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Modeling and experiments of high speed magnetic micromanipulation at the air/liquid interface Mohamed Dkhil, Aude Bolopion, Stéphane Régnier, Michaël Gauthier To cite this version: Mohamed Dkhil, Aude Bolopion, Stéphane Régnier, Michaël Gauthier. Modeling and experiments of high speed magnetic micromanipulation at the air/liquid interface. RSJ International Conference on Intelligent Robots and Systems, Sep 2014, Chicago, IL, United States. 10.1109/IROS.2014.6943222. hal-02927296 HAL Id: hal-02927296 https://hal.archives-ouvertes.fr/hal-02927296 Submitted on 1 Sep 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Modeling and experiments of high speed magnetic micromanipulation at the air/liquid interface Mohamed Dkhil(1;2), Aude Bolopion1, Stéphane Régnier2, Member, IEEE, Michaël Gauthier1, Member, IEEE Abstract— One of the greatest challenge in microrobotics is Complementary to smart surfaces proposed in the the development of miniaturized smart surfaces for a high speed literature, this paper proposes a planar magnetic conveying and positioning of micro-objects. This paper proposes micromanipulation principle. The micro-object is placed a new approach where objects are situated at the air/liquid interface and are manipulated through magnetic fields. It at the interface between two fluids, and the actuation is demonstrates that a good repeatability and a high speed can ensured by magnetic forces. The object is in equilibrium on be obtained. A physical modeling is presented to analyze the interface under the action of the surface tension and its the dynamic behavior of the micro-object. Experiments are weight and it moves on the surface with minimum friction. performed to determine the physical parameters of the model This approach enables to avoid adhesion issues and provides and to attest the good repeatability of the motion for an object of size 100x90x25µm3. A good agreement between the physical a high velocity motion. A model of the system is proposed, model and the experimental measurement is demonstrated. and the physical parameters, namely the drag coefficient Since the velocity of the micro-object can be 10 times higher and the magnetization, are identified. The repeatability and at the air/liquid interface than in the liquid this approach velocity are discussed and the dynamic model derived in represents a promising solution to design smart surfaces for this article can be used for closed loop control in future a high throughput conveying of micro-objects. works. I. INTRODUCTION This paper is organized as follows. In Section II, the Smart surfaces are well studied solutions to manipulate, dynamic behavior of the micro-object is modeled. The re- convey, and position objects of a few millimeters [1], [2], peatability of the motion is evaluated in Section III based [3]. For industrial tasks such as the assembly and packaging on experimental measurements. In Section IV, the physical of products automatic feeding of objects is crucial. To parameters of the model are identified and its validity is perform planar displacements a variety of actuation methods discussed. The advantages and limitations of this approach have been developed including electrostatic actuators [4], are discussed in Section V. Conclusions and perspectives of electromagnetic actuators [5] and air jets [6]. These methods this work are presented in Section VI. enable to manipulate the objects with no direct contact which avoids damages of fragile components such as II. DYNAMIC MODEL electronic cards [7]. Most of the magnetic actuation systems present similar designs. The modeling proposed in this paper is illustrated The miniaturization of these smart surfaces in order on a magnetic device composed of four electromagnets. The to manipulate objects of a few micrometers would be magnetic force produced induces the motion of the micro- an innovative solution with a wide range of application object on the air/liquid interface (see Figure 1). In this domains, from microassembly to cell manipulation. section a model of the motion of the object on a meniscus is Several actuation techniques are available to perform derived. Some hypothesis will then be assumed to simplify 2D displacement of micrometer size objects, such as the dynamic model and highlight the influence of the main magnetophoresis [8], [9], [10]; dielectrophoresis [11], [12], physical parameters (drag coefficient, magnetization) on the [13]; laser beams [14], [15] or acoustic waves [16], [17]. micro-object behavior. However, one of the greatest challenge consists in providing an ultra-rapid surface for transportation. Currently, the A. Model of the motion of a micro-object on a air/liquid proposed systems are either in ambiant environments or interface in liquids. At micrometer scale adhesion forces are a So that the object can be moved by magnetic fields major issue in ambiant environments, and the repeatability it must be composed of a magnetic material. The micro- of the manipulations is not guaranteed [18]. In a liquid object is then placed on the air/liquid interface. At this medium the velocity is limited due to the viscous forces [19]. scale the workspaces are small (at most some millimeters). A meniscus appears on the reservoir, which must be taken 1Authors are with FEMTO-ST Institute CNRS UFC/ENSMM/UTBM into account while modeling the motion (see Figure 1). The Automatic Control and Micromechatronic Systems Department, 24 rue shape of the meniscus can be concave surface depends on Alain Savary, 25000 Besançon, France. [email protected] the material properties of the reservoir. It is defined by the 2Authors are with Institut des Systèmes Intelligents et de Robotique (ISIR), Pierre et Marie Curie University, CNRS UMR 7222, 4 Place Jussieu, function f : 75005 Paris, France. z = f (x): (1) It will be considered in the following that the motion of the angle is evaluated numerically. A rectangular nickel object is object is on the (x;z) plane. considered (density: r = 8902 kg=m3, size: 100x90x25 µm3) and the liquid is water (surface tension: g = 72 10−3 N=m). The forces applied to the micro-object are: (i) the magnetic Based on Equation (4) the f angle is about 7:17 10−4 rad force ~Fmag generated by electromagnets, (ii) the weight ~P which is negligible. The shape of the meniscus is not affected (iii), the resultant force of surface tension ~T and (iv) the by the weight of the micro-object and Eq. (1) can be used drag force ~Fv. despite the presence of the object. z z α R r R c r c α x T r o T resultant of the surface tension meniscus r F r r mag F F v v P x magnetic particle o r meniscus magnetic particle δT φ r electromagnet workspace P Fig. 2. Equilibrium of the magnetic micro-object on the meniscus. The resultant force of surface tension ~T compensates the weight ~P. It can be shown that the contact angle f between the micro-object and the liquid is negligible, therefore, the shape of the meniscus in the reservoir is not Fig. 1. Example of a planar magnetic device. The electromagnets control deformed by the weight of the micro-object. the motion of the micro-object on the air/liquid interface. A meniscus of radius of curvature Rc is formed at the interface. a is the angle between the micro-object and the vertical direction. The magnetic force ~Fmag, the weight ~P, the resultant force of surface tension ~T of the air/liquid interface Using the second Newton’s law, the motion of the micro- and the drag force ~F are applied to the micro-object. v object can be expressed as follows: m~a = ~P + ~Fmag + ~Fv +~T; (5) The magnetic force ~Fmag applied to a magnetic micro- object is given by: where ~a is the acceleration of the micro-object. This equation is projected along (o;~x) and (o;~z): ~Fmag = V:∇(M~ :~B); (2) 8 mx¨ = F − hvcos(a) − T sin(a); where V is the volume of the object, M~ is its magnetization > magx > and ∇~B is the magnetic field gradient produced by the > mz¨ = Fmagz − P − hvsin(a) + T cos(a); <> magnetic source. The fluid flow is considered as a Stokes z = f (x); (6) flow. The drag force is given by: > > d f (x) ~ > tan(a) = ; Fv = −h~v; (3) : dx where h is the drag coefficient and ~v is the velocity of the where a is the angle between the vertical direction and the object. direction going from the center of the sphere tangent to the meniscus and the object (see Figure 1). The general behavior The weight of the micro-object ~P is compensated by the of the micro-object is given by Eq. (6). Some assumptions resultant force of the surface tension ~T (see Figure 2). The will now be made to highlight the influence of the physical equilibrium condition is given by: parameters on its behavior. gCsin(f) = mg; (4) B. Simplified dynamic model where g is the surface tension, C is the perimeter of the object, f is the contact angle between the micro-object and In order to study the characteristics of this system a linear the liquid, m is the mass of the object and g = 9:8 m:s−2 is model is derived based on the following assumptions: the acceleration of the gravity.

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