1. Introduction

Evanescent field-based optical trapping and transport using photonic structures [1,2], which have a long range of controllable transport and a large structural variety [3–5], can be applied in biomolecular research [6,7], such as forming cellular arrays [8], cancer cell cytometry [9] and drug delivery [10]. Kawata et al. demonstrated optical manipulation of microspheres with evanescent fields by a high refractive index prism in stationary water [1]. More compact dielectric waveguides structures have been used to trap and transport very small objects in fluids because these structures possess very small sizes and large fraction of evanescent waves [11]. For example, Yang et al. demonstrated trapping and transport of polystyrene (PS) particles and DNA molecules using slot silicon waveguides in a microfluidic flow perpendicular to the direction of light propagation [12]. Schmidt et al. demonstrated the propelling of micro-particles along a bend solid core waveguide which is directed opposite to the direction of the flow [13]. The on-chip waveguides are well suited for integration with fluidic channels to form functional optofluidic devices. Compared with the waveguides fabricated on substrates, optical nanofiber is more freestanding and flexible, which makes it more versatile for incorporating into natural fluidic environments such as narrow-spaced blood vessels and bio-capillaries in which the controllable transport of cells or drug particles, regardless of the direction of the fluidic flow, is extremely useful. However, particle trapping and transporting in such fluidic environment is challenging as fluidic motion is far less controllable than those in on-chip fluidic channels. An extreme example could be how to deliver drug particles with a direction opposite to the blood flow inside a vein. Peer works about trapping and transporting particles by an optical fiber in stationary water have been reported [14–17], but experimental study on backward transport of nanoparticles by such an optical nanofiber (NF) in fluidic flow with various flow velocities is still lacking. Therefore, here we report a backward optical transport of PS nanoparticles in a pressure-driven flow using an optical NF. The drag force of the fluidic flow and both the gradient and scattering forces induced by the evanescent field are considered. The relationship between the velocity of transported particles and the velocity of pressure-driven flow is studied. Simulations have also been used to analyze the mechanism of both the evanescent field and the fluid field. The NF-based particle backward transport could bring a potential application in realizing targeted drug delivery.

2. Experiment

Figure 1 illustrates the schematic of experiment. A 710-nm diameter NF, which was fabricated by direct drawing a telecom single-mode optical fiber using a flame heated technique, is positioned in a fluidic channel. A fluidic flow, prepared by diluting 713-nm PS particles into deionized water (volume ratio of particles to water ~1:1,000), was pumped into the fluidic channel by a micropump (KDS LEGATO 270). A 980-nm laser outputted from a diode laser was launched into the NF in the opposite direction of the flow. The use of 980-nm wavelength laser is because it can ensure a good viability of both mammalian cells and prokaryotic cells [18]. The experimental process was observed through an optical microscopy and the images were captured using a computer connected charge coupled device.

 

Fig. 1 Schematic of the experiment. F_d shows the drag force on the particle (in blue) induced by the fluidic flow. F_g and F_s show the gradient and scattering forces, respectively, induced by the evanescent field.

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Normally, PS particles in the suspension will experience a force induced by the fluidic flow. Once the laser is launched into the NF, additional optical force induced by the evanescent field will be applied to the PS particles which are near the NF. The optical force consists of two components. One is the gradient force (F_g) directing to the stronger optical intensity region, which traps the particles to the NF surface. The other is the scattering force (F_s) paralleling to the direction of the light propagation, which propels the particle to move along the NF. To indicate the moving directions of both the PS particles and the fluidic flow, we defined the light propagation direction as positive direction.

In experiment, the flow velocity was firstly set to be −2.7 μm/s, where the minus sign means that the flow velocity is opposite to the light propagation direction. The optical power launched into the fiber was changed from 0 to 90 mW. It was found that when the input optical power is less than 12 mW, there was no particle trapped to the fiber. When the optical power was increased to 12 mW (Fig.2a −c), particles A and B were trapped to the fiber and shake slightly on the surface of the fiber. In this case, the transport velocity can be regard as 0. It should be pointed out that the red circle indicates the particle which was not trapped by the fiber but moved with the flow with a velocity of −2.7 μm/s. The inset of Fig. 2(a) is the SEM image of 710-nm NF while the inset of Fig. 2(b) is the SEM image of 713-nm PS particles. When the optical power was increased above 12 mW, the trapped particles started to move along the fiber in a backward direction to the direction of the flow. Figure 2(d−f) as an example, shows that, at an optical power of 45 mW, three separate PS particles C, D, and E were trapped and transported along the NF. It can be seen that, from t = 0 to 1 s, the particles C, D, and E had moved distances of 8.98, 7.70, and 7.70 μm, respectively. From t = 1 to 2s, the transport distances of the particles C, D and E are 7.78, 7.66, and 7.70 μm, respectively. Therefore, an average backward transport velocity of 7.92 μm/s was calculated. It should be pointed that, the particle F in Fig. 2(d) was being trapped while in Fig. 2(e) had been backward transported by the NF.

 

Fig. 2 Backward transport of 713-nm PS particles in a fluidic flow with a nanofiber. (a−c) Input optical power: 12 mW; flow velocity: −2.7 μm/s. The inset of Fig. 2(a) is the SEM image of 710-nm NF while the inset of Fig. 2(b) is the SEM image of 713-nm PS particles. The scale bars in the two insets are 1 μm. (d−f) Input optical power: 45 mW; flow velocity: −2.7 μm/s.

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By further increasing the optical power to 90 mW, a higher backward transport velocity of 17.86 μm/s was obtained according to the moving distance of the particle G (Fig. 3a −c). The experiment has also been done by fixing the optical power at 90 mW while increasing the flow velocity from 0 to −20 μm/s. It has been found that the transport velocity decreased as the flow velocity increased. Figure 3(d−f) shows that, when the flow velocity was increased to −8.5 μm/s, the particle H was moved a distance of 9.35 μm from t = 0 to 1s and 8.48 μm from t = 1 to 2s. The calculated average backward transport velocity is 8.92 μm/s. When the flow velocity was increased to −18 μm/s or even above, no backward transported particle was observed because of the strong fluctuations at high flow velocity. Figure 4 shows detailed backward transport velocity as a function of the input optical power and flow velocity. Figure 4(a) shows that the transport velocity nearly linearly increases with the input optical power. It can be seen that, for a specific flow velocity, instability of the transport velocity of particles increases with the input optical power. It is because the high input optical power causes a large fluctuation of laser intensity and a high transport velocity which induces a considerable shaking of the NF. Figure 4(b) shows that at the power of 90 mW, the transport velocity is also nearly linearly decreased with the flow velocity. It can also be seen that, for a specific input optical power, the particle transport velocity and its instability are high at a very low flow velocity (< −2 μm/s). As mentioned above, it is because the particles transported in high velocity cause shaking of the NF. With the increasing of the flow velocity (−2 to −8 μm/s), the particle transport velocity becomes lower but more stable. After that, with a further increase of the flow velocity (> −8 μm/s), instability of the transport velocity of particles becomes obvious again. It is mainly because of larger shaking of the NF induced by higher flow velocity.

 

Fig. 3 Backward transport of 713-nm PS particles in a fluidic flow with a nanofiber. (a−c) Input optical power: 90 mW; flow velocity: −2.7 μm/s. (d−f) Input optical power: 90 mW; flow velocity: −8.5 μm/s.

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Fig. 4 Backward transport velocity as a function of (a) input optical power and (b) flow velocity. Error bars represent the standard deviation of measured particle velocities.

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3. Discussions

To explain the phenomena observed in the experiments, a three-dimensional finite element simulation (COMSOL Multiphysics 3.5a) was performed by setting the refractive indices of the water, PS, and NF to be 1.33, 1.573, and 1.445, respectively. The viscosity of water is set to be 8.39 × 10⁻⁴ Pa⋅s. The diameter of the PS particle and the NF are 713 and 710 nm, respectively. The PS particle is assumed to be trapped to the NF surface with a minimum space of 10 nm. The input power of the 980-nm wavelength light and the flow velocity are normalized to be 1 W and −1 μm/s, respectively. The optical force and drag force act on the PS particle can be calculated by solving the integral of the time averaged Maxwell stress tensor and the fluid stress tensor, respectively, along the total external surface of the PS particle. The time averaged Maxwell stress tensor can be expressed as [13]

The fluid stress tensor can be expressed as

Figure 5(a) shows the longitudinal cross-section view of the simulated total energy density distribution. It can be seen that, a part of light is leaked outside the NF as an evanescent field and acts on the PS particle. In our simulation, the calculated scattering force (F_s) induced by the optical power is 1.22 pN (pico Newton) while the gradient force (F_g) is 2.01 pN. Figure 5(b) shows the longitudinal cross-section view of the simulated distribution of flow velocity and flow streamlines, which were obtained by altering the frame of reference of fluidic domain so that the particle was stationary with respect to the flow. In simulation, the flow was assumed as an incompressible Navier-Stokes flow. From Fig. 5(b), it can be seen that, the flow velocity around the particle changes gradually and the drag force (F_d) was induced on the particle. The calculated drag force (F_d) induced by flow velocity of −1 μm/s is 5.4 fN (femto Newton), which is equal to the scattering force induced by 4.42 mW optical power.

 

Fig. 5 Longitudinal cross-section views of three-dimensional numerical simulations. (a) Optical field energy distribution around the 710-nm diameter NF and (b) velocity field of the flow and flow streamlines. F_s, F_g, and F_d represent scattering, gradient, and drag forces, respectively, acting on the PS particle.

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To study the influence of the flow velocity and the input optical power on the backward transport of the particles, a series of simulations were carried out and the results are shown in Fig. 6 . It can be seen that, for a specific input optical power, the transport velocity of the nanoparticle decreases linearly with the increase of the flow velocity. Simulations have also been performed in fluidic flow for studying the capability of backward transport of PS particles with diameters from 550 to 900 nm. Figure 7(a) shows the simulated scattering force (F_s) and drag force (F_d) acted on the particles, which were obtained by setting the optical power to be 90 mW and changing the flow velocity from −10 to −40 μm/s with an interval of 10 μm/s. It can be seen that, with the particle diameter increasing, the F_s increases from 0.036 to 0.335 pN. At the flow velocity of −10 μm/s, the F_d increases from 0.035 to 0.086 pN, which is less than F_s for all particles. It means that the backward transport of PS particles with diameters varying from 550 to 900 nm can all be realized under the 90 mW input optical power and −10 μm/s flow velocity. When the flow velocity is −20 μm/s, for particles with diameters smaller than 700 nm, F_d is larger than F_s while for particles with diameters larger than 700 nm, F_d is less than F_s. For example, for 550-nm diameter particle, F_d = 0.070 pN is larger than F_s = 0.036 pN while for 900-nm diameter particle, F_d = 0.172 pN is less than F_s = 0.335 pN. It means that under the 90 mW input optical power and −20 μm/s flow velocity, backward transport can only be realized on particles with diameters larger than 700 nm. When the flow velocity is −30 μm/s, particles with diameters larger than 800 nm experience a F_d which is less than F_s, which means that the backward transport can only be realized on particles with diameter over 800 nm. When the flow velocity is −40 μm/s, F_d is always larger than F_s, in this case, the backward transport cannot be realized on all particles with diameter varying from 550 to 900 nm. It can be concluded that under a specific input optical power, particle with a larger diameter can be backward transported in a faster fluidic flow. Figure 7(b) shows the maximum flow velocity for backward transport as a function of the particle diameter at different input optical powers. For each particle, backward transport can only be occurred if the flow velocity is lower than the maximum flow velocity. It can further be seen that, with the particle diameter increases from 550 to 900 nm, the maximum flow velocity for each particle at a specific input optical power increase. By comparing the curves of maximum flow velocity at different input optical power, it has been know that the particle diameter has a more obvious influence on the backward transport capability when the input optical power is higher.

 

Fig. 6 Simulated particle velocity versus flow velocity for backward transport at different input optical power. Data points are experiment results at 90 mW optical power.

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Fig. 7 (a) Scattering force (F_s) and drag force (F_d) as a function of particle diameter at different flow velocity. (b) Maximum flow velocity for backward transport of different diameter PS particles at different input optical power.

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4. Conclusions

We have experimentally demonstrated the trapping and backward transport of 713-nm PS particles with a 710-nm NF in fluidic flow. By varying the input 980-nm wavelength optical power from 0 to 90 mW and flow velocity from 0 to −20 μm/s, the backward transport velocity exhibits a linear dependence. We have also carried out numerical simulations for both the optical field and the fluid field to explain the phenomena and further study the dependence of backward transport capability on particle diameter. We hope that the backward transport of nanoparticles in fluidic flow with nanofiber can find applications in medical science and bioresearch such as drug delivery in blood and tissue fluid.