Introduction

The extraordinary ability of highly efficient non-contact manipulation based on optical systems has stimulated a number of breakthroughs in lab-on-a-chip techniques and research endeavors1,2. Keeping pace with the increasingly prevalent development of applications, various requirements for particle manipulation have been presented to accommodate various state-of-the-art microfluidic devices. In view of the current deficiency of light-driven manipulation, there are two fundamental challenges demanding prompt solutions. The first is strong compatibility with many lab-on-a-chip applications, enabling both multiform manipulation and tunable manipulation range. Optical tweezers3,4,5 can collectively trap various materials at the center of the laser beams to achieve various forms of manipulation, including transporting6, binding7,8, and sorting9,10,11. Plasmonic tweezers provide highly enhanced electromagnetic fields for the distributed trapping of particles into periodic arrays of metal structures12,13,14. However, because only a target in close proximity to the laser illumination can be successfully trapped, these conventional laser trapping techniques consistently suffer from limited manipulation area. To achieve light-driven manipulation with extensive scale, the synergistic integration of optical systems and microfluidic flow has been utilized to control particle movement in a process called optofluidic manipulation15,16. Previous works have demonstrated optofluidic flows, including buoyancy convection stimulated by plasmonic heating17,18,19,20,21 and thermocapillary flows stimulated by laser-induced microbubbles22,23,24,25. Despite fast fluid velocity and extensive scaling, photothermally induced fluidic trapping has been simply applied in massive aggregation and long-range transport17,18,19,20,21,22,23,24,25. At present, a comprehensive technique, possessing the synergistic capacities of multiform manipulation and tunable manipulation range, has not been well developed.

The second challenge is potential damage to the target materials. Photothermal heating is unavoidable, and the stimulated heat is highly localized at the laser center, which is commonly the stable position for trapped materials. Especially in plasmonic-based systems26,27,28, the effective heating resulting from high field enhancement of plasmonic resonance leads to a vast array of biochemical applications, including photothermal therapy29, drug delivery30, phase transition control31, reversible DNA melting32, photocatalysis33, and nanowire growth34. Permanent contact with the photothermal resource may possibly give rise to undesirable thermal damage or chemical reactions. In many optical strategies, the obstacle of this accessory effect should be successfully suppressed35,36, but suppression simultaneously diminishes the efficiency of optical manipulation. In many optofluidic strategies, photothermal heating is a unique excitation, which appears to be a quandary. An “ideal” approach, enabling valid manipulation without contact with the photothermal resource, has not been proposed.

Based on our previous study of particle manipulation37, which is valid only on a fluid surface (rather than inside the fluid), we develop in this paper an optofluidic system involving buoyancy and thermocapillary convection to achieve controllable fluid motion and multiform manipulation inside the fluid (instead of only on the surface), which can overcome the aforementioned challenges. The three-dimensional thermal transfer of fluid is induced by optical heating of a hybrid photothermal waveguide (HPW), which is motivated by a fiber laser without complex laser-illuminated systems. We both theoretically and experimentally demonstrate the use of hybrid optofluidic flow to selectively control vertical and horizontal vortices. The optofluidic flows are capable of controlling particles in the vortex centers rather than on the HPW, avoiding potential thermal damage to the targets. Compared with laser trapping over a limited area, optofluidic flow is applied to control the suspended particles with adjustable scaling, accompanied by a tunable distance from the HPW. Compared with plasmon-induced thermal trapping functions, the on-demand optofluidic modes exhibit multiform manipulation, including (collective or distributed) trapping and (vertical or horizontal) rotation/spin. Taking advantage of trapping and rotating/spinning in the vortex centers, we develop novel applications for the arrangement of the same components based on buoyancy convection and self-assembly of materials into stable architectures, such as particle networks and droplet capsules, based on thermocapillary convection.

Materials and methods

HPW fabrication

The HPW was fabricated by integrating graphene oxide (GO) with a SiO2 waveguide22,23. GO was prepared by the modified Hummers’ method. The SiO2 waveguide was drawn by the flame-heated technique. The GO-cladded HPW was fabricated by coating a droplet of GO-ethanol colloid on the waveguide surface, which shrank and automatically formed a thin film as the ethanol evaporated (see Figs. S1−3, Supplementary Information). The length of the GO cladding could be controlled by the droplet length. Experiments showed that after a droplet with volume Vdroplet ≈ 2 nL was deposited on the waveguide, the droplet length was fixed at 4 μm. The thickness of the GO cladding could be controlled by the GO concentration C. The quantitative expression between the GO concentration C (units: mg/mL) and the GO-cladding thickness t (units: μm) is t ≈ (0.0046·C + 0.25)1/2 − 0.5 (see Eq. S4, Supplementary Information). For a GO-ethanol colloid with C = 25 mg/mL, we could fabricate a HPW with a length of 4 μm and thickness of 100 nm (see Fig. S2, Supplementary Information). A 980-nm fiber laser with a power of 0−100 mW (PUMP-980-CW, Zhiying, China) was applied. Bubbles were generated when the optical power reached 80 mW, so an optical power of P = 5−60 mW was proper for optofluidic convection.

Chip fabrication

As shown in Fig. 1a, the fabricated HPW was deposited on a glass substrate, and the waveguide ends were fixed by paraffin wax. The microfluidic chamber was made from 50-μm thick adhesive tape (area: S = 1 cm × 1 cm), and the GO-cladded HPW was located at the center of the bottom of the chamber. Two microfluidic pumps were applied. One was used for the inlet to inject the solvent (volume: V) containing suspended materials, such as Ag nanowires, graphite powder, and polystyrene particles, into the microfluidic chamber. The other was used for the outlet to discharge the fluid (volume: Vout) from the microfluidic chamber. A computer-interfaced inverted microscope equipped with a charge coupled device camera (MDX4-T, M-shot, China) was used for observation of the tracing process. A flow situation would destroy the hybrid convection, and thus, the flow velocity and throughput were not considered in the experiments.

Fig. 1: a Experimental set-up.
figure 1

b SEM image of a typical HPW, showing its structure composed of GO cladding integrated with a silica waveguide. c Hybridization facilitates the selective control of vertical and horizontal vortices. Buoyancy convection provides a trapping circle inside the fluid, while thermocapillary convection allows for a trapping lattice at the fluid surface. d When buoyancy convection is dominant at δ ≈ 50 μm and P = 20 mW, graphite powders (diameter ≈ 5 μm) were trapped along the trapping circle and rotated vertically. e Vertically rotating Ag nanowires (length ≈ 2 μm and diameter ≈ 50 nm) and horizontally spinning graphite powder demonstrated the coexistence of buoyancy and thermocapillary convection at δ ≈ 25 μm and P = 20 mW. f When thermocapillary convection is dominant at δ ≈ 10 μm and P = 20 mW, polystyrene particles (diameter ≈ 1 μm) were separately captured and horizontally spun in each vortex, leading to the permutation of traps into a lattice array. The positions of the trapping materials are indicated by red arrows. Scale bars = 4 μm

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Simulation

Two simulation models were applied based on COMSOL Multiphysics 5.1 (COMSOL Co., Ltd.). The details of the theoretical models, including the geometric model, material model, and boundary conditions, were described in Fig. S4, Supplementary Information. First was the simulation of the optical heating of the HPW based on an electromagnetic wave model and a heat transfer model, which was used to calculate the temperature T at the front apex of the HPW and the temperature difference ΔT from the front apex to the end of the HPW. The dependences of T and ΔT on the GO-cladding length L and optical power P were studied to demonstrate the optimized HPW morphology to obtain a homogeneous and highest temperature. Second was the thermal-fluidic model simulating the temperature and velocity distribution in the optofluidic flow, based on a heat transfer of fluid model and a laminar flow model. The change in flow thickness δ and HPW temperature T (from the first model) were studied to theoretically show the hybridization and intensity of buoyancy and thermocapillary convection.

Experimental operation for hybrid optofluidic flow

In the experiment, we injected the solvent at V ≈ 5 μL, and the fluid thickness δ was 50 μm. The fluid in the chamber was discharged with Vout ≈ 0.5 μL each time to decrease the fluid thickness. The resulting fluid thickness was estimated by the volume difference between the injected and effluent fluid: δ = (V − Vout)/S. Then, the transition from buoyancy to capillary flow was observed as the change in liquid thickness. Here, the smallest particle diameter was limited to 300 nm. Suspensions of 300-nm polystyrene particles (BaseLine ChromTech Research Centre) were used for tracing the optofluidic flows. A Plan Apo (UPLSAP040X2, 40×, N.A. 0.95) was employed, which had a diffraction limit of approximately 290 nm. M-shot digital imaging software (Image-Pro Plus 6.0) was used for real-time recording of particle trajectories. The recording frame rate was set at approximately 10 Hz. The velocities of the particles were measured by the superposition of the particle trajectories. It was useful to distinguish the optofluidic modes and accurately measure the velocity of tracing particles when buoyancy and thermocapillary convection were dominant.

Experimental setup for optofluidic manipulation

To observe particle movement more clearly, various particles were applied to demonstrate particle manipulation regardless of their shape or surface properties. Suspensions of graphite powders with sizes of 0.5, 1, 2, and 5 μm (XFNANO Advanced Materials Supplier) were used when buoyancy convection was dominant, because the black color can display more distinct trajectories and positions. Suspensions of polystyrene particles with diameters of 0.5, 1, 2, and 5 μm (BaseLine ChromTech Research Centre) were used when thermocapillary convection was dominant, because their surface flexibility accelerated their interaction. The particle positions and distributions were measured by the Image-Pro Plus 6.0 software package.

Results and discussion

Construction of the optofluidic system

This novel optofluidic system is synergistically integrated with a photothermal source and a microfluidic device where the fluid surface is in full contact with air, as shown in Fig. 1a. GO is an ideal photothermal material, owing to its strong light confinement, high infrared absorption, and excellent thermal conductivity38,39,40, which ensure the stability of the HPW structure and the high efficiency of optical heating. The HPW was fabricated by coating GO on a silica waveguide (Fig. 1b) and served as a photothermal resource, in which the microstructure is capable of yielding strong convection. Activated by a fiber laser at a wavelength of 980 nm, the localized heating of the HPW is three-dimensionally transferred in the fluid, which induces optofluidic flow hybridized by buoyancy convection inside the fluid (vertical vortices) and thermocapillary convection at the fluid surface (horizontal vortices). The alteration of the fluid thickness δ is useful to selectively control the vertical and horizontal vortices, while adjustment of the optical power P is applied to tune the flow velocity and vortex scaling. Figure 1c shows that the tunable optofluidic modes facilitate three-dimensional optofluidic manipulation. Dominant buoyancy convection can attract and aggregate particles into the trapping circle to achieve collective trapping, while dominant thermocapillary convection enables particles to be separately captured in four independent and equivalent vortices. This trapping can confine the particles in the vortex away from the HPW, preventing the particles from being thermally damaged by the HPW. Figure 1d−f show typical examples of particle confinement without restrictions on the particle material or shape. At large thickness δ ≈ 50 μm, buoyancy convection is dominant, leading to the permutation of irregularly shaped graphite powder along the trapping circle (Fig. 1d). At small thickness δ ≈ 10 μm, thermocapillary convection is dominant, enabling the spheroidal polystyrene particles to be separately captured and horizontally spun in the trapping lattice (Fig. 1f). At the appropriate thickness δ ≈ 25 μm, vertically rotating Ag nanowires and horizontally spinning polystyrene particles were observed simultaneously, demonstrating the superposition of buoyancy and thermocapillary convection (Fig. 1e). The microscopic details of Fig. 1d−f can be viewed in Supplementary Movie 1.

Theoretical simulation for optical heating of the HPW

Figure 2a shows the geometry of the HPW. A 1000 nm-diameter SiO2 cylinder waveguide coupled with GO cladding with thickness t and length L was immersed in water, forming the HPW. We began the theoretical analyses by estimating the behavior of the electric field component E(r) in the HPW, based on the Helmholtz equation:

$$\nabla \times [\nabla \times {\bf E}({\bf r})] - k_0^2\varepsilon ({\bf r}){\bf E}({\bf r}) = 0,$$
(1)

where k0 = 2π/λ is the wavenumber corresponding to wavelength λ of the incident light in vacuum. In addition, ε (r) = ε′(r) + iε″(r) is the position-dependent permittivity with real part ε′(r) and imaginary part ε″(r), which are 2.10, (6.75 + 0.52i), and 1.77 for SiO2, GO41, and water, respectively, at wavelength of λ = 980 nm. The optical energy is evanescently coupled into the SiO2 core and GO cladding and absorbed by the GO cladding. Therefore, the optical energy will exponentially decay along the HPW, leading to non-uniform heat density, as described by42

$$q\left( {\bf r} \right) = k_0\varepsilon {\prime\prime}\left( {\bf r} \right)\left| {{\bf E}\left( {\bf r} \right)} \right|^2{\mathrm{/}}2\pi$$
(2)
Fig. 2: a Optical-thermal model.
figure 2

b Distributions of the electric field intensity for the HPW when t = 100 nm and λ = 980 nm. c Temperature distributions of the HPW when t = 100 nm and P = 40 mW for L = 2, 4, and 8 μm. d, e Dependence of the calculated temperature (T) and temperature difference (ΔT) on the waveguide length (L) (from 0 to 20 μm in increments of 1 μm) and optical power (P) (from 30 to 50 mW in increments of 10 mW), respectively

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In view of this, the HPW is divided into two parts, as shown in Fig. 2a. The front section is called the “thermal excitation” part, which can be heated sufficiently by integrating the Joule heat along the HPW, as described by42

$$Q = {\int \int \int} {q({{\bf r}}){\mathrm d}x{\mathrm d}y{\mathrm d}z}.$$
(3)

The end section of the HPW is called the “thermal dissipation” part, which is heated based on thermal dissipation41 from the front section due to its negligible q(r),

$$\nabla \cdot [\kappa ({\bf r})\nabla T({\bf r})] = - Q,$$
(4)

where κ (r) is the thermal conductivity (κGO = 600 W m−1 K−1, κcore = 27 W m−1 K−1, and κwater = 0.63 W m−1 K−1).

The optimized morphology of the HPW is considered to achieve high efficiency and high sensitivity optical heating, which is the key to yield and control the optofluidic flow. The GO thickness t determines the optical energy distribution in the GO-cladding region (Eq. 1). It is theoretically shown that the optical energy is largely confined to support a tube-like mode for t = 100 nm, as shown in Fig. 2b. The GO length L determines the interaction between thermal excitation (Eq. 3) and thermal dissipation (Eq. 4), dominating the temperature distribution in the HPW. Figure 2c shows temperature distributions of the HPW with t = 100 nm and P = 40 mW for L = 2, 4, and 8 μm, exhibiting a visual distinction in optical heating. Figure 2d, e shows the dependence of temperature T at the front apex and temperature difference ΔT between the front and end apex on L and optical power P, respectively. The optimized length Lm was calculated based on Eqs. 1−4. The waveguide with L < Lm achieved the minimal thermal inhomogeneity but exhibited a lower excited temperature due to its insufficient thermal excitation, while the waveguide with L > Lm presents strong thermal inhomogeneity and a lower excited temperature due to its strong thermal dissipation. For the HPW with t = 100 nm, the optimum condition occurs when L = Lm ≈ 4.0 μm, where both sufficient thermal excitation and negligible thermal dissipation are achieved, resulting in a homogeneous and high temperature along the HPW, despite the change in optical power. For example, as P is increased from 30 to 50 mW, the optimized temperature Tm increases substantially from 328.2 to 351.8 K, while ΔTm increased insignificantly from 0.05 to 0.1 K.

Theoretical simulation for hybrid optofluidics by the HPW

In the thermal-fluidic models, the temperature distribution T(r) in the surrounding water is governed by the steady-state liquid heat transfer equation21:

$$\rho C_p{\mathbf{u}}({\bf r}) \cdot \nabla T({\bf r}) - \kappa_{ {\rm water}}\nabla ^2T({\mathbf{r}}) = 0,$$
(5)

where T(r) and u(r) are the fluid temperature and velocity, respectively, ρ = 103 kg m-3 is the density, and Cp = 4200 J kg−1 K−1) is the specific heat capacity.

The velocity distribution u(r) of thermally induced fluid convection is governed by the steady-state incompressible Navier–Stokes equation21:

$$\rho {\mathbf{u}}({\bf r}) \cdot \nabla {\bf u}({\bf r}) - \eta \nabla ^2{\bf u}({\bf r}) = F({\bf r})\,{\mathrm {with}}\nabla \cdot {\mathbf{u}}({\bf r}) = 0,$$
(6)

where η = 10−3 Pa/s denotes the dynamic viscosity. The velocity distribution of the flow u(r) is driven by the F(r) term, representing external forces per unit volume (N m−3), which can be divided into two parts, buoyancy force and surface tension, due to temperature non-uniformity. For most Newtonian liquids, the density and surface tension increase linearly with the decreasing temperature. An imposing temperature gradient correspondingly produces a density gradient inside the fluid and surface tension gradient at the fluid surface, resulting in the external buoyancy force FB and the surface tension σM, respectively:

$$F_{\mathrm {B}} = \rho g\beta _{\mathrm {T}}[T({\bf r}) - T_0]$$
(7)
$$\sigma _{\mathrm {M}} = - \sigma _{\mathrm {T}}\cdot \nabla T({\bf r}),$$
(8)

where ρ = 1000 kg m-3 is the fluid density, g = 9.8 m s2 is gravitational acceleration, βT = 2.07 × 10−4 K−1 is the thermal expansion coefficient, and σT = 1.514 × 10−4 N m−1 K−1 is the temperature coefficient of surface tension. The difference in buoyancy force drives buoyancy convection, while the difference in surface tension drives thermocapillary convection.

The HPW-induced hybrid optofluidics is described as a “superposition” of buoyancy and thermocapillary convection, as shown in Fig. 3a. The temperature distribution of the fluid T(r) in steady state (Eq. 5) induced by the HPW temperature Tm and room temperature T0, as well as the total force F(r) acting in the fluid including the buoyancy force density FB inside the fluid (Eq. 7) and surface tension density σM at the fluid surface (Eq. 8), synergistically determine the velocity distribution v(r) of buoyancy and thermocapillary convection (Eq. 6). Figure 3b–e show the three-dimensional temperature and velocity distribution of the fluid (100 μm × 100 μm × 50 μm) excited by an HPW at the bottom center with [t, Lm, Tm] = [100 nm, 4 μm, 340 K]. From the side view (Fig. 3b) and top view (Fig. 3c), the temperature is dissipated from the bottom center (Tm = 340 K) to the surface center (TS = 296.98 K) and from the surface center (TS = 296.98 K) to the surface border (T0 = 293.15 K). Corresponding to the temperature distribution, buoyancy convection is characterized by a kind of three-dimensional toroidal internal flow, vertically flowing toward and away from the HPW (Fig. 3d). Thermocapillary convection is characterized by a type of two-dimensional toroidal surface flow, consisting of four equivalent vortices as a horizontal array (Fig. 3e). Further simulation results of the temperature and velocity distribution for various δ exhibit a more complete picture of the optofluidic flow (see Fig. S5, Supplementary Information).

Fig. 3: a Optical-thermal-fluidic model.
figure 3

b, c Temperature distributions on the yz-plane (b) and xy-plane at the fluid surface (c), excited by an HPW at temperature Tm = 340 K. d, e Velocity distributions on the yz-plane (d) and xy-plane at the fluid surface e, corresponding to buoyancy convection and thermocapillary convection, respectively. f Temperature differences Tm −TS (solid lines) and TS − T0 (dotted lines) as a function of δ for Tm = 328.2 K (red lines), 340 K (blue lines), and 351.8 K (black lines). g Velocities of buoyancy convection vBM (solid lines) and thermocapillary convection vTM (dotted lines) as a function of δ for Tm = 328.2 K (red lines), 340 K (blue lines), and 351.8 K (black lines)

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Alterations of δ and Tm are essential to control the hybridization and intensity of the optofluidic flow, respectively. Figure 3f plots the dependence of the temperature differences Tm − TS and TS − T0 on δ (from 5 to 100 μm) and Tm (328.2, 340, and 351.8 K). Figure 3g shows the maximum velocity of buoyancy (vBM) and thermocapillary convection (vTM), indicated by the black point in Fig. 3d, e, vs. fluid thickness. It is clear that an increase in δ will lower the temperature gradient at the liquid surface but increase the temperature gradient inside the liquid, accordingly leading to decaying thermocapillary convection and enhanced buoyancy convection. For example, at δ = 10 μm, the hybrid optofluidic flow supports dominant thermocapillary convection. While at δ = 60 μm, buoyancy convection is dominant. At δ = 30 μm, thermocapillary convection coexists with buoyancy convection. An increase in Tm will increase the temperature gradient inside the liquid and at the fluid surface and finally reinforce buoyancy and thermocapillary convection.

Experimental verification of the hybrid optofluidic flow

To experimentally demonstrate the generation of HPW-induced hybrid flows, we fabricated an HPW with L ≈ 4 μm and t ≈ 100 nm by transferring prepared GO onto a SiO2 waveguide with a radius of 500 nm and deposited it on a glass substrate (see Figs. S1–3, Supplementary Information). The temperature of the HPW and the temperature distribution in the surrounding liquid were experimentally demonstrated. We performed direct thermal characterization based on the phase transformation of a paraffin layer under excitation at different optical powers. According to the melted footprint in the paraffin, the HPW temperature could be estimated to be 332−368 K for P = 30−60 mW (Fig. S6, Supplementary Information). The flow modes were characterized by the dragged trajectories of the polystyrene particles (diameter = 300 nm) introduced in the chip, and the flow intensity was measured by the particle velocities (Figs. S7−9, Supplementary Information).

We first considered the difference between buoyancy convection and thermocapillary convection. As shown by the microscopic images in Fig. 4a i−iii, buoyancy convection could drive the particles toward the HPW by a closely centrosymmetric flow field, while thermocapillary convection kept the particles away from the HPW, forming four vortices. We studied the change in optofluidic modes under an optical power P = 40 mW. In Fig. 4a, we selected various particles and measured the distribution of the maximum velocities at different positions. Therefore, the error bars in Fig. 4a indicate the distribution of the measured maximum velocities. The measured maximum velocities of various particles (vBM and vTM) were dependent on the fluid thickness δ, as shown in Fig. 4a. The buoyancy convection began to appear at δ ≈ 20 μm, and the thermocapillary convection began to disappear at δ ≈ 30 μm. Therefore, three hybrid modes of HPW-induced convection were divided according to δ: dominant thermocapillary convection (δ ∈ [0, 20] μm), concomitant convection (δ ∈ [20, 30] μm), and dominant buoyancy convection (δ ∈ [30, 50] μm). The flow details are contained in Supplementary Movie 2.

Fig. 4: Hybrid optofluidic control.
figure 4

a For polystyrene particles with diameters of 300 nm, measured maximum velocities (|vBM| and |vTM|) vs. fluid thickness δ, indicating three optofluidic modes, including dominant thermocapillary convection (i), concomitant convection (ii), and dominant buoyancy convection (iii). b, c For optical power P = 20, 40, and 60 mW, experimentally measured velocity vs. y-positions when buoyancy convection is dominant at δ ≈ 50 μm (b) and when thermocapillary convection is dominant at δ ≈ 10 μm (c)

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For an individual particle, Fig. 4b, c shows the velocities VT and VB vs. radius position y under dominant buoyancy convection and thermocapillary convection, respectively, at P = 20, 40, and 60 mW. Here, VT and VB in Fig. 4b, c represent the value of the particle velocity only. When buoyancy convection was dominant at P = 40 mW, particles located at y ≈ 42 μm were accelerated toward the HPW and reached a maximum vBM of 11.3 μm/s at y ≈ 14 μm. When thermocapillary convection was dominant, particles located at y ≈ 36 μm were accelerated away from the HPW and reached a maximum vTM of 19.8 μm/s at y ≈ 12 μm.

We further studied the dependence of the optofluidic strength on the optical power. Increasing the optical power was demonstrated to increase the optofluidic strength, which was reflected in two aspects. The first was enlargement of the convection scaling upon increasing the optical power (see Fig. S7, Supplementary Information), because of the expansion of thermal transfer induced by the increasing temperature of the HPW. The second was the increase in the optofluidic velocity (see Fig. 4b, c), originating from the increase in the temperature gradient.

Theoretical analysis for three-dimensional manipulation

Here, we show a new type of three-dimensional optofluidic trapping and rotation/spin in the HPW-induced hybrid optofluidic system. Based on our previous work, the driving mechanism is attributed to the combination of drag force FD and inertial force FI in the optofluidic vortices37, as given by

$$F_{\rm{D}} = 3\pi \eta vD$$
(9)
$$F_{\rm I} = {\mathrm {Re}} \times F_{\rm {D}} = 3\pi \rho v^2DL_{\rm {S}},$$
(10)

where v denotes the flow velocity, D is the effective diameter of the particle, Re = ρvLS/η denotes the Reynolds number, and LS is the size of the optofluidic vortices. The inertial force FI, directed toward the vortex centers and perpendicular to the flow direction, is exerted to attract particles into vortex centers. While the drag force FD, directed along the flow direction, is responsible for circulating particles. The synergy between FI and FD drives particles to move spirally toward the vortex centers. Based on the quadratic dependence of FI on the fluid velocity, FI is incapable of manipulating particles in the vortex centers, which have minimal flow velocity and correspond to stable trapping positions. Buoyancy convection provides a trapping circle enveloped by the vortex centers inside the fluid, while thermocapillary convection allows for a trapping lattice consisting of four equilibrium positions. All the traps in the vortex centers are controlled by the dominating FD, leading to vertical rotation under buoyancy convection and horizontal rotation under thermocapillary convection.

Due to the linear dependence of FI on the particle size D, the rotation modes of particles with different sizes vary in the same vortices. The negligible FI, combined with the dominating FD along the flow direction, drives the trapping and rotation of smaller particles (as shown in Fig. 5a). In contrast, larger particles were steadily trapped with spin at the trapping circle or the trapping lattice resulting from the balanced FI and the predominant FD (as shown in Fig. 5b).

Fig. 5: Trapping and rotation/spin of particles in optofluidic vortices.
figure 5

a, b Inertial force FI (blue arrows) and drag force FD (black arrows) jointly acting over a particle drives particles to spirally move toward the vortex center, as indicated by red arrows. The movement is dominated by the drag force until the particle is at the center. Small particles will rotate around the center (a) while large particles will spin at the center (b). c−f Experimental verification. The figures on the left show the movement of the particles in vortices, including trapping trajectories (solid line) and rotation positions (scatter plots). The figures on the right show the probability density distribution P(d) vs. particle distance to the vortex centers (d) in scatter plots

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Experimental verification of three-dimensional manipulation

Polystyrene particles with diameters of 1 and 2 μm were used to study trapping modes when buoyancy convection was dominant at δ ≈ 50 μm and when thermocapillary convection was dominant at δ ≈ 10 μm (P = 30 mW), as shown in Fig. 5c–f and Supplementary Movies 3, 4. According to the trapping processes, the recorded movements of particles could be described by two parameters: the trapping transverse trajectories and rotation transverse positions. Under buoyancy convection, theoretically, the trapping trajectories should be a single straight line from the microscopic view (x–y plane) resulting from FI and FD in the y–z plane. However, buoyancy convection can provide vertical confinement but is incapable of horizontal confinement. Thus, experimentally, the trapping trajectories were always depicted by a polygonal line, and the rotation positions were shown to spread along the trapping circle (Fig. 5c, d). Under thermocapillary convection, which offers horizontal confinement, the trapping trajectories were described by four analogously helical curves, and the rotation positions were scattered around the trapping lattice as a result of FI and FD in the x–y plane (Fig. 5e, f).

Both buoyancy convection and thermocapillary convection showed similar trends in the confinement of particles of various sizes. Owing to the positive dependence of FI and FD on the particle size, smaller particles (1 μm) experienced a meandering trajectory around the trapping circle or trapping lattice, while larger particles (2 μm) were observed to immediately move into the trapping circle or trapping lattice. To study the trapping efficiency and stiffness, the probability density distribution P(d) vs. particle transverse distance to the vortex center (d) was summarized. Shifting of the particles with maximum probability was defined as the effective rotation radius R′. For small particles (1 μm) trapped with rotation, R′ ≈ 1.5 μm under buoyancy convection (Fig. 5c) and R′ ≈ 1.0 μm under thermocapillary convection (Fig. 5e). For larger particles (2 μm), R′ ≈ 0 under both buoyancy convection (Fig. 5d) and thermocapillary convection (Fig. 5f), showing trapping with spin at the vortex centers. In this case, the probability of P(d) (i.e., trapping efficiency) reached a maximum of 82% (Fig. 5d) and 96% (Fig. 5f), respectively. The results demonstrated that decreasing R′ decreased particle fluctuation and enhanced particle confinement, meaning that the trapping efficiency reached its maximum when the particles were trapped with spin.

Controlled by the tunable optical power P, varying the scaling of optofluidic flow would lead to a distinct particle trapping status. For different-sized particles, Fig. 6 shows the dependence of trapping, rotation and spin on optical power. Figure 6a, b show the trapping status of the particles, experimentally summarized under dominant buoyancy convection and thermocapillary convection, respectively. The optofluidic flow excited by the undersized optical power was too weak to realize valid confinement, whereas excessive optical power drove an exaggerated convection for particle trapping with rotation, causing the strong oscillation of particles. Under the appropriate optical power, the trapped particles with continuous spinning were exposed to the stiffest confinement. When buoyancy convection was dominant, the stiffest confinement of particles with different sizes can be achieved at various optical powers. Smaller particles were exposed to the stiffest confinement under lower optical power. Larger particles were subjected to the stiffest confinement over a broader range of optical powers. For example, in Fig. 6a, the stiffest confinement (i.e., trapping with spin) of particles with diameters of 500 nm occurred at P = 10−15 mW, whereas that of particles with diameters of 5 μm could be achieved at P = 20−60 mW. As shown in Fig. 6c−e, graphite powder with a diameter of 5 μm was trapped and spun vertically when buoyancy convection was dominant (δ ≈ 50 μm), and the distance to the HPW increased from 20 to 40 mW. When thermocapillary convection was dominant at δ ≈ 10 μm, the stiffest confinement of particles with different sizes can be achieved at the same optical power. For example, when excited at optical powers from 10 to 20 mW (Fig. 6b), particles with diameters of 500 nm to 5 μm can be effectively trapped. As shown in Fig. 6f−h, polystyrene particles with diameters of 1 μm and 500 nm when thermocapillary convection was dominant (δ ≈ 10 μm) were shown to be stiffly trapped and horizontally spun with distances to the HPW of 4 μm at 10 mW, 6 μm at 15 mW, and 8 μm at 20 mW.

Fig. 6: a, b Trapping status of various particles when buoyancy convection is dominant (a, δ ≈ 50 μm) and when thermocapillary convection is dominant (b, δ ≈ 10 μm) with tunable optical power P (from 0 to 60 mW in increments of 5 mW).
figure 6

c−e When buoyancy convection is dominant, trapped graphite powder (diameter ≈ 5 μm) is spun vertically at P = 20 mW (c), 30 mW (d), and 40 mW (e). f−h When thermocapillary convection is dominant, two trapped polystyrene particles (diameter = 1 μm and 500 nm) are spun horizontally at P = 10 mW (f), 15 mW (g), and 20 mW (h). Scale bars = 4 μm

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In addition to particle trapping with spin shown (Fig. 6), we provide more examples to identify the dependence of trapping with rotation on different-sized particles in Fig. S10, Supplementary Information. The high optical power drove exaggerated convection, leading to particle trapping with rotation. As the optical power increased, the rotation diameter R′ increased, causing strong particle oscillation. It was clear that particles with large R′ had strong oscillation and weakened confinement.

Applications for optofluidic arrangement and mixing

In addition to individual manipulation, we further examined real-life applications of the optofluidic system, especially the use of hybrid optofluidic flow for high-throughput particle arrangement and mixing. Control of microscale solid or liquid inclusions is generally a momentous feat in integrated physical detection43 and chemical reaction16. In contrast to other optofluidic systems that demand plasmonic structures19 or specific surface patterns44, hybrid optofluidic flow can aggregate particles without limitations on the particles material or the requirement of a substrate, giving a circular arrangement under buoyancy convection and a mixture of square lattices under thermocapillary convection.

By harnessing the dependency of trapping states on the particle size, dominant buoyancy convection can provide a straightforward method for confining particles with appropriate size and arranging them along the trapping circle. Figure 7a, b and Supplementary Movie 5 demonstrate the extraction of 2 μm particles from massive 500 nm particles when buoyancy convection is dominant (δ ≈ 50 μm and P = 30 mW). The typical escape trajectories (blue lines) indicate that the 500 nm-diameter particles rotated around the flow boundary with strong oscillation and were rapidly removed, while the typical trapping trajectories (red lines) show that the 2 μm-diameter particles were strongly confined along the trapping circle. Figure 7b shows that most of the 2 μm-diameter particles were arranged along the trapping circle. Some trapped particles could swim along the trapping circle, leading to a self-arranged circular chain. Fig. 7e–g and Supplementary Movie 6 further show that the 5 μm-diameter graphite powders were captured when buoyancy convection was dominant at δ ≈ 50 μm and P = 20 mW and then collided with each other, connected end to end, and finally self-arranged in a chain.

Fig. 7: a, b Extraction of 2 μm particles from massive 500 nm particles when buoyancy convection is dominant (δ ≈ 50 μm and P = 30 mW).
figure 7

c, d Mixing of particles with diameters of 500 nm, 1 μm, and 2 μm when thermocapillary convection is dominant at δ ≈ 10 μm and P = 10 mW. e−g When buoyancy convection is dominant, 5 μm-diameter graphite powders were trapped, spun anticlockwise, and finally assembled into a structure. h−j When thermocapillary convection is dominant, 300 nm-diameter polystyrene droplets were trapped, collectively rotated in every vortex center at δ ≈ 10 μm, and finally assembled into four spheres. Scale bars = 4 μm

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The aggregation of desired particles from a mixture can potentially be applied in enhanced sensing platforms. The circular arrangement of 2 μm-diameter fluorescent microspheres from massive 500 nm transparent particles is conducive to enhancing fluorescence detection (see Fig. S11, Supplementary Information). Therefore, it is anticipated that the technique can strengthen the sensing signal based on the aggregation of particles with the same component, providing inspiration for biochemical detection with enhanced sensitivity43 (for example, by fluorescence detection and Raman spectroscopy).

Dominant thermocapillary convection can trap different-sized particles into the vortex centers with the stiffest confinement under an optical power of 10–20 mW (Fig. 6b). Figure 7c, d and Supplementary Movie 7 demonstrate the collective aggregation of 500 nm-diameter 1 μm-diameter, and 2-μm-diameter particles when thermocapillary convection is dominant at δ ≈ 10 μm and P = 10 mW. The distribution of polystyrene particles was observed in the trapping lattice. The collective rotation was accompanied by collisions and squeezing, which strengthened the viscous bonding among the particles. By integrating the strong confinement and torque, different particles can be mixed with constant spins and finally assembled into four particle networks.

The ability to accelerate mass exchange among particles can potentially be used in mesoscopic materials mixing, as reported in previous works45,46. Figure S12 (Supplementary Information) shows the transformation process from individual nanoparticles (diameter = 300 nm) to a square lattice of particle clusters (δ ≈ 10 μm and P = 20 mW). In the trapping lattice, the nanoparticles were first randomly dispersed, then agglomerated into small particle islands, and finally assembled into large clusters. Fig. 7h−j and Supplementary Movie 8 show the fusion of 300 nm polystyrene droplets into four stable capsules (δ ≈ 10 μm and P = 10 mW). In the trapping lattice, the polystyrene droplets were first trapped with a constant spin, subsequently fused into extensive patches (diameter = 1−4 μm), and finally completely folded into capsules with a diameter of 1 μm. The resultant clusters and capsules were formed within a period of 1 min and stably maintained after the light was turned off. Based on the stiff confinement of 0.5−5 μm-diameter particles at optical power P = 10−20 mW, optofluidic mixing can progress steadily in the trapping lattice, providing future applications in microfluidic systems, including microreactors, micromixers, and micro-concentrators.

Conclusions

We developed a novel optofluidic technique using both theory and experiment that involves buoyancy convection and thermocapillary convection, which are characterized by vertical vortices and horizontal vortices, respectively. The respective manipulation characteristics of buoyancy and thermocapillary convection were comprehensively analyzed, showing that the former can support a trapping circle for collective trapping and vertical rotation, while the latter can provide a trapping lattice for distributed manipulation and horizontal rotation. The on-demand control of optofluidic modes and strengths can successfully achieve optofluidic manipulation with different dimensions, various scopes, and multiple functions, as well as without contact with the HPW. This presented approach is highly attractive for a broader range of lab-on-a-chip applications in detection with enhanced sensitivity, microreactors for multicomponent reactions, and material synthesis with abbreviated times.