Electropermanent magnet activated microfluidic droplet size modulation

Abstract

An active microfluidic droplet generation device includes a droplet generation junction joining at least one continuous phase channel for carrying a ferrofluid, and a dispersed phase channel for carrying a dispersed phase (e.g., aqueous) flow. A miniature electropermanent magnet (EPM) upstream from the junction generates a magnetic field to modulate a flow rate of a ferrofluid in the continuous phase channel so that dispersed phase droplets are generated with volumes actively controlled on-demand and under continuous flow.

Claims

1. A method for active microfluidic dispersed phase droplet generation, the method comprising: positioning a miniature electropermanent magnet (EPM) such that a magnetic field of the EPM overlaps with microfluidic channels connected to a droplet generation junction upstream from the droplet generation junction; controlling the magnetic field of the EPM to modulate a continuous phase ferrofluid flow rate in the microfluidic channels while a dispersed phase flows through a dispersed phase channel connected to the droplet generation junction; whereby dispersed phase droplets are generated with volumes actively controlled on-demand and under continuous flow.

2. The method of claim 1 wherein positioning the EMP comprises aligning the EMP such that the magnetic field is substantially orthogonal to the microfluidic channels containing the ferrofluid.

3. The method of claim 1 wherein controlling the magnetic field of the EPM to modulate the continuous phase ferrofluid flow rate comprises controlling the magnetic field to induce a change in viscosity of the ferrofluid through the magnetoviscous effect.

4. The method of claim 1 wherein controlling the magnetic field of the EPM to modulate the continuous phase ferrofluid flow rate comprises generating current pulses through a coil of the EPM to activate and deactivate the magnetic field of the EPM.

5. The method of claim 1 wherein controlling the magnetic field of the EPM to modulate the continuous phase ferrofluid flow rate comprises controlling a magnitude of current pulses in coils of the EPM to control a magnitude of the magnetic field.

6. The method of claim 1 wherein controlling the magnetic field of the EPM to modulate the continuous phase ferrofluid flow rate comprises controlling a magnitude of current pulses in coils of the EPM to produce a maximum magnetic field strength of at least 200 mT at a pole of the EPM.

7. The method of claim 1 wherein controlling the magnetic field of the EPM to modulate the continuous phase ferrofluid flow rate comprises generating current pulses through a coil of the EPM, where widths of the current pulses are less than 100 microseconds.

8. The method of claim 1 wherein controlling the magnetic field of the EPM to modulate the continuous phase ferrofluid flow rate comprises maintaining the EPM activated, whereby the volume of the generated dispersed phase droplets is constant.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1A is a cross-sectional top view of a conventional flow-focusing junction with two oil-based ferrofluid channels pinching off the water channel to create water droplets.

(2) FIG. 1B is a graph of droplet diameter as a function of oil-to-water flow rate ratio (Q.sub.o/Q.sub.w), showing that droplet size decreases for larger ratios.

(3) FIG. 2A is a schematic top view of input microfluidic channels and flow-focusing junction, where the positions of EPM poles are shown as dotted lines, according to an embodiment of the invention.

(4) FIG. 2B is a perspective view of an EPM, microfluidic channels and junction, showing pole-channel alignment and separation of EMP from the channels by the thickness of the glass coverslip, according to an embodiment of the invention.

(5) FIGS. 3A-F are perspective views of an EPM, microfluidic channels and junction, showing steps of active droplet size control process with EPM actuation, where the widths of the arrows reflect the flow rate of the ferrofluid, according to an embodiment of the invention.

(6) FIG. 4A is a graph of magnetic field modulation for different actuation currents, according to an embodiment of the invention.

(7) FIG. 4B is a graph of magnetic field modulation for different pulse lengths, according to an embodiment of the invention.

(8) FIG. 5 is a graph of relative viscosity increase in the ferrofluid for applied magnetic field, according to an embodiment of the invention.

(9) FIGS. 6A-B are diagrams of generated droplets in microfluidic channels, illustrating active droplet size control using mineral oil based ferrofluid and EPM actuation, where Q.sub.w represents the water flow rate and Q.sub.o the oil flow rate, according to an embodiment of the invention.

(10) FIG. 7 is a graph of droplet size tuning for multiple flow rates and actuation currents, where the water flow rate was fixed at 0.1 l/min, according to an embodiment of the invention.

(11) FIG. 8 is a graph of droplet diameter change at multiple flow rates and actuation currents with the water flow rate fixed at 0.1 l/min, illustrating that shear-thinning effect becomes dominant at higher flow rates, according to an embodiment of the invention.

(12) FIG. 9 is a diagram of generated droplets in microfluidic channels, illustrating on-demand droplet size increase by EPM ON time tuning, where single large droplet generation is demonstrated using 25-50 ms ON time, according to an embodiment of the invention.

DETAILED DESCRIPTION

(13) According to an embodiment of the present invention, active droplet size control using an EPM 200 is performed in a PDMS microfluidic chip 202 with flow-focusing configuration as shown in FIGS. 2A-B. The EPM's ferromagnetic poles 204, 206 are aligned underneath the two input ferrofluid lines 208, 210, separated from the channel by the glass coverslip 212 with thickness 0.13-0.16 mm. The ferrofluid channels join a water channel 214 at a junction 216, which is also joined to an output channel 218. The input ferrofluid microchannels width preferably should not exceed the EPM poles width to maximize actuation. This embodiment uses 200 m channels with 350 m EPM poles due to PDMS fabrication constrains. For 50 m tall channels, the maximum channel width should not exceed four times the height to prevent channel collapse. The length of the input ferrofluid channel straight section is designed to match the length of the EPM poles, 3.6 mm, again to maximize actuation.

(14) A process of active droplet size control using EPM according to an embodiment of the invention is shown in FIGS. 3A-F. The process starts with stabilized ferrofluid and water flow rates in ferrofluid and water inlet channels, generating droplets of uniform size in the output channel, and the EPM OFF (FIG. 3A). Using a positive current pulse, the magnetizations of the magnets are aligned and the EPM is turned ON (FIG. 3B). The magnetic field at the edge of the EPM poles induces a localized increase in the ferrofluid's viscosity by a process called the magnetoviscous effect (MVE) (FIG. 3C). MVE is described in more detail below. The increased viscosity increases the fluidic resistance of the input channels decreasing the flow rate (FIG. 3D). As seen in FIG. 1B, a decrease in the oil flow rate decreases the oil-to-water flow rate ratio leading to generation of larger droplets (FIG. 3E). Larger droplet size generation will be sustained while the EPM is ON but no power will be drawn since the EPM only draws power for switching but consumes zero power afterwards. Using a negative current pulse, the magnetizations of the magnets are reversed and the EPM is turned OFF (FIG. 3F), thus restoring to the original flow settings from FIG. 3A. This process can be repeated at high rates, and it is only limited by the switching time of the EPM (which is less than 100 s). Also, by using different actuation currents or pulse lengths, the EPM can be activated to multiple magnetization levels, each delivering droplets of different sizes. For example, FIG. 4A shows magnetic field modulation for different actuation currents, and FIG. 4B shows magnetic field modulation for different pulse lengths.

(15) A key feature of the present invention is the exploitation of the magnetoviscous effect to induce a localized increase in the ferrofluid's viscosity. The magnetoviscous effect, or MVE, is the process in which the magnetic moments of the ferrofluid's nanoparticles try to align with the applied magnetic field, generating a magnetic torque that will hinder the free rotation of the particles, macroscopically increasing viscosity. The viscosity increase can be quantified by a rotational viscosity term

(16) $\begin{array}{cc}{}_r=\frac{3}{2}{}_s\frac{-\tanh }{+\tanh }.Math.{\sin }^2.Math.& \mathrm{Eq}.1\end{array}$
and the total viscosity is given by
=.sub.0+.sub.r.Eq. 2

(17) In Eq. 1 and 2 above, .sub.s is the carrier oil viscosity, is the volume fraction of magnetic solids in the ferrofluid, is angle between the magnetic field and flow vorticity, and is the Langevin parameter given by

(18) $\begin{array}{cc}=\frac{}{6}\frac{{}_0{M}_d{\mathrm{Hd}}_p^3}{\mathrm{kT}},& \mathrm{Eq}.3\end{array}$
where .sub.0 is the permeability of free space, H is the magnitude of the magnetic field, d.sub.p is the diameter of the magnetic core of the nanoparticles (6 nm), k is the Boltzmann constant and T is the temperature.

(19) From Eq. 1-3, there are several important concepts to consider. First, the applied magnetic field should be orthogonal (=90) to the flow vorticity for maximum viscosity change. Collinear magnetic field (=0) will result in zero change in viscosity. In microfluidic channels, the vorticity is defined as orthogonal, but in plane, to the flow direction. The EPMs generate a magnetic field that crosses the channel in the out-of-plane direction, orthogonal to the flow vorticity. Second, the choice of ferrofluid locks the rest of the variables except H. This implies the active viscosity control depends entirely on the magnetic field strength. FIG. 5 shows the change in viscosity for magnetic fields in the range of operation of the EPMs.

(20) The EPM design used in this embodiment can generate a magnetic field of 0.3 T at the edge of the poles. With the microfluidic channels located approximately 130 m from the poles (glass thickness), the magnetic field is roughly 0.2 T, corresponding to a 3-4% increase in viscosity. Stronger EPMs or thinner substrates can lead to even higher viscosities, but due to the saturation of the ferrofluid magnetization, the viscosity will saturate too at approximately 6% increase. Ferrofluids with higher saturation magnetization could be used for larger viscosity changes.

(21) The change in viscosity is related to a change in flow rate through the Hagen-Poiseuille law

(22) $\begin{array}{cc}Q=\frac{p}{R_{\mathrm{hyd}}},& \mathrm{Eq}.4\end{array}$
where p represents the pressure differential and R.sub.hyd is the fluidic resistance across the channel. For a rectangular channel, R.sub.hyd can be approximated by

(23) $\begin{array}{cc}{R}_{\mathrm{hyd}}=\frac{12L}{h^{3}w\left(1-0.63\frac{h}{w}\right)},& \mathrm{Eq}.5\end{array}$
where h, w, and L represent the height, width, and length of the channel, respectively. From Eq. 4-5, an increase in viscosity increases the fluidic resistance and decreases the flow rate, assuming constant p.

(24) Another phenomenon that will affect the viscosity change, and resulting droplet size, is shear thinning. Ferrofluids display non-Newtonian behavior when nanoparticles form chains under applied magnetic field. Chain formation is accounted for in more complex magnetoviscous effect models, but in simple terms, longer chains lead to higher viscosity. At higher shear rates (flow rates), these chains are broken, or not allowed to form, thus reducing the magnetoviscous effect.

(25) In experimental tests of the embodiment described above, active droplet size control was demonstrated using EPM actuation. Mineral oil based ferrofluid with 4.5% v/v solid magnetic content and 5% w/w Span80 surfactant was used for the continuous phase and water for the discrete phase. FIGS. 6A-B show increased droplet size generation for multiple actuation currents and two different flow rate settings. Actuation currents from 4 to 6.7 A were used. The leading droplet (far right) on each image represents the last droplet generated without EPM actuation and the rest of the droplets (all larger) generated after EPM activation. Besides droplet size, EPM actuation also affects inter-droplet spacing. FIG. 6A shows images of the output channel containing droplets generated under low flow rate, where droplets increase from 135 m to 185 m in diameter. FIG. 6B shows images of the output channel containing droplets generated under high flow rate, where droplets increase from 86 m to 115 m in diameter.

(26) EPM droplet size control was demonstrated for multiple flow rate settings as shown in FIG. 7. As shown in the control curve for the EPM OFF (0 A), droplet sizes can be tuned from approximately 140 to 85 m using flow rate adjustment, a slow and transient process. Using the maximum actuation current (6.7 A), droplet sizes can be tuned from 185 to 115 m, in instant step response, as seen in FIGS. 6A-B. There are no transient droplet sizes generated between the OFF and ON setting.

(27) Shear thinning was recorded at higher operating flow rates, as shown in FIG. 8. Droplet size increase diminishes at higher flow rates since particle chain formation is suppressed. Operating at higher actuation currents seems to overcome shear thinning to some extent at lower flow rates, as seen by the droplet size increase for actuation currents above 5.3 A, but eventually dominates at higher flow rates.

(28) Droplet size tuning with continuous uniform size was demonstrated and it can enable many applications, but on-demand droplet size tuning is also appealing for many reasons. We have demonstrated that by controlling the ON time of the EPM, few large droplets can be generated on-demand, as shown in FIG. 9. Decreasing the ON time even further can lead to single large droplet generation in between normal smaller droplets. This fine level of control can be useful for sorting, sample preparation or other applications where a larger droplet can be used as a marker. Since EPM ON/OFF switching only requires approximately 100 s, fast on-demand actuation rates can be achieved.

(29) In summary, we have demonstrated that droplet size can be controlled in a flow-focusing geometry by coupling EPM and oil-based ferrofluids. Using EPM actuation, immediate droplet size change was demonstrated without any noticeable size tapering. Even though shear thinning limits the droplet size change at higher flow rates, it was demonstrated that stronger magnetic fields can mitigate this effect. We also demonstrated that EPM switching can be used for on-demand droplet size tuning.