A 3D-printed microdevice for dielectrophoretic torque–driven rotation of dielectric microspheres to support development of manipulation systems for zebrafish eggs

Abstract

Precise control of microscale object rotation is essential for numerous biomedical and microelectromechanical applications. For example, somatic cell nuclear transfer for aquatic biomedical models such as zebrafish faces significant technical challenges, particularly in egg trapping and alignment of an injection needle with the micropyle. In this study, we developed a 3D resin-printed microdevice to achieve frequency-selective electrorotation of dielectric microspheres using a quadrupole electrode configuration driven by phase-shifted alternating current (AC). Theoretical analysis based on the Clausius–Mossotti factor, which governs the polarization of a particle concerning its surrounding environment, highlights the critical role of its imaginary component in the induced dipole moment from the AC field that generates torque. Simulations conducted in COMSOL Multiphysics confirmed the formation of symmetric torque-driven rotation without significant micro-scale object translation. The frequency response of angular velocity exhibited a unimodal profile, with a peak near 4 MHz corresponding to maximum torque efficiency. Experimental validation using 700 μm polystyrene microspheres in Dulbecco’s Phosphate Buffered Saline demonstrated consistent clockwise rotation, with a peak angular velocity of 8.1° s⁻¹ observed at 900 kHz and 16 Vp–p. Although the experimental peak angular velocity occurred at a lower frequency than the theoretical maximum, the rotational trend followed the polarization relaxation behavior captured by $\mathrm{I}\mathrm{m}\left[K_{\mathrm{c}\mathrm{m}}\right]$. Parameter studies further revealed that increasing microscale object permittivity amplified torque generation, while higher medium permittivity reduced it, underscoring the tunability of electrorotation via dielectric properties. This work demonstrates a robust and scalable platform for manipulating large microscale objects. It lays the foundation for future applications involving biologically relevant objects, such as eggs of biomedical research models.

1. Introduction

Precise manipulation of microscale objects and biological objects is a fundamental requirement in many areas of biotechnology [1]. This includes, but is not limited to, applications such as somatic cell nuclear transfer (SCNT) [2, 3], single-cell analysis [4, 5], high-resolution cell imaging [6], studies of cellular function in different organisms [7], and morphological characterization [8]. SCNT is a pivotal assisted reproductive technique that involves transplanting the nucleus of a somatic cell into an enucleated oocyte [2]. This requires at least two precise positioning of the embryo for laser ablation and microinjection. In recent decades, zebrafish (Danio rerio) have drawn increasing attention in the development of SCNT technologies, particularly due to the demand for generating, cryopreserving, and managing genetic lines through germplasm repositories aimed at conserving aquatic biodiversity. However, the SCNT process in zebrafish presents significant technical challenges, particularly in efficiently trapping the egg and aligning it with the micropyle. Beyond biological applications, microscale object manipulation is also critical for the direct assembly of nanowires, which can be applied in the development of micro-batteries, artificial fibers, and sensors [9].

A wide range of physical techniques has been developed to enable the controlled positioning, translation, and rotation of microscale and nanoscale objects. These include micromanipulators [10, 11], optical tweezers [12], magnetic devices [13], acoustic devices [14], electrical devices [15], and robotic systems [16]. Among these, electric field-based techniques, particularly dielectrophoresis (DEP) and electrorotation, offer several compelling advantages: they are label-free, non-contact, highly tunable, compatible with microfluidic integration, and are applicable to biological and synthetic microscale objects. When integrated into lab-on-a-chip platforms, these techniques enable automated and parallel control of microscale and nanoscale targets, making them particularly suitable for microfluidic applications [17, 18]. Overall, electrical devices have attracted more attention in microscale object manipulation due to their low cost, high throughput, and precision.

Electrophoresis refers to the movement of charged microscale objects in an electrolyte under the influence of a uniform electric field. This motion is driven by interactions between the surface charges of the microscale object and the surrounding electrical double layer. Electrophoretic techniques are effective for charged microscale objects, but more neutral microscale objects, such as aquatic species eggs, require alternative electrokinetic approaches, such as electrorotation and DEP for manipulation [19]. Electrorotation occurs when microscale objects rotate continuously due to the torque generated by electrostatic interactions between the electric field and the polarization charges within the cells. This can be achieved using four planar electrodes arranged symmetrically around a central point, where phase-shifted alternating current (AC) signals are applied [8, 20].

DEP refers to the motion of electrically neutral but polarizable microscale objects when subjected to a spatially non-uniform electric field. This effect arises from the induced polarization of the microscale object; when the dielectric properties of the microscale object differ from those of the suspending medium, a net force is generated that drives the microscale object either toward or away from regions of high electric field intensity. This behavior depends on the effective polarizability of the microscale object relative to the medium and is classified as positive DEP (pDEP) when the microscale object is attracted to high-field regions or negative DEP (nDEP) when it is repelled toward lower-field regions [4, 9, 21]. The direction and magnitude of the DEP force depend on several factors, including microscale object size, the dielectric properties of the microscale object and the surrounding medium, the frequency of the applied electric field, and the gradient of the field intensity [22]. A key parameter governing this force is the Clausius–Mossotti factor ($K_{\mathrm{c}\mathrm{m}}$), which quantifies the polarization of the microscale object relative to the medium.

Previous electrorotation studies have primarily focused on manipulating cells and sub-micron to micron-scale particles using cleanroom-fabricated microelectrode arrays [7, 23, 24]. Only a few works have extended these techniques to large biological objects such as zebrafish eggs, and these relied on conventional microfabrication, which is costly and less accessible. In contrast, our study introduces the first resin-based, 3D-printed electrorotation microdevice (ERM) for egg-scale specimens, providing rapid, low-cost prototyping and straightforward customization of electrode geometry. This approach not only bridges a critical gap between fundamental electrokinetic studies on cells and practical applications in reproductive biotechnology but also highlights how resin 3D printing can lower barriers for open-source hardware development. Because designs can be easily shared, reproduced, and modified by other laboratories without specialized cleanroom facilities, this platform promotes broader adoption and collaborative innovation. By targeting millimeter-scale biological specimens, this work establishes both a technical advance in device fabrication and new biological insights into electrorotation of large microscale objects, positioning the system as a foundation for future applications in aquatic egg manipulation and beyond.

This study aimed to develop prototypes of a 3D-printed ERM capable of achieving the controlled orientation of microspheres using rotating electric fields. The specific objectives were to: (1) design and fabricate the ERM using high-resolution 3D resin printing; (2) theoretically investigate the effects of key parameters, such as electric field frequency, amplitude, and electrical properties of medium and microsphere on microsphere rotational velocity and $K_{\mathrm{c}\mathrm{m}}$; (3) simulate (using COMSOL Multiphysics) the rotational dynamics of microspheres under varying electric field conditions to assist design and testing, and (4) validate the feasibility of using the fabricated prototypes to achieve controlled rotation of microspheres by comparing the experimental results with simulation predictions. In this work, a microdevice system was developed in which DEP torque was applied to induce its rotation. Using a rotating electric field, stable and controllable electrorotation of a large polystyrene microsphere (PS microsphere ~700 μm in diameter) was produced within a 3D resin-printed microdevice. This work lays a strong foundation for adapting electrorotation-based platforms to address challenges in biomedical research, enabling future development of reproducible, scalable, high-throughput techniques for gamete manipulation and preservation.

2. Materials and methodology

DEP was used to manipulate microscale objects based on their frequency-dependent polarizability contrast with the surrounding medium. The direction of DEP motion, whether toward or away from high-field regions, was characterized experimentally under varying field frequencies and medium conductivities.

2.1. ERM design and fabrication

A key innovation of this study was the fabrication of a microdevice using 3D resin printing (Profluidics 285D, CADworks3D, Concord, ON). The microdevice design was created using computer-aided design (CAD) software (Fusion 360, Autodesk, San Rafael, CA, USA), allowing precise control over geometry and electrode alignment. Unlike traditional photolithography-based methods, which are often costly and time-intensive, this 3D printing approach provided a rapid and cost-effective alternative for microdevice prototyping and fabrication [25–27]. The printed microdevice featured a central semi-spherical chamber with a diameter of 850 μm, designed to accommodate large biological objects such as zebrafish eggs, which typically range around 700–800 μm in diameter [28]. This central chamber was fabricated using clear microfluidic resin V7.0a (Product ID: CW3D-R-CMV7A-1 KG, CADworks3D, Concord, Ontario), enabling visual tracking and alignment during experimentation. Surrounding the chamber, a quadrupole electrode configuration was implemented using four copper wires with square cross-sections (500 μm × 500 μm; Thermo Fisher Scientific, US). These electrodes were manually inserted into 3D-printed guide channels that matched their dimensions, providing stable alignment. A small internal shoulder was integrated into each guide channel adjacent to the semispherical chamber to physically stop the electrode at a defined depth, preventing over-insertion and ensuring consistent electrode positioning relative to the chamber center. Each electrode was recessed approximately 50 μm into the printed base to ensure mechanical stability and consistent contact. The electrodes were symmetrically arranged in a square layout around the chamber to generate a rotating electric field suitable for electrorotation. The white 3D-printed base served as a fixture for connecting the quadrupole electrodes to the alligator clips using male-female pin connectors.

This configuration enabled precise DEP manipulation of dielectric microspheres (figure 1). To generate the required four phase-shifted AC signals, two synchronized function generators (SDG2122X, Siglent Technologies, Ohio, US) were used. Phase alignment between the generators was achieved through external triggering and manual adjustment to ensure accurate 90° phase shifts. The synchronization accuracy was verified using a digital oscilloscope (SDS1000X-U Series, Siglent Technologies, Ohio, US), confirming stable and repeatable waveform outputs across all four channels. The rotation of the 700 μm polystyrene (Polysciences, PA, US) beads in Dulbecco’s Phosphate Buffered Saline (DPBS; Thermo Fisher Scientific, US) was monitored in real-time using an inverted microscope (Nikon Diaphot 300, NY, US) equipped with an AmScope MU1003 digital camera (10 MP APTINA CMOS sensor; AmScope, CA, US), operating at an acquisition rate of up to 27 frames per second.

Figure 1.

Experimental setup showing the electrorotation microdevice (ERM) integrated with dual-function generators, oscilloscope, and microscope for real-time monitoring of microsphere rotation. The close-up images highlight the central region of the device, showing the electrode and the semispherical well where the droplet containing the microsphere is positioned.

2.2. Theoretical modeling of frequency and material effects

The Clausius–Mossotti factor $K_{\mathrm{c}\mathrm{m}}$ is a complex function that relates the dielectric properties of the microscale object (${\epsilon }_{\mathrm{p}}$) and the medium $\left({\epsilon }_{\mathrm{m}}\right)$ [29]. It is given by:

$$K_{\mathrm{c}\mathrm{m}}={\epsilon }_{\mathrm{p}}^{\mathrm{*}}-\raisebox{1ex}{${\epsilon }_{\mathrm{m}}^{\mathrm{*}}$}\!\left/ \!\raisebox{-1ex}{${\epsilon }_{\mathrm{p}}^{\mathrm{*}}$}\right.+2{\epsilon }_{\mathrm{m}}^{\mathrm{*}}$$ (1)

$${\epsilon }^{\mathrm{*}}=\epsilon -j\frac{\sigma }{\omega }$$ (2)

where ${\epsilon }_{\mathrm{p}}^{\mathrm{*}}$ is the complex permittivity of the microscale object, ${\epsilon }_{\mathrm{m}}^{\mathrm{*}}$ is the medium’s complex permittivity, $\sigma$ is the conductivity and $\omega$ is the angular frequency of the electric field. The real part of $K_{\mathrm{c}\mathrm{m}}$ indicates the strength and direction of the DEP force. In contrast, the imaginary part is associated with the rotational behavior of microscale objects in a nonuniform electric field. The dielectrophoretic force ($F_{\text{DEP}}$) acting on a spherical microscale object can be expressed as:

$$F_{\mathrm{D}\mathrm{E}\mathrm{P}}=2\pi R^3{\epsilon }_{\mathrm{m}}\mathrm{R}\mathrm{e}\left[K_{\mathrm{c}\mathrm{m}}\right]\nabla E^2$$ (3)

where $R$ is the radius of the microscale object, ${\epsilon }_{\mathrm{m}}$ is the permittivity of the surrounding medium, $\mathrm{R}\mathrm{e}\left[K_{\mathrm{c}\mathrm{m}}\right]$ is the real part of the Clausius–Mossotti factor, $\nabla E^2$ is the gradient of the square of the electric field intensity [30]. In addition to translational forces, DEP can also induce rotational torque on a microscale object due to the interaction of its induced dipole with the time-varying electric field. This is referred to as electrorotation [31], and the resulting torque (${\mathrm{\Gamma }}_{\text{ROT}}$) on a spherical dielectric microscale object is given by:

$${\mathrm{\Gamma }}_{\mathrm{R}\mathrm{O}\mathrm{T}}=-4\pi R^3{\epsilon }_{\mathrm{m}}\mathrm{I}\mathrm{m}\left[K_{\mathrm{c}\mathrm{m}}\right]E^2$$ (4)

where $\mathrm{I}\mathrm{m}\left[K_{\mathrm{c}\mathrm{m}}\right]$ is the imaginary part of the Clausius–Mossotti factor, which determines the rotational effects on the microscale object, and $E^2$ is the square of the electric field intensity. This torque causes the microscale object to spin about its axis and is particularly pronounced when the microscale object experiences a rotating electric field created by applying phase-shifted AC signals to microelectrodes. The crossover frequency ($f_{\text{crossover}}$) is a key parameter in DEP, marking the transition point between nDEP and pDEP [32],

$${\mathrm{f}}_{\text{crossover}}=\frac{1}{2\pi }\cdot \frac{{\sigma }_{\mathrm{m}}-{\sigma }_{\mathrm{p}}}{{\epsilon }_{\mathrm{p}}-{\epsilon }_{\mathrm{m}}}.$$ (5)

It occurs when the real part of the Clausius–Mossotti factor, $\mathrm{R}\mathrm{e}\left[K_{\mathrm{c}\mathrm{m}}\right]$, equals zero, resulting in no net dielectrophoretic force. This frequency depends on the relative conductivities and permittivities of the microscale object and the surrounding medium, as well as the frequency of the applied AC field. When the medium is more conductive than the microscale object (${\sigma }_{\mathrm{m}}>{\sigma }_{\mathrm{p}}$), nDEP dominates at low frequencies due to stronger polarization of the medium. As frequency increases, dielectric effects become more significant, and if the microscale object has a higher permittivity (${\epsilon }_{\mathrm{p}}>{\epsilon }_{\mathrm{m}}$), it becomes more polarizable than the medium, resulting in pDEP. This shift reflects the transition of the system from conduction-dominated to polarization-dominated behavior, governed by how charges respond to varying field frequencies. To achieve rotational motion, a rotating electric field was applied by energizing the quadrupole electrodes with four sinusoidal signals phase-shifted by 90°. The induced torque on the microscale object is described by

$${\mathrm{\Gamma }}_{\text{ROT}}\propto \mathrm{I}\mathrm{m}\left[{\alpha }_{\text{eff}}\left(f\right)\right]E^2.$$ (6)

To describe how a heterogeneous microscale object, such as a biological cell or composite material, interacts with an external electric field when suspended in a medium, we used the concept of effective polarizability, ${\alpha }_{\text{eff}}\left(f\right)$, which is frequency-dependent and given by the following equation [33–35]. Here, ${\alpha }_{\text{eff}}\left(f\right)$ is the frequency-dependent effective polarizability of the microscale object, which incorporates energy dissipation and phase lag:

$${\alpha }_{\mathrm{e}\mathrm{f}\mathrm{f}}\left(\mathrm{f}\right)=4\pi {\epsilon }_{\mathrm{m}}\mathrm{I}\mathrm{m}\left(\frac{{\epsilon }_{\mathrm{p}}^{\mathrm{*}}-{\epsilon }_{\mathrm{m}}^{\mathrm{*}}}{{\epsilon }_{\mathrm{p}}^{\mathrm{*}}+2{\epsilon }_{\mathrm{m}}^{\mathrm{*}}}\right).$$ (7)

The imaginary component of ${\alpha }_{\text{eff}}\left(f\right)$ captures the phase lag between the applied field and the induced dipole of the microscale object, which drives rotation. The Clausius–Mossotti relation embedded in this expression determines the response of the microscale object based on the permittivity contrast between the microscale object and the surrounding medium. The imaginary component of this relationship plays a crucial role in phenomena, such as torque generation and dielectrophoresis, both of which are particularly relevant in microfluidic and bioelectronic applications [36]. The viscous drag torque on a spherical microscale object in a fluid is proportional to its angular velocity ($\mathrm{\Omega }$):

$${\tau }_{\text{drag}}=-8\pi \eta r^3\mathrm{\Omega }$$ (8)

where $\eta$ is the viscosity of the surrounding medium. This expression assumes low Reynolds number flow, where viscous forces dominate and inertial effects are negligible. At the steady state, the driving torque ($\tau$) balances the viscous drag torque (${\tau }_{\text{drag}}$):

$$\tau +{\tau }_{\text{drag}}=0.$$ (9)

The driving torque depends on the effective polarizability (${\alpha }_{\text{eff}}$) of the microscale object, which quantifies how strongly the microscale object responds to the applied electric field. Specifically:

$$\tau \propto \mathrm{I}\mathrm{m}\left({\alpha }_{\text{eff}}\right)E^2.$$ (10)

Then, the angular velocity $\mathrm{\Omega }\left(f\right)$ of a microscale object subjected to a rotating electric field is frequency-dependent and can be expressed as:

$$\mathrm{\Omega }(\mathrm{f})=\frac{1}{8\pi \eta }\mathrm{I}\mathrm{m}(\alpha \text{eff}){\mathrm{E}}^2=\frac{{\epsilon }_{\mathrm{m}}}{2\eta }\mathrm{I}\mathrm{m}\left(\frac{{\epsilon }_{\mathrm{p}}^{\mathrm{*}}-{\epsilon }_{\mathrm{m}}^{\mathrm{*}}}{{\epsilon }_{\mathrm{p}}^{\mathrm{*}}+2{\epsilon }_{\mathrm{m}}^{\mathrm{*}}}\right){\mathrm{E}}^2.$$ (11)

This relationship underscores how the interplay between the viscous drag of the medium and the electrical response of the microscale object governs its rotational behavior [23]. The imaginary component of the Clausius–Mossotti factor accounts for energy losses due to phase delays between the applied field and the induced dipole moment, which directly impacts the torque acting on the microscale object. The effective polarizability (${\alpha }_{\text{eff}}$) depends on the frequency of the applied field through the complex permittivities (${\epsilon }_{\mathrm{p}}^{\mathrm{*}}$ and). At low frequencies, charges have more time to redistribute, leading to strong polarization but minimal phase lag and thus low torque. As frequency increases, the phase lag grows while polarization remains substantial, producing the peak torque. At high frequencies, polarization weakens due to insufficient charge response time, causing torque and rotational velocity to decline.

2.3. Simulation of electrorotation behavior

Finite element simulations were conducted using COMSOL Multiphysics^® (version 6.3, COMSOL Inc., Burlington, MA, USA) to model the electric field distribution and electrorotational torque generated within the 3D-printed microdevice. The simulated geometry represented a suspended PS microsphere in DPBS medium, surrounded by four embedded copper electrodes arranged in a quadrupole configuration. Each electrode was driven by a sinusoidal signal phase-shifted by 90°, producing a rotating electric field intended to induce torque on a suspended PS microsphere. While the experimental setup involved a suspended droplet with more complex boundary conditions, the simulation employed a simplified, symmetric structure to isolate and highlight the fundamental mechanisms driving electrorotation. Three physics interfaces were used: Electric Currents to solve the AC electric field, Domain ODEs and DAEs (ordinary differential equations and differential-algebraic equations) to compute angular velocity based on torque balance, and Particle Tracing for Fluid Flow to visualize microscale object behavior and confirm minimal translational displacement. The simulation incorporated the complex permittivities of the PS microsphere (relative permittivity 2.6, conductivity 0.01 S m⁻¹) and DPBS medium (relative permittivity 80, conductivity 1.4 S m⁻¹) using equation (2), with terminal boundary conditions applying a 16 Vp–p sinusoidal voltage to the electrodes. Frequencies were swept from 100 kHz to 10 MHz to resolve the frequency-dependent electrorotational response. The driving torque was calculated using the imaginary part of the effective polarizability, $\mathrm{I}\mathrm{m}[{\alpha }_{\text{eff(f)}}]$, and the resulting angular velocity was determined by solving the rotational equation of motion, $\mathrm{I}\frac{\mathrm{d}\mathrm{\Omega }}{\mathrm{d}\mathrm{t}}+{\tau }_{\text{drag}}=\tau$, Where $\mathrm{I}=\frac{2}{5}{\mathrm{m}\mathrm{R}}^2$ is the moment of inertia of the microscale object.

2.4. Experimental setup and validation of microsphere rotation

To validate the performance of the fabricated device and assess its ability to achieve controlled rotation of microspheres, we conducted electrorotation experiments at various frequencies (100–1.5 MHz) and voltages (5–20 V). Rotational behavior was observed in real time using the inverted microscope. The geometry of electrodes plays a pivotal role in shaping the electric field distribution, which in turn governs the effectiveness of DEP and electrorotation. While sharp-tipped electrodes are often utilized to enhance electric field gradients, an advantage in DEP applications where the force depends on the gradient of the squared electric field ($\nabla E^2$), they are not ideal for manipulating large microscale objects such as the 700 μm PS microspheres used in this study. Sharp tips, typically on the order of ~100 μm, generate highly localized fields [37] that interact with only a limited portion of the surface of a large microscale object. This mismatch in scale can result in uneven force distribution, destabilizing rotational behavior, and reducing the uniformity of torque applied across the microsphere. Furthermore, sharp electrodes tend to create field hotspots, which can lead to localized heating under high-voltage conditions, potentially damaging the surrounding medium or the microscale object itself. To overcome these limitations, we employed electrodes with rounded and blunt tips, which promoted a more uniform electric field distribution around the entire surface of the microsphere. This configuration enabled more stable and continuous rotation by ensuring that the quadrupole field engaged the microscale object symmetrically, while also reducing potential thermal hotspots commonly associated with sharp-tip geometries. The design adaptation ensured effective electromechanical interaction across the full surface area of the microscale object, making it well-suited for the scale and functional requirements of the present study.

To assess the electrorotation performance of the ERM, experiments were conducted by loading a single 700 μm PS microsphere suspended in DPBS into the central chamber of the microdevice using a pipette. During early trials, rotation was inhibited due to contact friction between the microsphere and the chamber floor. To resolve this, the device was inverted, allowing the bead to hang from the chamber ceiling within a droplet of DPBS. This adjustment minimized substrate contact, enabling stable and unobstructed rotation. AC signals were applied to the electrodes using two synchronized signal generators to produce four phase-shifted outputs. The input frequency was swept from 100 kHz to 1.5 MHz, and voltage amplitudes were varied from 5 Vp–p to 20 Vp–p. Real-time videos of the rotating microsphere were recorded using the inverted microscope. Angular velocity and rotation rate in degrees per second were determined from video analysis. Each condition was repeated three times to ensure reproducibility. The resulting angular velocity data were plotted as a function of frequency and compared with simulation outputs for validation.

3. Results

3.1. ERM design and fabrication verification

The key advancement of this study was the fabrication of the ERM using high-resolution 3D resin printing, which offered a rapid and cost-effective alternative to conventional photolithography. Each ERM required ~20 min to print and consumed less than a dollar in resin material, making the process highly scalable for iterative design and prototyping. Compared with standard photolithography, the printing process reduces work and material costs by around two orders of magnitude and fabrication time by at least one order of magnitude. The open hardware-compatible design also facilitates easy replication across laboratories. The printed device featured a quadrupole electrode configuration composed of 500 μm-thick copper tracks embedded around a semi-spherical chamber (figure 2). Assembly of the ERM was straightforward, requiring no cleanroom facilities or specialized alignment steps. Copper electrodes were manually inserted and connected to alligator clips via standard pin connectors. This architecture was designed to produce a rotating electric field suitable for inducing electrorotation in dielectric microspheres, and signal testing verified reliable delivery of four phase-shifted AC inputs to the electrodes. Initial validation experiments were conducted using 700 μm PS microspheres suspended in DPBS.

Figure 2.

Schematic of the 3D resin printed microdevice featuring a quadrupole copper electrode configuration designed to generate a rotating electric field for microsphere manipulation.

3.2. Theoretical analysis of frequency and material effects on electrorotation

The frequency-dependent behavior of the Clausius–Mossotti factor was analyzed to understand torque generation under varying dielectric conditions (figure 3(a)). The frequency sweep for PS microspheres suspended in DPBS, the real part of the Clausius–Mossotti factor, remained negative throughout the examined range, consistent with the lower conductivity of the microscale object (0.01 S m⁻¹) relative to the medium (1.4 S m⁻¹). This condition resulted in negative dielectrophoresis, with no crossover frequency observed. Meanwhile, the imaginary component exhibited a pronounced unimodal peak near 4 MHz. In contrast, suspending PS microscale objects in deionized (DI) water, where the medium conductivity (5.5 × 10⁻⁶ S m⁻¹) was lower than that of the microscale object, resulted in a positive (${\sigma }_{\mathrm{p}}-{\sigma }_{\mathrm{m}}$) contrast (figure 3(b)). This configuration led to a distinct crossover in $\mathrm{R}\mathrm{e}\left[K_{\mathrm{c}\mathrm{m}}\right]$, transitioning from positive to negative values near 1.5 MHz, enabling both positive and nDEP depending on the applied frequency.

Figure 3.

(a) Real and imaginary components of the Clausius–Mossotti factor (${\mathrm{K}}_{\mathrm{c}\mathrm{m}}$) as a function of frequency for polystyrene microscale objects in DPBS medium. (b) Real and imaginary parts of the Clausius–Mossotti factor (${\mathrm{K}}_{\mathrm{c}\mathrm{m}}$) as a function of frequency for polystyrene microscale objects in deionized (DI) water. (c) Theoretical angular velocity of a 700 μm polystyrene microsphere as a function of frequency, computed based on the imaginary part of the Clausius–Mossotti factor ($\mathrm{I}\mathrm{m}\left[{\mathrm{K}}_{\mathrm{c}\mathrm{m}}\right]$). (d) Theoretical angular velocity as a function of applied voltage (Vp–p), evaluated across five frequencies ranging from 500 kHz to 1.5 MHz. (e) Imaginary part of the Clausius–Mossotti factor as a function of frequency with varying relative permittivity of the microscale object (${\epsilon }_{\mathrm{p}}$). (f) Imaginary part of the Clausius–Mossotti factor versus frequency for various medium relative permittivity values (${\epsilon }_{\mathrm{m}}$).

The corresponding angular velocity of a 700 μm PS microsphere, computed from $\mathrm{I}\mathrm{m}\left[K_{\mathrm{c}\mathrm{m}}\right]$, followed a similar unimodal profile (figure 3(c)). A maximum of approximately 0.17 rad s⁻¹ occurred near 4 MHz, with sharp declines at lower and higher frequencies. The relationship between angular velocity and applied voltage was also explored at discrete frequencies ranging from 0.5 MHz to 1.5 MHz (figure 3(d)). There were quadratic increases in angular velocity with voltage, in agreement with electrorotation torque predictions. Stronger rotational responses were observed at higher frequencies, with the largest velocities occurring at 1.5 MHz. The influence of microscale object permittivity (${\epsilon }_{\mathrm{p}}$) on $\mathrm{I}\mathrm{m}\left[K_{\mathrm{c}\mathrm{m}}\right]$ was examined over a broad frequency range (figure 3(e)). Increasing ${\epsilon }_{\mathrm{p}}$ from 2 to 20 resulted in progressively higher peak amplitudes of $\mathrm{I}\mathrm{m}\left[K_{\mathrm{c}\mathrm{m}}\right]$, while the peak frequency remained relatively constant near 4 MHz.

The effect of the permittivity of the medium (${\epsilon }_{\mathrm{m}}$) on $\mathrm{I}\mathrm{m}\left[K_{\mathrm{c}\mathrm{m}}\right]$ was evaluated (figure 3(f)). As ${\epsilon }_{\mathrm{m}}$ increased from 40 to 120, a significant reduction in peak $\mathrm{I}\mathrm{m}\left[K_{\mathrm{c}\mathrm{m}}\right]$ amplitude was observed, along with a slight shift of the peak frequency to higher values.

3.3. Simulation analysis of electrorotation behavior

Finite element simulations of the electric field magnitude and electric potential distribution at 90° phase intervals over a full AC cycle (figures 4(a)–(e)) confirmed the generation of a symmetric, rotating electric field centered on the microsphere (supplementary video 1). Electric field simulations revealed a symmetrical surface vector distribution around the microsphere. To evaluate the resulting motion, particle trajectory simulations were performed using the Particle Tracing interface in COMSOL (figures 5(a)–(d)). The microsphere exhibited clear rotational behavior while remaining nearly stationary, with the color scale indicating negligible displacement. The frequency response of the electrorotational system (figures 5(e) and (f)) showed that the angular velocity exhibited a unimodal profile, peaking near 4 MHz at just over 0.1 rad s⁻¹, coinciding with the maximum in DEP torque. At both lower and higher frequencies, the torque magnitude decreased.

Figure 4.

(a) Simulated electric field magnitude (|E|, V m⁻¹) around the microsphere, showing a quadrupole field distribution produced by the four-electrode configuration. (b)–(e) Simulated electric potential distribution around the microsphere at 90° phase intervals over one AC cycle, illustrating the rotation of the applied electric field. (b) 0°, (c) 90°, (d) 180°, (e) 270°. The color scale represents the electric potential in volts (V), where red indicates regions of higher potential and blue indicates lower potential. The field distribution confirms the formation of a symmetric, rotating electric field centered on the microsphere. Inset vector plots on the microsphere surface highlight the tangential electric field components responsible for inducing torque.

Figure 5.

Simulated microscale object trajectories at different time and frequencies, shown in (a)–(d) points under a rotating electric field, visualized using the Particle Tracing interface in COMSOL. The color scale indicates the total translational displacement (μm) of the microsphere from its initial position at each time point, with red representing greater displacement and blue representing minimal movement. These results confirm rotational motion with minimal translational displacement, supporting a torque-dominated mechanism. (e) Frequency-dependent angular velocity computed from the torque balance equation, showing a unimodal profile with a peak near 4 MHz. (f) Frequency-dependent DEP torque, derived from the imaginary part of the ${\mathrm{K}}_{\mathrm{c}\mathrm{m}}$, illustrating torque magnitude variations with frequency.

3.4. Experimental analysis of electrorotation behavior

Experimental validation of the ERM was performed using 700 μm PS microspheres suspended in DPBS under a rotating electric field. The optical microscopyimages (figures 6(a)–(c)) showed sequential clockwise rotation of a microsphere at frequencies of 0.8 MHz, 0.9 MHz, and 1 MHz, driven by an applied voltage of 16 Vp–p (supplementary videos 2, 3, 4). The maximum angular velocity (figure 7) of around 8.1° s⁻¹ (0.14 rad s⁻¹) was observed at a frequency of 0.9 MHz and an applied voltage of 16 Vp–p. This value was determined by analyzing time-lapse video recordings captured through an inverted microscope. The rotational motion of the microsphere was tracked frame by frame, and the angular displacement over time was used to calculate the angular velocity. This peak occurred below the theoretical maximum predicted near 4 MHz, yet remained consistent with the expected electrorotational behavior governed by the imaginary component of the $K_{\mathrm{c}\mathrm{m}}$ factor. Theoretical trends were further validated by the observed frequency-dependent rise and fall in rotational speed, consistent with the polarization relaxation process. Additional experimental trials revealed practical voltage constraints. Voltages below 16 Vp–p failed to induce observable microsphere rotation, whereas voltages above 16 Vp–p often resulted in bubble formation (supplementary video 5). These conditions introduced instability and limited the usable operating range for stable rotation. Attempts to perform electrorotation in deionized (DI) water were unsuccessful under the conditions tested herein. In some cases, the beads drifted slightly or oscillated in place, but no sustained or directional rotation was achieved.

Figure 6.

Experimental validation of electrorotation of dielectric microspheres. Time-lapse (in seconds) optical microscopy images showing controlled clockwise rotation (red arrows) of a 700 μm polystyrene microsphere under a rotating electric field at, (a) 800 kHz, (b) 900 kHz, and (c) 1 MHz.

Figure 7.

Experimentally measured angular velocity of the microsphere as a function of applied frequency. A peak rotation speed of approximately 8.1 degrees/s (0.14 rad/s) was observed at 900 kHz, indicating optimal electrorotation performance at this frequency.

4. Discussion

A key motivation behind this work was to develop a resinbased, 3D-printed ERM as a simple, cost-effective, and customizable platform capable of manipulating large biological objects (typically 500–1000 μm in diameter), such as zebrafish eggs, without the complexity of traditional micromanipulation systems (supplementary video 6). In traditional SCNT workflows, egg handling and orientation are typically performed manually under a microscope using micro-pipettes or mechanical micromanipulators, procedures that are time-consuming, operator-dependent, and often require extensive training [2]. The ERM developed in this study provided a non-contact, tunable alternative for controlled rotation and alignment of large dielectric specimens. This approach reduced operational complexity and enabled broader accessibility for laboratories working in developmental biology and aquatic biotechnology. Such systems could perform key steps in SCNT, including egg alignment and manipulation, thereby accelerating the establishment of clonal lines and germplasm repositories. These repositories can play a vital role in preserving the genetic resources of ecologically and economically important aquatic species and in supporting long-term efforts in conservation and reproductive research [38].

4.1. Design advantages and fabrication efficiency of the ERM

Unlike many existing systems that target small biological objects (1–20 μm) using complex electrode arrays and rely on induced charge electroosmosis (ICEO), electrorotation, or combined ICEO, DEP with patterned Indium Tin Oxide (ITO) electrodes [17, 21, 39], the ERM developed in this study was specifically designed for larger microscale objects (~700 μm), such as polystyrene microspheres with future potential for use with zebrafish eggs. While most prior work has focused on manipulating single cells or small particles, efficient control of larger dielectric objects remains relatively underexplored. Such objects are relevant to applications including bio-inspired microrobotics, calibration standards, and studies of hydrodynamic or electrokinetic behavior at larger dimensions. The ERM platform demonstrated stable and controllable rotation of these larger microscale objects using frequency-selective electrorotation in a simple, low-cost 3D-printed device. The results presented herein highlight the practical advantages of using 3D resin printing in microdevice fabrication, particularly for rapid prototyping and tailoring of geometry. Unlike traditional cleanroom-based microfabrication methods, which can be time-consuming, expensive, and inflexible, high-resolution 3D resin printing enables fast, low-cost fabrication of complex, custom microstructures. In addition, this was accompanied by easy electrode integration, which facilitates efficient device assembly. This fabrication approach supports scalable and reproducible production, aligning with open hardware devices that enable easy sharing, customization, and replication of designs across laboratories and various research applications. A comprehensive system for SCNT processing with multiple microdevice is currently being developed by our team. The use of resin 3D printing allows for development of modular units that can be integrated in an open-source platform. This could also facilitate the participation by researchers in the community for future development [40, 41].

The geometry of the electrode tips also played a critical role in shaping the electric field distribution and ensuring stable torque generation. In this device, the electrodes with rounded and blunt tips provided a more uniform tangential field around the rotation zone. This configuration minimized localized field enhancement and Joule heating that can occur with sharp tips, thereby promoting consistent torque and thermal stability during electrorotation. Furthermore, the electrode gap was designed to be approximately equal to the particle diameter, since a smaller gap enhances the electric field strength and thus the electrorotation torque. The electrode thickness was maintained at roughly half the particle diameter to minimize thermal gradients and ensure mechanical stability, providing a practical balance between torque efficiency and thermal safety.

4.2. Theoretical analysis of key parameters

Theoretical analysis emphasized the central role of the Clausius–Mossotti factor, particularly its imaginary component, in governing torque generation and angular velocity. The consistently negative $\mathrm{R}\mathrm{e}\left[K_{\mathrm{c}\mathrm{m}}\right]$ for PS microspheres in DPBS indicates persistent nDEP, unlike in DI water systems where reversed conductivity contrast can enable a crossover to pDEP, this highlights the importance of selecting appropriate particle–medium combinations. Although DI water supports greater electrokinetic tunability, it is unsuitable for some biological samples due to its hypotonic nature and lack of buffering ions [42]. Exposure to DI water risks osmotic stress and premature activation of oocytes. Given the aim of developing a biologically compatible microfluidic system for aquatic egg manipulation, DPBS would be a better medium. It preserves biological integrity while enabling consistent nDEP control.

The unimodal shape of $\mathrm{I}\mathrm{m}\left[K_{\mathrm{c}\mathrm{m}}\right]$ observed in the theoretical analysis (figure 3(a)) reflected a resonance-like behavior governed by polarization relaxation dynamics. At low frequencies, the induced dipole remained nearly in phase with the electric field, generating minimal torque. As the frequency increased, a phase lag develops between the field and dipole, reaching an optimal point where the torque, and thus angular velocity, was maximized. The peak in $\mathrm{I}\mathrm{m}\left[K_{\mathrm{c}\mathrm{m}}\right]$ near 4 MHz marked this optimal frequency, consistent with the theoretical prediction of maximum electrorotational torque. Beyond this point, the dipole failed to follow the rapidly oscillating field, resulting in a decline in $\mathrm{I}\mathrm{m}\left[K_{\mathrm{c}\mathrm{m}}\right]$ and reduced torque generation. This frequency-dependent behavior defined the operational bandwidth for effective electrorotation and highlighted the importance of tuning the excitation frequency near the $\mathrm{I}\mathrm{m}\left[K_{\mathrm{c}\mathrm{m}}\right]$ peak. The angular velocity profile (figure 3(c)) theoretically followed a unimodal trend similar to $\mathrm{I}\mathrm{m}\left[K_{\mathrm{c}\mathrm{m}}\right]$, with the peak rotation occurring at the frequency where the phase lag between the field and dipole was greatest. The predicted quadratic relationship between angular velocity and applied voltage confirmed the scaling of torque with the square of the electric field amplitude.

The influence of microscale object permittivity (${\epsilon }_{\mathrm{p}}$) on $\mathrm{I}\mathrm{m}\left[K_{\mathrm{c}\mathrm{m}}\right]$ was also investigated. Higher ${\epsilon }_{\mathrm{p}}$ values led to increased peak $\mathrm{I}\mathrm{m}\left[K_{\mathrm{c}\mathrm{m}}\right]$ amplitudes, enhancing torque generation without significantly shifting the peak frequency. This implied that permittivity tuning offers a route to amplify rotational effects while preserving frequency selectivity, an advantage for applications such as microscale object sorting, dielectric sensing, or selective manipulation based on material properties. In contrast, increasing the medium’s permittivity (${\epsilon }_{\mathrm{m}}$) weakened the dielectric contrast between the microscale object and the medium, reducing torque magnitude and electrorotation efficiency. A modest rightward shift in the $\mathrm{I}\mathrm{m}\left[K_{\mathrm{c}\mathrm{m}}\right]$ peak frequency was also observed, indicating altered relaxation dynamics. Although limited imaging speed prevented direct measurement of initial angular acceleration (α), the shift suggested changes in transient rotational behavior. These findings emphasize the importance of aligning microscale objects and medium permittivities to optimize system performance.

4.3. Simulation analysis of rotational behavior

Finite element simulations played a critical role in validating the electrorotational functionality of the ERM and informing design decisions. Simulations confirmed that the 90° phase-shifted AC signals generated a symmetric rotating electric field across the quadrupole electrodes. Surface vector plots revealed strong tangential components around the microsphere, confirming effective torque application. Particle tracing further verified that the microsphere exhibited rotational motion with minimal lateral displacement, supporting torque-dominated behavior. The simulated angular velocity followed a unimodal profile, peaking near 4 MHz, in agreement with the frequency-dependent maximum in the imaginary part of the $K_{\mathrm{c}\mathrm{m}}$, which governed torque generation. This peak in torque confirmed the dominant role of the imaginary component of the Clausius–Mossotti factor in governing rotational response. At lower and higher frequencies, the torque magnitude decreased, reflecting the polarization relaxation behavior that defines the effective bandwidth for electrorotation. Beyond confirming expected behavior, simulations enabled rapid optimization of electrode geometry and operating parameters without repeated fabrication. By analyzing frequency, voltage, and permittivity effects on torque, the ERM design was efficiently refined. This simulation-guided approach accelerated development and supported the creation of a scalable, open-access electrorotation platform. This approach was enhanced substantially by resin printing instead of relying on photolithography.

4.4. Experimental analysis of rotational behavior

Using the inverted ERM, which suspended the microspheres within a droplet of medium at the chamber ceiling, likely allowed gravitational and buoyant forces to partially balance, reducing surface contact and minimizing friction. This adjustment improved rotational behavior, allowing stable and continuous rotation under the applied field. In addition to these forces, edge effects at the liquid–air interface and surface tension forces at the droplet boundary may also have influenced microsphere positioning and movement, particularly given the relatively large microscale object. This simple yet effective modification demonstrated the importance of mechanical boundary conditions in electrorotation experiments, particularly when working with larger microscale objects that are more susceptible to surface interactions.

The experimental results supported the theoretical model, although with a shift in peak performance. The observed maximum angular velocity occurred near 0.9 MHz, lower than the ~4 MHz predicted by theoretical and simulation analysis. It should also be noted that both the experimental and numerical analyses were based on a simplified microsphere–medium system rather than a biologically heterogeneous structure. These discrepancies can be attributed to both modeling simplifications and experimental nonidealities. In the simulations, a simplified geometry was employed to represent the idealized field symmetry and to emphasize the tangential electric fields responsible for torque generation. This approach was intended to capture the frequency-dependent electrorotation behavior under controlled assumptions rather than replicate the exact droplet geometry used experimentally. Consequently, effects such as electrode edge fields, droplet curvature, and spatial variations in medium conductivity and temperature were not included, all of which can alter the local field distribution and shift the characteristic rotation frequency. Similar discrepancies have been reported in other electrorotation studies and are typically attributed to nonidealities such as electrode configuration, fabrication tolerances, thermal effects, and the dielectric relaxation of the suspending medium and particle [43, 44]. As such, the model serves as a foundational framework for understanding the electrorotation mechanism, while future work involving biological objects may exhibit additional dielectric dispersion and interfacial polarization effects that could further shift the characteristic frequency. Despite these differences, the simulated and experimental results exhibit consistent qualitative trends, including a unimodal frequency response and voltage-dependent increase in angular velocity, confirming that the model effectively represents the underlying electrorotation physics.

The apparent variation in microsphere size across different frequencies (figure 6) is primarily due to the ±10% manufacturing tolerance of the polystyrene beads and slight differences in optical focus during imaging. Although the real part of the Clausius–Mossotti factor varies slightly with frequency, producing a slight change in the vertical dielectrophoretic component, this effect only causes marginal upward displacement within the droplet. The balance between gravitational and buoyant forces mainly defines the particle’s resting position slightly below the electrode plane, where the weak upward DEP force, less than 2% of the gravitational-buoyant force, has no measurable impact on the in-plane electrorotation or the frequency at which the torque peaks.

The experimental voltage dependence of angular velocity followed a quadratic trend, consistent with torque theory, and voltage thresholds observed near 16 Vp–p reflected practical constraints [45]. The optimum 16 Vp–p voltage level was determined experimentally, as higher voltages caused bubble formation due to Joule heating or localized electrolysis at the electrode surfaces, disrupting field symmetry and rotational stability (figure 4(a)). However, the relatively high frequency used in this study (900 kHz) likely helped reduce electrolysis and bubble formation. At such frequencies, ions in the solution are unable to effectively follow the rapid oscillations of the electric field, which limits charge accumulation at the electrode surfaces. Similar effects have been documented in microchannel electrokinetic studies, where bubble formation limited system performance and highlighted the importance of voltage thresholds [46].

Notably, electrorotation could not be achieved in DI water for the 700 μm PS microspheres used in this study. This result aligned with theoretical expectations, as the low conductivity of DI water failed to provide dipole polarization and torque generation. In contrast, DI water has been employed for electrorotation of smaller biological cells. For example, effective electrorotation has been achieved for ~6 μm yeast cells suspended in DI water incorporating a surfactant to reduce cell adhesion and Joule heating [47]. These findings underscore the critical importance of selecting an appropriate suspending medium based on particle size and dielectric properties to achieve efficient electrorotation. The present electrode configuration operated reliably in a medium of moderate conductivity and permittivity (DPBS), confirming its capability to sustain stable rotation under such conditions. Although variations in buffer composition, conductivity, permittivity, or osmolarity can shift the frequency at which maximum torque occurs, these effects can generally be compensated for by adjusting the applied voltage and frequency to identify the optimum operating point for a given medium. However, for extremely low-conductivity media such as DI water, the lack of charge accumulation at the large particle-medium interface prevents torque generation even after tuning. These results indicate that while the device can be readily adapted to a variety of buffer environments through electrical adjustment, its operational limit is ultimately determined by the intrinsic dielectric properties of the suspending medium.

Dielectrophoresis and AC electric fields have been successfully applied to aquatic organisms and cells for various purposes, such as manipulation, collection, and label-free separation and enrichment, reinforcing their compatibility and gentle handling of living aquatic samples under DEP without causing damage [48–52].

This work lays the foundation for addressing key technical challenges in zebrafish SCNT, particularly the need for precise, non-contact manipulation of the egg during nuclear transfer. One of the most critical steps in SCNT is aligning the micropyle of the egg, a narrow fertilization canal that must be correctly oriented for successful nucleus injection. While this study experimentally validated the model using polystyrene microspheres, the broader motivation involves electrorotation of zebrafish eggs in cloning and developmental studies. Biological objects, such as zebrafish eggs, exhibit a far more complex architecture than uniform dielectric beads, consisting of an outer chorion, a perivitelline space, a plasma membrane, and a cytoplasmic interior with distinct electrical properties. These structural and compositional heterogeneities introduce multiple dielectric interfaces, each contributing to interfacial polarization and frequency-dependent dispersion. As a result, biological targets typically exhibit lower characteristic rotation frequencies and broader spectral responses than idealized microspheres. Furthermore, their irregular geometry and non-uniform surface conductance can reduce field symmetry and torque efficiency. Nonetheless, the electrorotation-based manipulation demonstrated here provides a promising, scalable approach for achieving controlled orientation without mechanical probes. Moving forward, the ERM can be adapted to enable automated alignment and rotation of zebrafish eggs, potentially improving SCNT efficiency and reproducibility in germplasm preservation and developmental biology research. For such automated applications, characterizing the initial angular acceleration ($\alpha$) will be critical for achieving rapid and predictable rotational responses. Although experimental measurement was constrained by the limited imaging frame rate, future simulations can be done to estimate transient rotational dynamics during field activation and cessation, providing a foundation for real-time control strategies.

5. Conclusions

This study demonstrated a robust and scalable electrorotation-based approach for manipulating dielectric microspheres, providing stable performance and easy customization through 3D resin printing. Through a combination of theoretical modeling, finite element simulations, and experimental validation, we confirmed the frequency-selective nature of electrorotational torque governed by the imaginary component of the Clausius–Mossotti factor. The unimodal angular velocity profile, its quadratic dependence on applied voltage, and the critical role of dielectric contrast between a microscale object and medium were all in strong agreement with theoretical predictions. Experimental results revealed a peak rotation frequency near 900 kHz, below the theoretical maximum, highlighting the influence of real-world factors such as electrode geometry, thermal effects, and interfacial polarization, as well as uncertainty in material properties. Practical constraints including voltage thresholds, media conductivity, field stability, and surface interactions, further shaped device performance underscoring the need for experimental calibration in future applications. Notably, the use of biocompatible DPBS as a working medium preserved negative dielectrophoresis and ensured system compatibility with biological specimens. This positions the ERM platform as a promising foundation for future microfluidic systems targeting the controlled manipulation of large biological microscale objects such as eggs from aquatic species. Looking forward, resin-printed ERMs have the potential to bridge fundamental electrokinetic studies and practical reproductive biotechnologies. The platform was designed with appropriate scaling and electrode optimization to enable the capture and manipulation of zebrafish eggs, an important model in developmental biology, thereby streamlining SCNT. These advancements lay the foundation for on-chip maturation, fertilization, and quality-control assays supporting cryopreservation and germplasm repository development, ultimately contributing to the conservation of economically and ecologically important aquatic species.

Data availability statement

All data that support the findings of this study are included within the article (and any supplementary files).

S1: Electric potential simulation available at https://doi.org/10.1088/1361-6439/ae2518/data1.

S2: Rotation at 800 kHz available at https://doi.org/10.1088/1361-6439/ae2518/data2.

S3: Rotation at 900 kHz available at https://doi.org/10.1088/1361-6439/ae2518/data3.

S4: Rotation at 1 MHz available at https://doi.org/10.1088/1361-6439/ae2518/data4.

S5: Bubble formation test available at https://doi.org/10.1088/1361-6439/ae2518/data5.

S6: Zebrafish egg rotation available at https://doi.org/10.1088/1361-6439/ae2518/data6.