From century-long studies to emerging frontiers: The power of light force

Graphical abstract

A light beam, such as a laser beam, carries photons that possess both momentum and energy. When a laser beam illuminates a microscopic object, the momentum and energy of these photons can be converted into a light force, which can set the object in motion or even cause it to levitate within a medium by counteracting the gravitational force. The nature of the light force depends on the properties of the object’s material. If the material is transparent to light, the photon’s momentum is transferred to the object, creating a light force known as the radiation pressure force, which has two components: the scattering force, which pushes the object away, and the gradient force, which pulls it toward the higher intensity region, such as the focal point of a laser beam. If the material absorbs light, the object takes up the photons’ energy, resulting in heat generation and an increase in the object’s temperature. This heating induces gas molecular dynamics around the object’s surface, producing a net force called the photophoretic force. This force arises from a temperature gradient across the object’s surface (e.g., one side becoming hotter than the other) and/or a difference in the object’s thermal accommodation coefficients.

In the 1970s, Ashkin et al. [1, 2] demonstrated the first particle levitation using radiation pressure force. His pioneering work uses a tightly focused laser beam (so-called optical tweezers) to create a stable optical field that confines non-absorbing particles at the focal point of the laser beam. The radiation pressure force is highly effective for levitation, trapping, and manipulating micron-sized objects [3−6]. However, as an object’s size increases, the gravitational force dominates, reducing the effectiveness of the radiation pressure force on larger objects.

Alternatively, the use of photophoretic force to manipulate objects can be traced back to the late 19th century, with Crookes’s experiments [7] and the invention of the Crookes radiometer [Fig.1(I)] [8]. In his experiments, light-induced heating on vanes produced motion driven by radiometric force — a form of photophoretic force — that occurs when one side of the vane’s surface is heated more than the other. This causes gas molecules on the hotter side to gain additional kinetic energy and impart greater momentum upon collision. The resulting asymmetry in the momentum flux generates a net force that pushes the object away from the hotter side. Unlike radiation pressure force, this force depends on differential heating across the surface and can be several orders of magnitude stronger, allowing object manipulation to extend from microscopic to macroscopic domains. Applications of light forces in the study of microscopic objects have expanded rapidly over the last two decades across diverse research fields, including physics, materials science, chemistry, atmospheric science, and plasma physics [9−12]. However, the manipulation of macroscopic objects using light forces remains rare. Only limited studies have reported the use of radiometric force to drive objects of up to centimeters in size [13−16].

Fig.1 The evolution of experimental designs showing radiometric force, spanning over a contrary. (I) The invention of Crookes’ radiometer in which the parts marked as A, B, and C are the coated surface, the uncoated surface, and the partial vacuum glass bulb, respectively. (II) A micromotor with curved vanes incorporating light-absorbing materials that are evenly distributed, such that the convex side absorbs more photon energy than the concave side, causing the motor to rotate in the direction of the light when it shines on the convex side. (III) Motors with curved vanes of 16 mm × 16 mm × 0.05 mm in size, designed for rapid local thermal equilibrium on both surfaces of the vanes, resulting in rotation from the convex to the concave side, regardless of which side is illuminated by the light. (I) Reproduced from Ref. [8], (II) from Ref. [13], with copyright permissions from APS, and (III) reproduced using Fig. 4 from Ref. [16] with permission.

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Achieving a better understanding of radiometric force has involved contributions from several renowned scientists such as Maxwell, Reynolds, and Einstein over a century. Yet an accurate and quantitative illustration of radiometric force remains elusive [17−20]. Today, radiometric force is generally categorized into three components: the area force, the edge force, and the shear force, their production mechanisms depend on the Knudsen number Kn (the ratio of the mean free path of gas molecules to the flow characteristic length scale).

If we define Kn in four regimes, Kn > 10, the free molecule regime; 0.1 < Kn < 10, the translational flow regime; 0.001 < Kn < 0.1, the slip flow regime; and Kn < 0.001, the continuum flow regime [21−23], predominant radiometric forces are observed in the translational and slip flow regimes. At a large Kn, the area force is dominant and acts from the hotter side to the cooler side, as demonstrated in the Crookes radiometer [Fig.1(I)]. To achieve a large Kn, we can either increase the mean free path of gas molecules by decreasing the pressure or reduce the size of the vane at a given pressure. The area force is created by the differential momentum flux of gas molecules between the hot and cold surfaces, e.g., in the flat vane. At a small Kn, both edge force and shear force become more dominant than the area force. The edge force results from the thermal creep of the flow of gas molecules, where gas molecules move along surfaces from regions of lower temperature to higher temperature, e.g., from the edge to the central area of the vane, generating a larger momentum flux difference at the edges of the vane. The edge force is similar to the area force, both acting in the same direction from the hot surface to the cold surface. This transitional regime often provides the maximum total radiometric force — for example, at Kn ≈ 0.1. The shear force takes precedence in small Kn, typically one order of magnitude smaller than the area force. The thermal creep driving the lateral flow along the vane’s surface is attributed to the shear force mechanism. The shear force in a thin flat vane, e.g., h/d $\ll$ 1 where h and d are the thickness and dimension of the vane respectively, is trivial as compared to the area force and the edge force. Experimental observations, kinetic theory, and computational simulations for these three radiometric forces acting on flat vanes housed in a partial vacuum, all have agreed well. However, defining a precise quantitative boundary among the three radiometric forces remains unresolved.

In addition to pressure and vane size (defining the Knudsen number, Kn), radiometric force is influenced by the shape of the vanes. The impact of vane shape on radiometric force — affecting both the force’s amplitude and the type — is arguably highlighted in recent studies by Han et al. [13] and Chen et al. [16]. These studies used similar but distinct vane designs, as illustrated in Fig.1(II) and (III).

The most recent study by Chen et al. [16] represents a comprehensive exploration of radiometric forces, demonstrating how light can be used to manipulate centimeter-sized curved vanes [Fig.1(III)] and how the shape of the vane influences the type of radiometric force. This study extends the design of the earliest Crookes radiometer, in which one side of flat vanes is coated and heated [Fig.1(I) and (III-b)], causing the vanes to rotate from the hotter side to the cooler side, driven by both area force and edge force in the slip flow regime, to the design of curved vanes that are uniformly painted on both sides [Fig.1(III-a)] and where motion is driven by shear force, maximizing at Kn ≈ 0.1.

The experiment by Chen et al. [16] also includes the case presented in the work by Han et al. [13] in which curved vanes were used to form a micromotor. The major difference between these studies lies in two different force mechanisms. Han’s motor rotates in the direction of the light propagation when illuminated on the convex side, which absorbs more light energy than the concave side. In the slip flow regime, the vanes are several millimeters in size; the force mechanism is explained by edge force arising from the thermal creep of gas molecules, which generates uneven momentum flux of gas molecules in the direction normal to the edge surface, driving the motion of the motor. However, in Chen’s setup [Fig.1(III)], the curved vanes rotate in a single direction regardless of whether the laser beam shines on the concave (case III-c) or convex (III-e) side, with the radiometric force attributed to shear force. Although both studies operate at similar Knudsen numbers, one mechanism is due to edge force, while the other is due to shear force, demonstrating that the radiometric force can be in the opposite direction of light propagation. Both cases are well explained by their computational simulations of gas flow dynamics.

It remains unclear whether Han’s study also investigated laser interaction on the concave side of the vane [13]. Nevertheless, integrating these two studies into a cohesive framework for radiometric forces remains a significant challenge. In Chen’s work [16], a pressure force (Fn) was introduced, attributed to differences in the molecular gas kinetics due to unbalanced collision frequencies on the convex and concave sides of the vanes. Their computational simulations show that the temperature gradient dT/dx of the gas molecules differs in the convex and concave regions, generating a differential momentum flux. This raises an interesting question: Fn is neither the area force, the edge force, nor the shear force, as defined previously for the flat vanes; yet the Fn is fundamentally of the nature of the area force. This difference is arguably not directly related to the temperature gradient on the surface of the vanes, as both sides reach local thermal equilibrium rapidly at specific points on the vane’s surface due to the high thermal conductivity of the thin metal sheet sandwiched between two uniformly coated surfaces. Rather, the difference in the momentum flux results from the shape-driven temperature gradient of the gas molecules in the front and the back regions. This argument is supported by the experiment with the design of flat vanes shown in Fig.1(III-d), in which a net Fn is zero as the dT/dx is the same in the front and back of the flat vane and shear forces cancel out.

Their computational simulations show that Fn is as significant as the shear force [16]. Even without accounting for Fn​ in cases (c) and (e) [Fig.1(III)], the radiometric force consistently acts in a single direction toward the concave side, which can be adequately explained by the direction of the net shear force alone. This experiment highlights that object geometry is as important as the gas pressure and size of the object in determining radiometric forces. The findings suggest that the temperature gradient should broadly include two distinct cases: the temperature gradient on the surface of the vane (e.g., in the case of a flat, unevenly coated vane) and the surfaces of the vane are in the local thermal equilibrium but gas molecules have different temperature gradients in the front and back regions of the vane (e.g., in the case of a curved, evenly coated vane). We anticipate that future studies using even more diverse vane geometries, such as a curved vane with micro-holes, a vane surface of a sinusoidal wave shape, or a vane of a shallow-vertex shape, will further advance the understanding of radiometric forces.

Compared to numerous experimental studies of radiometric forces, which span more than a century, there are limited computation studies to date, partially due to the evolution of fast computing that is available and continuously updated only in the last decades. Computational simulations of radiometric forces in rarefied gas flows face several challenges. Highly detailed approaches like molecular dynamics (MD) provide precise insights but are computationally prohibitive for larger or multi-scale domains, while the direct simulation Monte Carlo (DSMC) method, although more scalable, remains costly in low-speed or high-resolution scenarios, where long timescales and low signal-to-noise ratios increase the computational burden [13]. Simplified kinetic models like ES-BGK offer efficiency by assuming equilibrium conditions yet may fail to capture essential non-equilibrium dynamics in transitional flow regimes, where radiometric forces are highly sensitive [25, 26]. Additionally, many applications require modeling mixed boundary conditions, such as specular and diffuse reflections, which DSMC can handle but at significant computational expense when high spatial resolution is needed. Balancing micro- and macro-scale interactions poses further challenges, as applications demand an understanding of localized molecular effects and broader flow patterns. Hybrid methods, such as combining MD with DSMC or selectively using DSMC alongside ES-BGK, attempt to manage these issues yet achieving a seamless integration of these methods without computational penalties remains complex. Chen et al. [16] used the Comsol Multiphysics^TM simulation software to simulate the distributions of velocity and temperature gradient of the gas molecules near the vanes. They derived the area force and shear force from the temperature gradient using the DSMC method [24]. This two-step approach represents one of the best options to date. Taking advantage of ever-increasing computation power, future studies are expected to include new computational methods and direct side-by-side comparisons of methods when applied to the same cases. Such contributions could bridge the gap in our understanding of radiometric forces across diverse experimental settings and provide a conclusive and quantitative framework for radiometric force.

One reason the topic of radiometric force has fluctuated in interest over more than a century could be due to two main factors: (i) the challenge of finding analytical solutions to the complex, multi-variable gas kinetic problems in different settings, and (ii) the continued advent of fast computing, which periodically renews interest in the topic with increasingly clear illustrations of radiometric forces, as seen in recent studies. The driving force behind these revisits and the continued effort over the decades stems not only from scientists’ eagerness to satisfy their curiosity but also from the potential of demonstrated or proposed applications of radiometric forces. The latter is exemplified by several recent works [27−31], which involve, but are not limited to, the following highlighted areas of applications.

　1) High-altitude and space propulsion systems: Radiometric forces could support low-cost, solar-powered flight systems in low-pressure space environments. Such systems could propel lightweight, autonomous vehicles in near-space atmospheres, enabling cost-effective space exploration.

　2) Biomedical applications: The precise, non-contact manipulation with radiometric forces could facilitate micromachining and the handling of delicate biological samples. Using controlled optical fields to direct microscopic and mesoscopic tools offers potential for microsurgical advancements.

　3) Manufacturing and material sorting: Radiometric forces could revolutionize manufacturing by enabling automated, contamination-free sorting and manipulation of materials without mechanical contact. In settings requiring extreme sterility, such as pharmaceutical manufacturing, light-induced manipulation could offer advantages over traditional mechanical sorting systems.

　4) Hybrid systems: A hybrid system combining radiometric forces with electrostatic or magnetic controls could enhance precision by offering multi-axis manipulation capabilities, making this technology adaptable for diverse applications, from micro-robotics to environmental monitoring.

Therefore, exploring novel applications of radiometric force is highly encouraged in future studies.

This commentary highlights the fascinating potential of radiometric forces, particularly in manipulating macroscopic objects using light. The evolving understanding of these forces, supported by advancements in experimental techniques and computational simulations, has opened new avenues to push boundaries further across various fields. The recent work by Chen et al. [16] exemplifies how radiometric forces can be harnessed effectively at larger scales, pushing the boundaries beyond traditional applications, e.g., from driving a micromotor to lifting a macroscopic object.

The unique characteristics of radiometric forces — including their dependence on Knudsen number, temperature gradient, and object geometry — offer exciting opportunities for applications in high-altitude propulsion, biomedical micromanipulation, contamination-free manufacturing, and hybrid systems for multi-axis control. As computation power continues to grow, future studies may focus on developing new models and conducting direct comparisons of methodologies to refine the theoretical framework of radiometric forces. In the meantime, novel experimental systems utilizing radiometric force, showcasing the promise of future applications, are highly encouraged.

A unified model that comprehensively explains different types of radiometric forces, across varying experimental settings and object geometries, has yet to be fully developed. The evolution of experimental observations of radiometric forces as highlighted in Fig.1 implies the complexity of this task, as different force mechanisms (e.g., edge force, shear force) arise under similar conditions, each influenced by specific parameters. Integrating these findings into a coherent theoretical foundation will be crucial.

In conclusion, radiometric forces present an invaluable area of exploration for future technological innovation. Their diverse applications and the increasing clarity in their theoretical underpinnings offer a promising frontier. Continued research, particularly with innovative vane geometries and computational approaches, will likely drive this field forward, bringing radiometric force closer to practical implementation in areas that have light and material interactions. The concept of radiometric force was introduced over a century ago, and while our understanding of its mechanisms has become increasingly clear and is nearing completion, its potential applications are still in their infancy.

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Acknowledgements

The author is grateful for the support of the National Science Foundation, Plasma Physics Program via grant No. 2308947 and the support of the NASA Emerging Worlds NNH22ZDA001N-EW with grant No. 22-EW22–0016. This work was also supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences under award number DE-SC-0021030.

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