Efficient modeling approach for optimization of a system based on passive diamagnetic levitation as a platform for bio-medical applications”
Résumé
Constrained optimization may use time-consuming analysis on standard methods such as the finite-element method (FEM). In order to decrease the optimization time and to enable flexible gradient based optimization, this paper reports, a semi-analytical modelling approach and optimization of two variants of a diamagnetic levitation system as contactless manipulation platform for bio-medical and biochemical applications. The magnetic biochips are in increasing development and evolution supported by several applications in the biochemical and biomedical fields [1-4]. This family of microsystems includes partial or complete integrations of elementary or complex tasks processed by traditional laboratories of our scale. The automation and parallelization of these tasks [2] in the small world avoids human handling which is frequently not precise and likely of errors, and reduces times and the costs necessary to achieve operations such as diagnostic, analyzes and particles sorting [2-4]. This evolution of micro-actuators based on magnetic actuation has lead to an increasing need for specific modeling methodologies especially for optimization requirements. Thus, in order to facilitate the use of gradient based optimization process [5], this work deals with a realistic semi-numerical modeling approach of a system based diamagnetic levitation declined in two variants. Indeed, these systems have more and more applications, especially in biomedical field [6-7]. Diamagnetic contactless handling of bioparticles brings amazing perspectives to biochips and avoids serious problems as adhesion, adsorption and contamination. II. MAGNETOPHORESIS FORMULATION AND MODELING Currently, existing modeling approaches treating diamagnetic levitation problems are numerical methods such as finite elements method or magnetic moments method [8]. Theses modeling approaches are not adequate for full design studies. Therefore, in order to permit an adaptable optimization with gradient based algorithms, semi-analytical modeling was chosen and then established to compute outputs and formally exact sensitivities according to the inputs parameters of design [9]. The proposed device comprises four fix magnets and a levitating diamagnetic object. In order to approach both possible diamagnetic materials: anisotropic and isotropic and both possible fluids for biological bodies: air and liquid, the models of a levitating anisotropic graphite plate in air, and a levitating isotropic latex sphere in fluid were established. The magnetic field generated by these four parallelepiped magnets was expressed using equivalent surface method [10]. In this formulation the induced induction of the diamagnetic levitating object was neglected. This induced field did not affect significantly the external field due to the low magnetic susceptibilities of the diamagnetic materials. Hereafter is reported the magnetophoretic force [11] formulations corresponding to both proposed cases. A. Modeling of an anisotropic diamagnetic graphite plate in air A diamagnetic anisotropic plate in air with (2a, 2b, 2c) dimensions, having magnetic susceptibilities (x, y, z) respectively on x, y and z-axis and within a magnetic field induction expressed by its components Bx, By and Bz, experiences a magnetic force obtained from integral over whole diamagnetic plate volume (2). According to Ostrogradsky theorem (3) [12], magnetic force components (magFx, magFy and magFz) can be simplified leading to surface integrals (4-6). This simplification allows to establish a flexible semi-numerical model based on surface integrals to compute the magnetic force components and thus to enables a faster optimization. 2 2 2
Domaines
Energie électrique
Origine : Fichiers produits par l'(les) auteur(s)
Loading...