Dielectrophoretic assembly of gold nanoparticles into conductive microwires. (a) Typical top-down optical micrograph of the process of bulk microwire assembly. (b) Side-view of the electrostatic simulation of bulk assembly mode—the white region represents the electrode and the growing microwire; the branching pattern predicted by the simulation is similar to the one observed experimentally in (a). (c) Parallel array of surface microwires assembled at low voltage and high frequency of the applied field. Scale bars: (a) 25 m m, (c) 5 m m. 

Dielectrophoretic assembly of gold nanoparticles into conductive microwires. (a) Typical top-down optical micrograph of the process of bulk microwire assembly. (b) Side-view of the electrostatic simulation of bulk assembly mode—the white region represents the electrode and the growing microwire; the branching pattern predicted by the simulation is similar to the one observed experimentally in (a). (c) Parallel array of surface microwires assembled at low voltage and high frequency of the applied field. Scale bars: (a) 25 m m, (c) 5 m m. 

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We overview the ways in which electric fields can be used for on-chip manipulation and assembly of colloidal particles. Particles suspended in water readily respond to alternating (AC) or direct current (DC) electric fields. Charged particles in DC fields are moved towards oppositely charged electrodes by electrophoresis. Dielectrophoresis, particl...

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... rate of microwire growth was found to be controlled by diffusion-limited aggregation. 146 We observed two distinct assembly modes for gold nanoparticles in aqueous suspensions. In bulk assembly mode, the nanoparticles form cylindrical microwires through the bulk of the suspension. The microwires typically grow in a characteristic branched pattern (Fig. 5a). In surface assembly mode the microwires were assembled as half-cylinders on the surface of the glass slide. 146 The assembly mode of the microwires and their branching and structure can be controlled by the operating field parameters. Single bulk microwires are formed at low frequency in 1 : 1 glycerol : water suspensions, whereas ...
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... in 1 : 1 glycerol : water suspensions, whereas parallel surface micro- wire arrays can be formed at low field intensity and high frequencies in aqueous suspensions. 146 The assembly process can be simulated well by a model of an electric-field driven dielectrophoretic assembly. The electric field calculation around a growing bulk microwire in Fig. 5b points out that the field intensity is highest at the tip of the microwire. This reflects the fact that as the wire grows, it extends the electrodes into the solution (cf. also with Fig. 2b). The gold nanoparticles are attracted towards the growing microwire and aggregate at the tip in the areas of highest intensity. The microwires ...
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... it extends the electrodes into the solution (cf. also with Fig. 2b). The gold nanoparticles are attracted towards the growing microwire and aggregate at the tip in the areas of highest intensity. The microwires branch at the point of bifurcation of the field. Some degree of electroosmotic flow in vortices around the wire tip can also be seen in Fig. 5a, an effect commonly observed in electrodeposition. In general, however, the electrostatic model describes realistically the dynamic process and the resulting pattern of microwire assembly, including the periodic branching and self-centring on con- ductive objects in the media. 146 An example of typical surface microwires grown at low ...
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... In general, however, the electrostatic model describes realistically the dynamic process and the resulting pattern of microwire assembly, including the periodic branching and self-centring on con- ductive objects in the media. 146 An example of typical surface microwires grown at low voltage and high electric field frequency is shown in Fig. 5c. It was found from the simulations that the electric field intensity is always highest near the glass surface and the field-driven process may favour the formation of surface microwires. However, fluid motion at low frequencies likely disturbs this surface growth and leads to bulk wires. At higher frequencies, the AC electroosmotic ...

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... This contributes to the particles' chain. So, this kind of electrostatic force (F c ) is also called as the 'chain' force [35] and it is often described as below. ...
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... Soft matter systems respond to several types of external fields [1][2][3] such as e.g. electric [4,5], magnetic [6,7], gravitational [8][9][10], optical [11], and mechanical [12,13] fields. The response of the many-body system to the external perturbation can be highly non-trivial, particularly in non-equilibrium situations. ...
... In PFT, a functional (with units of power) is minimized with respect to the current profile (or the velocity profile) at fixed density profile and fixed time. The functional is constructed such that the associated Euler-Lagrange equation is the exact force balance equation (4). The functional depends functionally not only on the density (as it is the case in equilibrium DFT) but also on the velocity profile. ...
Preprint
We combine power functional theory and machine learning to study non-equilibrium overdamped many-body systems of colloidal particles at the level of one-body fields. We first sample in steady state the one-body fields relevant for the dynamics from computer simulations of Brownian particles under the influence of randomly generated external fields. A neural network is then trained with this data to represent locally in space the formally exact functional mapping from the one-body density and velocity profiles to the one-body internal force field. The trained network is used to analyse the non-equilibrium superadiabatic force field and the transport coefficients such as shear and bulk viscosities. Due to the local learning approach, the network can be applied to systems much larger than the original simulation box in which the one-body fields are sampled. Complemented with the exact non-equilibrium one-body force balance equation and a continuity equation, the network yields viable predictions of the dynamics in time-dependent situations. Even though training is based on steady states only, the predicted dynamics is in good agreement with simulation results. A neural dynamical density functional theory can be straightforwardly implemented as a limiting case in which the internal force field is that of an equilibrium system. The framework is general and directly applicable to other many-body systems of interacting particles following Brownian dynamics.
... In current study, we further orient the CMC microfiber in PDMS applying DC electric field with the target of designing high dielectric allorganic polymer composite. In our case, although both electrophoresis force and electrostatic force were involved, the latter that drive the alignment of CMC into chains along the direction of the field lines should play a leading role (Velev & Bhatt, 2006). The SEM morphology, chemical structure, crystalline structure and surface charge of the used CMC are presented in Fig. 1. ...
... stress transfer of fluids (Yeh, Seul & Shraiman 1997;Velev & Bhatt 2006;Sheng & Wen 2012;Li et al. 2018;Driscoll & Delmotte 2019). Playing a crucial role in the driving mechanism of such fluids, nonlinear electrokinetic phenomena have been widely exploited in a variety of fields, among which are material science, bioengineering, nanofluidics and microfluidics (Feng et al. 2020;Xuan 2022). ...
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The rheological behaviour of dense suspensions of ideally conductive particles in the presence of both electric field and shear flow is studied using large-scale numerical simulations. Under the action of an electric field, these particles are known to undergo dipolophoresis (DIP), which is the combination of two nonlinear electrokinetic phenomena: induced-charge electrophoresis (ICEP) and dielectrophoresis (DEP). For ideally conductive particles, ICEP is predominant over DEP, resulting in transient pairing dynamics. The shear viscosity and first and second normal stress differences $N_1$ and $N_2$ of such suspensions are examined over a range of volume fractions $15\,\% \leq \phi \leq 50\,\%$ as a function of Mason number $Mn$ , which measures the relative importance of viscous shear stress over electrokinetic-driven stress. For $Mn < 1$ or low shear rates, the DIP is shown to dominate the dynamics, resulting in a relatively low-viscosity state. The positive $N_1$ and negative $N_2$ are observed at $\phi < 30\,\%$ , which is similar to Brownian suspensions, while their signs are reversed at $\phi \ge 30\,\%$ . For $Mn \ge 1$ , the shear thickening starts to arise at $\phi \ge 30\,\%$ , and an almost five-fold increase in viscosity occurs at $\phi = 50\,\%$ . Both $N_1$ and $N_2$ are negative for $Mn \gg 1$ at all volume fractions considered. We illuminate the transition in rheological behaviours from DIP to shear dominance around $Mn = 1$ in connection to suspension microstructure and dynamics. Lastly, our findings reveal the potential use of nonlinear electrokinetics as a means of active rheology control for such suspensions.
... However, the electric force applied to the manipulated objects dramatically relies on the electrical properties of the apparatus, such as size & shape. The application of electric micromanipulation includes; DNA analysis [102], measurement of single-cell mechanics [103], micro-assembly of nanowires and nanoparticles (NPs) [104], and manipulation of microbeads. ...
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Microrobots are motile microsystems constructed using physical, chemical and biological components for operations with respect to definite applications. In the present review, we have discussed the various aspects of microbiorobots, their history, and design. While designing a microrobot, two critical parameters (and their varities)- actuation and sensing affect the different micromanipulation techniques to be employed (Magnetic, Optical, Electric, fluidic, or acoustic). The controlling and actuation system (Vision-based or Force-sensing) selected for the specific application can dictate the fabrication type to be used for manufacture the microrobot. The type of propulsion systems, Powering system, and mobility in a complex environment, and applicability of the microrobot further influence the controlling parameters. Presently, microbiorobotics have applications in biomedical and environmental engineering. In this review, we have analyzed various aspects of microbiorobot design, fabrication, and applications that can help future works in nanosciences and microbiorobotics.
... In an electric field, the electrophoretic mobility for charged particles relies on the ion composition of the media, zeta potential (i.e., surface charge), and the shape of the particles. [27][28][29][30] Accordingly, the difference in the electric double layer (EDL) can be regarded as an entry point to analyze the accumulation ability. Hence, it is essential to measure the zeta potential of the particles to understand their accumulation behaviors better. ...
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Significance: Plasmo-thermo-electrophoresis (PTEP) involves using plasmonic microstructures to generate both a large-scale convection current and a near-field attraction force (thermo-electrophoresis). These effects facilitate the collective locomotion (i.e., swarming) of microscale particles in suspension, which can be utilized for numerous applications, such as particle/cell manipulation and targeted drug delivery. However, to date, PTEP for ensemble manipulation has not been well characterized, meaning its potential is yet to be realized. Aim: Our study aims to provide a characterization of PTEP on the motion and swarming effect of various particles and bacterial cells to allow rational design for bacteria-based microrobots and drug delivery applications. Approach: Plasmonic optical fibers (POFs) were fabricated using two-photon polymerization. The particle motion and swarming behavior near the tips of optical fibers were characterized by image-based particle tracking and analyzing the spatiotemporal concentration variation. These results were further correlated with the shape and surface charge of the particles defined by the zeta potential. Results: The PTEP demonstrated a drag force ranging from a few hundred fN to a few tens of pN using the POFs. Furthermore, bacteria with the greater (negative) zeta potential (|ζ|>10 mV) and smoother shape (e.g., Klebsiella pneumoniae and Escherichia coli) exhibited the greatest swarming behavior. Conclusions: The characterization of PTEP-based bacteria swarming behavior investigated in our study can help predict the expected swarming behavior of given particles/bacterial cells. As such, this may aid in realizing the potential of PTEP in the wide-ranging applications highlighted above.
... In particular, electro-hydrodynamics (EHDs) have been extensively investigated in microsystems to realize the flexible manipulation of leaky dielectric working fluid or nanoparticle samples monodispersed within it [10][11][12][13][14][15][16][17][18]. Within quasi-electrostatic limits, the common trait of EHDs manifests as an action of the local electric field on the space-charge density it induces to impart a net electrostatic body force and actuate the motion of the target medium via structural polarization [19]. ...
Article
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We propose herein a novel microfluidic approach for the simultaneous active pumping and mixing of analytes in a straight microchannel via the AC field-effect control of induced-charge electro-osmosis (ICEO) around metal–dielectric solid Janus cylinders of inherent inhomogeneous electrical polarizability immersed in an electrolyte solution. We coin the term “Janus AC flow field-effect transistor (Janus AC-FFET)” to describe this interesting physical phenomenon. The proposed technique utilizes a simple device geometry, in which one or a series of Janus microcylinders are arranged in parallel along the centerline of the channel’s bottom surface, embedding a pair of 3D sidewall driving electrodes. By combining symmetry breaking in both surface polarizability and the AC powering scheme, it is possible, on demand, to adjust the degree of asymmetry of the ICEO flow profile in two orthogonal directions, which includes the horizontal pump and transversal rotating motion. A comprehensive mathematical model was developed under the Debye–Hückel limit to elucidate the physical mechanism underlying the field-effect-reconfigurable diffuse-charge dynamics on both the dielectric and the metal-phase surfaces of the Janus micropillar. For innovation in applied science, an advanced microdevice design integrating an array of discrete Janus cylinders subjected to two oppositely polarized gate terminals is recommended for constructing an active microfluidic pump and mixer, even without external moving parts. Supported by a simulation analysis, our physical demonstration of Janus AC-FFET provides a brand-new approach to muti-directional electro-convective manipulation in modern microfluidic systems.
... Recently, the advancement of nanotechnology [1] has made it possible to assemble nanoscale objects into desired structures [2][3][4][5]. Furthermore, control of polymer sequences [6,7] and assembly of colloidal particles [5,[8][9][10][11][12] have been vigorously studied. ...
... Here, we briefly outline the proof of Eqs. (8) and (9). A rigorous proof is given in Appendix. ...
... In this Appendix, we prove Eqs. (8) and (9). Before we begin the proof, we define the assembly pathway more formally. ...
Article
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We propose a phase transition on the feasibility of efficient parallel assembly. By introducing the parallel efficiency that measures how efficiently the parallel assembly works, the parallelizable phase is defined by its positive value. The parallelizable-unparallelizable transition is then identified by the nonanalytic change in the parallel efficiency from a positive value to zero. We present two analyzable models to demonstrate this phase transition in the limit of infinite system size.
... 10 Directing the transport and assembly of colloidal particles using electric fields is a central topic in the area of electrokinetics, owing to the ability to precisely control the motion and assembly of these particles. 11 While AC and DC fields both have been extensively utilized for colloidal separation, 11,12 AC electric field has been commonly used to drive colloidal assembly since the use of AC can not only easily induce strong particle dielectrophoresis, but also effectively eliminate any unwanted electroosmotic flows and Faradaic reactions, both of which commonly arise in DC electrokinetics. 11 As such, DC electric fields, despite being a straightforward mechanism to induce directional colloidal transport, may be seen as an impractical driving force for colloidal segregation and assembly, yet there exist a considerable number of studies reported over the past few decades demonstrating colloid assembly using DC fields. ...
... 10 Directing the transport and assembly of colloidal particles using electric fields is a central topic in the area of electrokinetics, owing to the ability to precisely control the motion and assembly of these particles. 11 While AC and DC fields both have been extensively utilized for colloidal separation, 11,12 AC electric field has been commonly used to drive colloidal assembly since the use of AC can not only easily induce strong particle dielectrophoresis, but also effectively eliminate any unwanted electroosmotic flows and Faradaic reactions, both of which commonly arise in DC electrokinetics. 11 As such, DC electric fields, despite being a straightforward mechanism to induce directional colloidal transport, may be seen as an impractical driving force for colloidal segregation and assembly, yet there exist a considerable number of studies reported over the past few decades demonstrating colloid assembly using DC fields. ...
... 11 While AC and DC fields both have been extensively utilized for colloidal separation, 11,12 AC electric field has been commonly used to drive colloidal assembly since the use of AC can not only easily induce strong particle dielectrophoresis, but also effectively eliminate any unwanted electroosmotic flows and Faradaic reactions, both of which commonly arise in DC electrokinetics. 11 As such, DC electric fields, despite being a straightforward mechanism to induce directional colloidal transport, may be seen as an impractical driving force for colloidal segregation and assembly, yet there exist a considerable number of studies reported over the past few decades demonstrating colloid assembly using DC fields. ...
Article
Manipulating the transport and assembly of colloidal particles to form segregated bands or ordered supracolloidal structures plays an important role in many aspects of science and technology, from understanding the origin of life to synthesizing new materials for next-generation manufacturing, electronics, and therapeutics. One commonly used method to direct colloidal transport and assembly is the application of electric fields, either AC or DC, due to its feasibility. However, as colloidal segregation and assembly both require active redistribution of colloidal particles across multiple length scales, it is not apparent at first sight how a DC electric field, either externally applied or internally induced, can lead to colloidal structuring. In this Perspective, we briefly review and highlight recent advances and standing challenges in colloidal transport and assembly enabled by DC electrokinetics.
... 9 Directional colloidal assembly techniques using external fields such as magnetic fields, [10][11][12][13] electric fields [14][15][16][17] and light 18,19 offer efficient ways of overriding the common colloidal interactions and guiding the particles to form out-of-equilibrium structures by accelerating the assembly kinetics. Further, external fields offer more precise control of the dynamics of the assembly process by changing the field parameters and can be used to assemble structures ranging from oriented 2D crystals, 20 nanowires, 21 electro and magnetorheological fluids to other stimuli responsive materials. 22 By tuning the field parameters, researchers are able to form multiple structural patterns that can be re-configured on-demand. ...
Article
The long-ranged interactions induced by magnetic fields and capillary forces in multiphasic fluid-particle systems facilitate the assembly of a rich variety of colloidal structures and materials. We review here the diverse structures assembled from isotropic and anisotropic particles by independently or jointly using magnetic and capillary interactions. The use of magnetic fields is one of the most efficient means of assembling and manipulating paramagnetic particles. By tuning the field strength and configuration or by changing the particle characteristics, the magnetic interactions, dynamics, and responsiveness of the assemblies can be precisely controlled. Concurrently, the capillary forces originating at the fluid-fluid interfaces can serve as means of reconfigurable binding in soft matter systems, such as Pickering emulsions, novel responsive capillary gels, and composites for 3D printing. We further discuss how magnetic forces can be used as an auxiliary parameter along with the capillary forces to assemble particles at fluid interfaces or in the bulk. Finally, we present examples how these interactions can be used jointly in magnetically responsive foams, gels, and pastes for 3D printing. The multiphasic particle gels for 3D printing open new opportunities for making of magnetically reconfigurable and "active" structures.