The depolarization field in polarizable objects of general shape
2009; Mexican Society of Physics; Volume: 48; Issue: 5 Linguagem: Espanhol
ISSN
2683-2224
Autores Tópico(s)Magnetic and Electromagnetic Effects
ResumoLA POLARIZACION DE PARTICULAS O CELDAS BIOLOGICAS SE ESTUDIA COMUNMENTE A TRAVES DE LA MEDICION DE LA IMPEDANCIA DE SUSPENSIONES, O BIEN POR UNA VARIEDAD DE METODOS DE PARTICULAS SENCILLAS, QUE SE BASAN EN EFECTOS DIFERENTES DE FUERZA. PARA CELDAS BIOLOGICAS, LOS CAMBIOS EN LA POLARIZACION MAS NOTABLES DEPENDIENDO DE LA FRECUENCIA, RESULTAN DE FENOMENOS ESTRUCTURADOS DE POLARIZACION (EFECTO MAXWELL-WAGNER). MODELOS DIELECTRICOS CONSIDERAN LAS PROPIEDADES ESTRUCTURALES DE CELDAS SUPONIENDO GEOMETRIAS ESFERICAS O ELIPSOIDALES, PUESTO QUE SOLO EN MUY POCOS CASOS SE CONOCE EL CAMPO EFECTIVO LOCAL EI(R) EN PRESENCIA DE UN OBJETO DIELECTRICO. ESTO SE REFIERE A CUERPOS DIELECTRICOS DE FORMA ESPECIAL, QUE ESTAN EXPUESTOS A UN CAMPO ELECTRICO ESPECIAL E0(R). EN EL PRESENTE TRABAJO SE MUESTRA UN PROCEDIMIENTO DE APROXIMACION PARA EL CASO GENERAL QUE PERMITE EL CALCULO DEL CAMPO LOCAL EI(R) GENERADO EN PRESENCIA DE UN OBJETO DIELECTRICO DE FORMA ARBITRARIA, INTRODUCIDO EN EL ESPACIO DE CAMPO ~E0(~R). LA APLICABILIDAD DEL METODO ES DEMOSTRADA PARA UN CILINDRO DIELECTRICO NO-ELIPSOIDAL A TRAVES DE LA MEDICION DE SU MOMENTO DIPOLAR EN UN CAMPO DE MICROONDAS. LA CORRESPONDENCIA CON LOS RESULTADOS CALCULADOS SE ENCUENTRA UN ORDEN DE MAGNITUD MEJOR QUE EN EL PROCEDIMIENTO COMUN DE APROXIMAR EL CILINDRO POR UN ESFEROIDE CON LAS MISMAS RELACIONES AXIALES. Abstract THE POLARIZATION OF PARTICLES OR BIOLOGICAL CELLS IS COMMONLY INVESTIGATED BY MEASURING THE IMPEDANCE OF SUSPENSIONS OR BY A VARIETY OF SINGLE PARTICLE METHODS, THAT EXPLOIT DIFFERENT FORCE EFFECTS. FOR BIOLOGICAL CELLS THE MOST STRIKING FREQUENCY-DEPENDENT CHANGES IN POLARIZABILITY RESULT FROM STRUCTURAL (MAXWELL-WAGNER) POLARIZATION PHENOMENA. EXPLICIT SOLUTIONS OF THE LAPLACE EQUATION ARE AVAILABLE ONLY FOR OBJECTS WITH FINITE SURFACES OF THE SECOND DEGREE. THUS, DIELECTRIC MODELS CONSIDER THE STRUCTURAL PROPERTIES OF CELLS BY ASSUMING SPHERICAL OR ELLIPSOIDAL GEOMETRIES, SINCE ONLY IN VERY FEW CASES IS THE EFFECTIVE LOCAL FIELD EI(R) IN THE PRESENCE OF A DIELECTRIC OBJECT KNOWN. THIS CONCERNS DIELECTRIC BODIES OF SPECIAL SHAPE, WHICH ARE EXPOSED TO A SPECIAL ELECTRIC FIELD E0(R). IN THE PRESENT PAPER AN APPROXIMATION PROCEDURE IS PRESENTED FOR THE GENERAL CASE, ALLOWING TO CALCULATE THE DEPOLARIZATION FIELD EI(R), WHICH IS GENERATED IN THE PRESENCE OF AN ARBITRARILY SHAPED DIELECTRIC OBJECT, INTRODUCED INTO A FIELD SPACE ~E0(~R). CONTRARY TO RECENT NUMERICAL METHODS (FINITE ELEMENT TECHNIQUE), WHICH REQUIRE EXTENSIVE COMPUTER RESOURCES DUE TO THE UNAVAILABILITY OF ANALYTICAL SOLUTIONS, THE HERE PRESENTED APPROACH RESULTS IN CLOSED ANALYTICAL EXPRESSIONS. THE APPLICABILITY OF THE METHOD IS DEMONSTRATED FOR A NON-ELLIPSOIDAL CYLINDRICAL DIELECTRIC BY MEASURING ITS DIPOLE MOMENT IN A MICROWAVE FIELD. THE ACCORDANCE WITH THE CALCULATED RESULTS IS FOUND TO BE ONE ORDER OF MAGNITUDE BETTER THAN IT WOULD BE IN THE COMMONLY PRACTICED PROCEDURE, WHERE THE CYLINDER IS SUBSTITUTED BY A SPHEROID OF THE SAME AXIS RELATION.
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