Paperfuge - Ian Taylor

Motivation

The centrifuge plays and important role in the medical industry. Centrifuges are used to separate plasma from blood and are used in studies of viruses, bacteria, proteins, and nucleic acids. One example is the use of centrifuges in blood hemocrit measurements for malaria. A centrifuge is a device that rapidly spins materials to achieve a separation by density. The major problems associated with the use of a centrifuge is the need for electricity and the need for capital to purchase the equipment. These are not always accessible, especially when trying to diagnose on site in rural developing countries. Alternatives considered to replace the centrifuge include egg beaters and salad spinners methods which produced low rotational speeds of about 1,200 r.p.m.¹ This speed is not nearly enough to replace the traditional centrifuge. Manu Prakash of Stanford University went on a mission to solve the centrifuge problem. The paperfuge is a whirligig inspired centrifuge capable of spinning at 125,000 r.p.m. that costs 20 cents and weighs only 2 grams.¹ Being powered by hand, there is also no need for electricity. The paperfuge is so lightweight and cheap due to the fact that it is made from cardstock paper discs, braided fishing line, wood/PVC handles, drinking straws, and Velcro.¹

Whirligig

Whirligigs are circular discs that are spun using string. Examples of this toy have been found at archaeological sites dating back to around 3,300 BC.² Whirligigs can be broken down into four categories: button, friction, string, and wind driven.³ Figure 1 shows a button whirligig which looks very similar to the paperfuge.

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  Figure 1 Example of a button whirligig. [1]

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  Figure 2 Example of a wind driven whirligig, much like one would put in a yard. This example of a whirligig is powered via blowing wind. [2]

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  Figure 3 Example of a friction whirligig, which works by turning a propeller due to friction. [3]

Supercoiling

The paperfuge is powered through human hands, mediated by the winding and unwinding of supercoiled string. Video 1 shows the paperfuge in use. The unwinding phase occurs when the hands are pulled apart, allowing the paperfuge to reach the maximum rotational speed. When the hands are at maximum extension, the input force is zero. This means the inertia allows the string to wind and the hands to be drawn inwards. Since the string is flexible it allows for supercoiling, otherwise known as the coiling of coils. The supercoiling is what drives the winding and unwinding of the strings, thus spinning the paperfuge at 125,000 r.p.m.

Figure 4 Example of supercoiling. Supercoiling is the coiling of coils. Imagine a phone cord further coiled.[4]

Bhamla, et al. used a high-speed camera at 6,000 frames per second to quantify the speed of the paperfuge. Although the achieved r.p.m. was 125,000 r.p.m., it has been found that the theoretical speed the paperfuge can achieve is 1,000,000 r.p.m. Video 1 shows the paperfuge in use. The unwinding phase occurs when the hands are pulled apart, allowing the paper fuge to reach the maximum rotational speed. When the hands are at maximum extension, the input force is zero. This means the interia allows the the string to wind and the hands to be drawn inwards. Since the string is flexible it allows for supercoiling, otherwise known as the coiling of coils. The supercoiling is what drives the winding and unwinding of the strings, thus spinning the paperfuge at 125,000 r.p.m.

Video explaining the Paperfuge featuring Manu Prakash. From youtube.com.[5]

Mathematical Methods

The whirligig is classified as a nonlinear, non-conservative oscillator. This means that the only energy input comes from the human hands and the only output is through drag and the strings.

Equation 1: [math]\displaystyle{ \mathrm{I \ddot{\phi}} = \tau_{Input}(\phi) + \tau_{Drag}(\ddot{\phi}) + \tau_{Twist}(\phi) }[/math]

Equation 2: [math]\displaystyle{ \mathrm\tau_{Input} = -sgn(\phi)2R_sF\frac{|\phi|R_s+R_h+R_w}{\sqrt{L^2-(|\phi|R_s+R_h+R_w)^2}} }[/math]

Equation 3: [math]\displaystyle{ \mathrm\tau_{Drag}(\dot{\phi}) = -sgn(\dot{\phi})a_R(\frac{4 \pi}{5}+2 \pi R_d^4) \dot{\phi}^2 }[/math]

Equation 4: [math]\displaystyle{ \tau_{Twist}(\phi)=-sgn(\phi)A[\frac{1}{(B-|\phi|^\gamma}-C] }[/math]

Plugging in values for A, B, and C into Equation 4 yields Equation 5:

Equation 5: [math]\displaystyle{ \tau_{Twist}=-sgn(\phi)\frac{1}{\gamma}(\phi_m-\phi_c)^{\gamma+1}[\frac{1}{(\phi_m-|\phi|)^\gamma}-\frac{1}{\phi_m^\gamma}] }[/math]

where,

• I is the inertial moment of the disc
• [math]\displaystyle{ \phi }[/math] is the angular displacement
• [math]\displaystyle{ \tau_{Input} }[/math] is the input torque component
• [math]\displaystyle{ \tau_{Drag} }[/math] is the air-drag torque component
• [math]\displaystyle{ \tau_{Twist} }[/math] is the string twisting torque component

Equations 2-5 are the equations that describe the torque for the input, air-drag, and string twist. The radius of the device matters because a larger radius means the device can spin faster towards the outside of the disk. The closer the holes in the middle, the faster the device can spin. However, if the holes are too close it can become impossible to get the device spinning. Supercoiling allows the device to start and continue spinning

Figure 5 Equations represented in a graphical manner. This image highlights the different torque components that create the spin on the Paperfuge. The input torque is the dominating force during the unwinding phase. The drag torque is dominating during the winding phase. The disc reaches a momentary halt when transitioning from winding to unwinding and vice versa. From Bhamla, et al. [6]

Applications

The paperfuge has many applications. The paperfuge can be implemented in any process a traditional centrifuge would be used in. It shows great promise in the point of care application in blood analysis in rural developing countries. The paperfuge can be operated with two hands or with one hand if one side is tethered to a wall. Bhamla, et al. showed that the paperfuge could be used to separate red blood cells from plasma in just two minutes, a process that takes a traditional centrifuge fifteen minutes¹. Since the plasma separation was done in a capillary tube, it can be analyzed under a microscope without disturbance of the sample.

Figure 6 Depiction of capillary tubes being filled with blood and being subsequently loaded into the paperfuge. Capillary tubes are affixed to the device using tape. The tops of the tubes are covered to prevent any spillage or contamination. From Bhamla, et al. [7]

References

1. Bhamla, M. S.; Benson, B.; Chai, C.; Katsikis, G.; Johri, A.; Prakash, M. Hand-Powered Ultralow-Cost Paper Centrifuge. Nat. Biomed. Eng. 2017, 1 (1), 1–7. https://doi.org/10.1038/s41551-016-0009.

2. Collins, A. T. Manual Centrifuge Inspired by Whirligig Toy Tornado Mystery Solved at Long Last. 2017, 30 (2).

3. [8]Whirligig https://en.wikipedia.org/wiki/Whirligig (accessed Mar 5, 2020).

4. [9]Wired. This Simple Paper Centrifuge Could Revolutionize Global Health _ WIRED; YouTube, 2017.