnetic dipole elements embedded in its base. In the presence of an applied field, the beads become magnetized and assemble into discrete chain-like structures.  These structures in turn, are attracted to the anchored dipole elements. The analysis shows the self-assembly of particle chains and the subsequent attachment of the chains onto the embedded dipole elements. The computational model takes into account fully-coupled particle fluid interaction where the fluid provides a viscous drag on particle motion and the moving particles, in turn, alter the fluid flow. Modeling results courtesy of the University of Buffalo. Go here for more information about the University at Buffalo’s work with FLOW-3D.

Courtesy of University at Buffalo

Microfluidic Circuits

There have been recent developments in the field of microfluidic circuit devices for use in biological sciences to transport matter from one place to another, or to perform hundreds of assays in parallel. Typically, these circuits are based on a certain logic (like AND, OR, XOR, etc.) or a combination of multiple logics. Hence these circuits are also known as microfluidic logic circuits. Analogous to an electronic circuit, the fluid runs through channels and pneumatic valves, and is driven by pressure differentials (as opposed to the traditional potential/voltage differentials in an electronic circuit). FLOW-3D‘s moving objects model, coupled with the fluid flow, can simulate the motion of the pneumatic valves.

Simulation of a pneumatic latching valve used in microfluidic demultiplexer. The animation starts at stage 3 – the open stage, and finally evolves to stage 7 – the closed stage. Read the Microfluidic Circuit – Pneumatic Latching Valve blog.

Mixing Dynamics

FLOW-3D can be used as an effective tool for modeling the droplet/bubble dynamics in microfluidic devices, including simulating a novel device called the Hong Chamber. The Hong Chamber is an innovative in-plane passive micromixer using modified Tesla structures, which are used as passive valves. This has been designed, simulated, fabricated and successfully characterized by Hong et al.[3].

Hong chamber simulations
Multiphase FLOW-3D simulation of Hong Chamber using conformal mesh to accurately capture entrapped bubble phase.

This novel micromixer has shown excellent mixing performance over a wide range of flow conditions in the micro scale. We simulated the Hong Chamber with two fluids coming in from the inlet, to look at the mixing patterns as a function of time. The series above shows the mixing pattern as a function of time. The two streams represent two water-based reagents.

The fluid fraction varies from 0 to 1, where 0 indicates a region completely occupied by fluid one and 1 indicates a region completely occupied by the second fluid. Fixed velocities were used at the inlet and an outflow boundary condition was used at the outlet. The initial region was filled with the blue fluid. Figure 10 shows results from the filling simulation. Here no fluid was defined in the initial region. Fixed velocities were used at the inlet boundary conditions and the adiabatic bubble model was used to trap bubbles. What is notable is that at each Tesla valve unit, the flow in the reverse direction is prevented, which leads to the formation of bubbles.

Simulation Setup

The simulation below shows the mixing of blood plasma and water as the fluids come in from the two inlets. The flow rates for both streams are 1e-8 m3/sec. The simulation is colored by fluid fraction. Red is water.

Hong chamber CFD simulation
The mixing pattern as a function of time at 0.04s, 0.2s, 0.5s, and 0.65s. Courtesy of Stanford University.

Particle Sorting

Ubiquitous gravity can be used for sorting micro particles in microfluidic devices. When gravity acts perpendicular to the motion of the particles, the particles settle down at a velocity dependent on their radius. Additionally, the motion of the particles is influenced by the hydrodynamic effects originating from the difference between the density of the particles, the density of the fluid and the viscosity of the fluid.

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