V M Volgin
email: volgin@tsu.tula.ru

V V Lyubimov

V D Kukhar

Modeling of Electromagmetic Processes in Wire Electric Discharge Machining

Keywords: Wire electric discharge machining, electromagnetic force, finite element method

The work is devoted to the modeling of electromagnetic processes during wire electric discharge machining and calculation of electromagnetic force. The Maxwell-Ampere's law was used as the mathematical model; the numerical solution was performed by the finite element method. It is shown that the electromagnetic force significantly increases in relation to its initial value in the course of machining due to a decrease of an average distance between the wire tool electrode (WTE) and workpiece surfaces. The results of modeling characterize the effect of machining conditions (workpiece and WTE materials, diameter of WTE, interelectrode gap, parameters of current pulse, length of slit in the workpiece, etc.) on the electromagnetic force.

Introduction

Wire electric discharge machining (WEDM) is an industrially well established machining process for advanced materials [1 -3]. The accuracy of WEDM depends on lag and vibration of low rigid wire tool electrode (WTE) under forces acting on it [START_REF] Herrero | Proc. ISEM XV[END_REF]. In WEDM, four kinds of forces are applied to the wire electrode [START_REF] Tomura | [END_REF]: discharge reaction force caused by rapid expansion of a dielectric fluid bubble at the discharge spot during discharge duration, electrostatic force when open voltage is applied between the wire and workpiece during ignition delay time, electromagnetic force caused by discharge current flowing through the wire, arc column, and workpiece during discharge duration, and hydrodynamic force generated by the flow of dielectric fluid. The electromagnetic force due to the interaction between currents passing through WTE and workpiece can contribute considerably to the total force acting on WTE, especially in the micro-WEDM. In several works, the numerical modeling of the electromagnetic field taking into account electromagnetic induction was performed by the 2D finite element method [START_REF] Tomura | [END_REF]6]. In this case, the worpiece surface was taken to be plane, which corresponds only to the initial instant of time of machining. In the course of machining, the workpiece geometry varies essentially; this will have an effect on the electromagnetic force. However the regularities of electromagnetic processes at WEDM considering change of geometry (a shape and the sizes) of the processed preparation in processing in details are not investigated. This work is devoted to the modeling of electromagnetic processes during wire electric discharge machining and calculation of electromagnetic force with taking into account of the changes of the workpiece shape and size during machining.

Mathematical Model

Fig. 1 presents the scheme WEDM (Fig. 1a), and also the shape and the relative positioning of WTE and the workpiece at the beginning of machining (Fig. 1a), at partial deepening of WTE (Fig. 1b) and at full deepening of WTE (Fig. 1c). It is supposed that the direct current flows along WTE, i.e. along an axis z. When machining of the workpiece from diamagnetic or paramagnetic material (for example, copper or aluminum) the distribution of the magnetic flux is almost symmetric concerning the axis of WTE, and the magnetic field are directed counterclockwise as WTE and workpiece have almost identical magnetic permeability. When machining of the workpiece from ferromagnetic material (for example, steel) the magnetic flux is not symmetric concerning the WTE axis, because magnetic permeability of the workpiece is much more, than WTE. The magnetic flux in the bottom part of WTE is higher, than in the top. Thus, the resulting electromagnetic force acting on WTE is directed to the workpiece. When the current in WTE increases, the magnetic flux increases and the electromagnetic induction in the workpiece is resulted by eddy currents which flow parallel to the WTE axis. Thus the repulsive electromagnetic force acts on WTE. At the reduction of the current at the end of the pulse the direction of eddy currents in the workpiece changes to the opposite, and the attracting electromagnetic force acts on WTE [START_REF] Tomura | [END_REF]. This phenomenon arises both in paramagnetic, and in ferromagnetic materials. For calculation of the electromagnetic force acting on WTE we will use the system of the Maxwell equation:

           D B E B D J H t t ( 1
)
where D is the electric displacement; J is the current density; H, B are intensity and induction of the magnetic field, respectively;  is density of electric charge; t is the time.

Between the variables characterizing an electromagnetic field there are following ratios:

E J H B E D       , , (2)
where r 0     is the magnetic permeability of the material; 0  is the magnetic permeability of vacuum; r  is the relative magnetic permeability;  is the specific conductivity.

Considering that the magnetic field does not depend on z coordinate, instead of the variable B it is possible to enter the potential A connected with В by the following ratio:

A B rot  (3)
Substituting Eq. 3 in the first equation of the system of the Maxwell equations (1), we will receive the equation for the potential of the magnetic field:

t E J y A y x A x z z z z                                  1 1 (4)
From the third equation in the system (1) when using the assumption that only one component of the electric field directed along WTE axis is other than zero, we will receive:

t A E z z     (5) z z E J J    0 (6)
and  <<1, we will receive:

t A J y A y x A x z z z                                  0 1 1 (7)
Where z J is the full density of current; 0 J is the current density in WTE at the pulse created by the pulse generator. The equation ( 7) can be solved with the following initial and boundary conditions:

0 , 0 0    B z t z A A (8)
where B is the boundary of computational domain.

The components of the electromagnetic force acting on WTE can be calculated with the use of the following equations:

, , W TE W TE W TE W TE W TE W TE 0 0 dxdy x A t A J dxdy x A J dxdy B J F dxdy y A t A J dxdy y A J dxdy B J F S z z S z z S y z y S z z S z z S x z x                                           (9)
where WTE S is the cross section of WTE.

Owing to the symmetry the component of F

x has to be equal to zero. The positive F y value corresponds to the repulsive electromagnetic force, and the negative value to the attracting electromagnetic force.

Results

The numerical solution of the boundary value problem (7, 8) was carried out by the finite element method with the use of the FlexPDE program. By the results of the numerical solution the value of the electromagnetic force acting on WTE was calculated. Three various relative positions of the workpiece and WTE were considered: the starting position of the tool-electrode at the beginning of the machining (Fig. 1b), at the partial deepening of WTE to the workpiece (Fig. 1c), at a full deepening of WTE to the workpiece (Fig. 1d). From these three arrangements of WTE the greatest interest is presented by the scheme with WTE being in the working position (to Fig. 1d) as when the tool electrode is in this situation practically all the time during machining. The calculations of the electromagnetic force acting on WTE when passing the pulse of the current duration 1 μs with the forward and back fronts having duration on 50 ns for the three various materials of the workpiece were carried out: ferromagnetic (steel), paramagnetic (aluminum) and diamagnetic (copper) (Fig. 2). On the basis of the published data the amplitude value of the current was accepted equal 5 A [START_REF] Tomura | [END_REF]. The tungsten wire with a diameter of 30 microns was used as WTE. From the obtained results (Fig. 2) it is well visible that the greatest value of the electromagnetic force acting on WTE takes place when the machining of ferromagnetic material (steel). When the machining of copper and aluminum the values of the electromagnetic force significantly less and are almost equal among themselves. It is caused by the fact that the magnetic permeability of these materials is approximately equal. The negative F y value when the machining of steel, corresponds to WTE attraction to the workpiece. When the machining of copper and aluminum F y accepts positive values, i.e. under the acting of the electromagnetic force of WTE repelled from the workpiece. Let's consider the major factors of WEDM influencing the electromagnetic force. One of such parameters is the value of the current. From Fig. 3a one can see that with the increase in the current the electromagnetic force increases. Depending on the magnetic permeability, the force acting on WTE is the attraction force for ferromagnetic (Fig. 3a, curve 1) and repulsive force for paramagnetic and diamagnetic materials (Fig. 3a, curves 2 and 3). One can see that when machining a ferromagnetic material the electromagnetic force increases in the process of deepening of WTE in the workpiece, and when processing paramagnetic and diamagnetic, on the contrary, decreases. At rather big deepenings the value of the electromagnetic force is stabilized and reaches the constant value not depending on the deepening. It proves the correctness of the choice of this scheme of the calculation (Fig. 1d).

Conclusion

The theoretical analysis is carried out and the numerical calculations of the value of the electromagnetic force acting on WTE at electric discharge micromachining are conducted. It is shown that the electromagnetic force has essential impact on WTE during machining. The key parameters influencing this force are: the current, the diameter of WTE, the interelectrode gap, deepening of WTE in the workpiece. By the numerical calculations it is shown that the electromagnetic force acting on WTE most depends on the workpiece material: when processing the workpiece from ferromagnetic material the greatest value of this force which attracts WTE to the workpiece is reached; when machining the workpiece from paramagnetics and diamagnetics this force is much less and it causes pushing away of WTE from the workpiece.

Fig. 1 :

 1 Fig. 1: Geometric models for the analysis of electromagmetic processes in WEDM: (a) at initial WTE position; (b) at partial deepening of WTE; (c) at fully deepening of WTE; (1) WTE; (2) workpiece; (3) dielectric fluid; h is the deepening of WTE in the workpiece; s is the interelectrode gap

Fig. 2 :

 2 Fig. 2: The dependence of the electromagnetic force of F y on time at h=60 μm, s=10 μm when the machining of the workpieces from various materials: (1) steel, k=1; (2) copper, k=10; (3) aluminum, k=10.

Fig. 3 :

 3 Fig. 3: The dependences of the electromagnetic force F y from (а) current; (b) diameter of WTE; (c) deepenings of WTE into the workpiece On Fig. 3d the influence of the relative position of the workpiece and WTE on the value of the electromagnetic force is shown.One can see that when machining a ferromagnetic material the electromagnetic force increases in the process of deepening of WTE in the workpiece, and when processing paramagnetic and diamagnetic, on the contrary, decreases. At rather big deepenings the value of the electromagnetic force is stabilized and reaches the constant value not depending on the deepening. It proves the correctness of the choice of this scheme of the calculation (Fig.1d).

Acknowledgment

The financial support from Ministry of Education and Science of the Russian Federation under project no. 1096 of the Basic Part of the State Program is gratefully acknowledged.


H Aono

H Hirazawa

T Naohara

Heat generation ability in AC magnetic field of bead-milled nanosize Y 3 Fe 5 O 12 and preparation of microsphere for embolization therapy

Keywords: Y 3 Fe 5 O 12, Thermal coagulation therapy, AC magnetic field, Microsphere, Bead milling, Embolization method

Y 3 Fe 5 O 12 microspheres having high heat generation ability in AC magnetic field for embolization therapy were prepared by a spray dryer using a bead-milled nano-size powder. After sifting using 20 µm and 32 µm sieves, the yield was 13.5 % for the 20-32 µm microspheres. The heat generation ability (W•g -1 ) of the microsphere sample was expressed as 3.5x10 -4 •f•H 2 , where f and H are frequency (kHz) and magnetic field (kA•m -1 ), respectively. This value was almost the same with that for the bead-milled powder, because the main temperature enhancement was due to the Néel relaxation of the superparamagnetic material.

Introduction

For a new treatment of cancerous tissues, thermal coagulation therapy using powdered magnetic materials in an AC magnetic field has been expected. A drug delivery system using nano-sized magnetic particles encapsulated in a liposome with an antibody (< 100nm) is possible as a cancer therapy. For this therapy, Fe 3 O 4 (magnetite) nanoparticles have been studied as the candidate material. One of the reasons for utilization of the nano-sized Fe 3 O 4 particles is ease preparation using a conventional chemical coprecipitation method in solution [1,2]. However, the preparation of nanosized ferrite particles is very difficult using the chemical method except for the magnetite [3]. For the preparation of the nanosized powder, physical milling method can effectively achieve a high heat generation ability. We studied the heat generation ability in an AC magnetic field of nano-sized MgFe 2 O 4 and Fe 3 O 4 powders prepared using a bead-milling method [4,5]. We also reported that the bead-milled Y 3 Fe 5 O 12 ferrite had the highest heat generation ability in the nanosized superparamagnetic materials [6,7]. For the superparamagnetic materials, the Néel relaxation and the Brownian relaxation become calorigenic causes in solution. As the thermal coagulation therapy using another type of magnetic particle, an embolization method of blood vessels using a magnetic microsphere is a conceivable and convincing method. We have tested the preparation of microspheres using the spray-drying method of bead-milled magnetic materials [8,9]. In this study, we prepared the Y 3 Fe 5 O 12 microspheres with a 20-32 µm diameter range the spray-drying method of bead-milled nano-sized particles and investigated their heat generation ability in the AC magnetic field.

Experimental

The nano-sized ferrite powder was prepared using a bead-milling mehod (DMS65, Ashizawa Finetech, Ltd.). The apparatus consisted of a zirconia vessel and beads. A commercial Y 3 Fe 5 O 12 (99.9%, Kojyundo Chemical Lab.) powder and ethanol were used as the milling sample and the solvent, respectively. The bead size and milling time were 0.1 mmφ for 4 h after milling using the 0.3 mmφ beads for 2 h. After the bead milling, the solvent was evaporated at 100 o C. Figure 1 shows the spray-drier apparatus used for the preparation of the microspheres. The slurry for the spray-drier (ADL311S, Yamato Co.) was obtained as a mixture of the bead-milled Y 3 Fe 5 O 12 (4.0g) and purified water (11.3 ml). The slurry was thoroughly mixed by ultrasonication for 3 min and then sprayed as small droplets by a spray-drier with a 0.711-mm diameter orifice nozzle atomizer, and a 52-cm high chamber with a 13-cm inside diameter. The droplets were isotropically dried in the chamber to form the ferrite microspheres. The temperature and flow rate of the heated dry air were 200 o C and 0.4 m 2 /min, respectively. The air pressure for atomization was 0.03 MPa. The slurry feed rate was 4.0 ml/min. The spray-dried powder was washed using purified water on a 32-µm sieve to screen out the larger particles. The sifted slurry containing the particles under 32-µm and purified water was then thoroughly washed on a 20-µm sieve to remove any smaller particles. The powder on the 20-µm sieve, which contained 20-32 µm particles, was then dried at 100 o C. The crystallite size of the Y 3 Fe 5 O 12 was estimated by the FWHM (full-width at half maximum) of the X-ray diffraction peaks (XRD, Model Rint 2000, Rigaku Co., using Cu-Kα radiation). The specific surface area was measured by the one-point BET method (Flowsorb II 2300, Shimadzu Co.) and then the particle diameter was calculated by assuming a spherical particle size. Figure 2 shows the apparatus for measuring the heat generation ability of the ferrite powder in the AC magnetic field. The heat generation ability (W•g -1 ) of the Y 3 Fe 5 O 12 powder (2.0 g) with 10 ml water in a glass case (Pyrex: 20 mmφ, 45 mm) was quantitatively measured. The coil consisted of eight loops of copper pipe (6 mmφ) wound around a polypropylene (PP) bobbin (48 mmφ×40 mm). The copper pipe was cooled by flowing water to maintain its temperature and impedance. The coil was connected to a power supply (T162-5712B, Thamway Co., Ltd.) through an impedance tuner. The temperature of the sample was measured using a radiation thermometer (TP-L0225EN, Chino Co.). Air was bubbled into the glass case for stirring the water. We tested that the temperature of the water was not increased by the air bubbling. The heat generation ability was calculated using the temperature enhance ratio (dT/dt = K•s -1 ) for the initial 5 min of the ΔT measurement using the following equation:

Heat generation ability (W•g -1 ) = C•(dT/dt)/M (1)
where M and C are the sample weight (g), and the estimated total heat capacity (J•K -1 ) of 10 ml of water and the glass case, respectively. The temperature measurement was started after maintaining the sample at room temperature in ambient air for several hours.

Results and Discussion

Figure 3 shows the XRD results for three powder samples of the commercial Y 3 Fe 5 O 12 powder sample, the bead-milled sample, and the spray-dried sample using the bead-milled powder. Sharp peaks were obtained for the commercial powder due to the large crystallite size. The XRD peaks of the bead-milled powder were very broad, because the crystallite diameter had been significantly reduced by this physical milling method. The estimated crystallite and particle diameters using the Scherrer equation from the XRD peak at 2θ=55.5° (642) and the BET method were 16 nm and 26 nm, respectively. The particle size was greater than the crystalline size due to the aggregation of the small crystals to show larger value of the particle size from the BET method. The broad XRD peaks for the spray-dried microsphere sample were almost same with that of bead-milled powder. No contamination from the zirconia vessel and beads by the bead milling and the spray drying was detected by XRD. Figure 4 shows SEM photos of the spray-dried particles (a) before and (b) after the sifting using 20-µm and 32-µm sieves. The microspheres having a variety of particle sizes were obtained using the spray drying (Fig. 4(a)). The nano-particles were aggregated to form these microsphere particles by this drying process in the air. The collected weight in the powder collection container was 1.70 g from the initial 4.0 g Y 3 Fe 5 O 12 powder in the slurry. The weight loss in the collection container was due to the powder remaining on the wall and bottom of the chamber. The microspheres of the 20-32 µm sifted particles (Fig. 4(b)) were completely sifted by our method. The collected weight of the 20-32 µm particles was 0.54 g, whose yield was 13.5 wt% versus the starting 4.0 g powder. A commercial powder sample (non-milled sample) having large particle size did not show any temperature enhancement in an AC magnetic field. However, the high heat generation ability in the AC magnetic field was obtained by a decrease in the average crystallite size for the bead-milled Y 3 Fe 5 O 12 ferrites. The highest heat ability in the AC magnetic field was obtained for the fine Y 3 Fe 5 O 12 powder milled for 4 h using 0.1 mmφ beads [6,7]. This milled sample was utilized for the preparation of the microsphere sample. Figure 5 shows the relationship between the square of the AC magnetic field (H 2 ) at 370 kHz and the heat generation ability of the two types of samples. The heat generation ability was proportional to the square of the magnetic field for both materials. The heat generation ability of the microsphere sample was very close with that for the bead-milled sample. Low temperature treatment at 200 o C using the spray-drier for the preparation of the microspheres did not influence to the heat generation ability. Figure 6 plots the relationship between the frequency of the AC magnetic field (200-370 kHz) at 1.77 kA•m -1 ) and the heat generation ability of the two types of samples. The heat generation ability for both samples was also proportional to the frequency of the AC magnetic field. The energy losses (heat generation ability) of the superparamagnetic nanoparticles due to the Néel relaxation and Brownian relaxation are proportional to the square of the magnetic field (H 2 ) and its frequency (f). The equation is expressed as:

Heat generation ability (W•g -1 ) = k•f•H 2 (2)
where k, f, and H are a constant value, frequency (kHz), and magnetic field (kA•m -1 ), respectively [10][11][12]. The estimated k value in Eq. ( 2) using the results of Figs. 5 and 6 was 3.5x10 -4 for the total loss of this sample having the best heat generation ability. For the Néel relaxation and the Brownian relaxation, the energy loss is due to the magnetic moment rotation within the crystal and particle rotation in the dispersed solvent, respectively. The result of the beadmilled sample in water is the total energy loss value of the Néel relaxation and Brownian relaxation. The heat generation for the Brownian relaxation of the particle rotation could be ignored for the large microsphere sample. The heat generation ability of the microsphere sample was slightly lower than that for the bead-milled sample. This difference (several %) would be due to the Brownian relaxation. These results suggested that the main reason for the high heat generation property of the milled samples was an increase in the Néel relaxation.

Conclusions

We obtained Y 3 Fe 5 O 12 microspheres with a 20-32 µm diameter range using a spray dryer from the bead-milled nanosized particles. The Y 3 Fe 5 O 12 microspheres having a high heat generation ability were applicable for the thermal coagulation therapy using the embolization method.

Fig. 1 :Fig. 2 :

 12 Fig. 1: The spray dryer apparatus for preparation of Y 3 Fe 5 O 12 microspheres.Fig.2:The apparatus for measuring the heat generation ability.

Fig. 3 :

 3 Fig. 3: XRD results for the commercial sample, fine Y 3 Fe 5 O 12 powder prepared by bead milling (using 0.1 mmφ beads for 4 h), and microspheres having 20-32 µm particle size.

Fig. 4 :

 4 Fig. 4: SEM photos of the spray dried particles (a) before and (b) after sifting using the sifting method.

1 •:Fig. 5 :

 15 Fig. 5: Relationship between the square of the magnetic field (370 kHz, 1.5-2.0 kA•m -1 ) and heat generation ability for (a) the bead-milled Y 3 Fe 5 O 12 powder samples (using 0.1 mmφ beads for 4 h) and (b) the microsphere sample.

Fig. 6 :

 6 Fig. 6: Relationship between the frequency of the AC magnetic field (200-370 kHz, 1.77 kA•m -1 ) and heat generation ability for (a) the bead-milled Y 3 Fe 5 O 12 powder samples (using 0.1 mmφ beads for 4 h) and (b) the microsphere sample.


M Bullo

F Dughiero

M Forzan

E Sieni

Pulsed electric field applied to biological tissue: measurement set-up to evaluate electrical resistivity

Keywords: electrical resistivity, biological tissues, measurement set-up, electroporation

In this paper we present the design of a measurement set-up to evaluate electrical resistivity of biological tissues.

Introduction

Electrochemotherapy (ECT) uses voltage pulses (e.g. 8 rectangular pulses at 1000V @ 5 kHz) applied to a biological tissue by means of pairs of implanted needles. Electroporation modifies cell membrane permeation to genes or drugs by opening transmembrane pores [1], [2]. This technique is currently exploited in medicine to treat some cutaneous and subcutaneous tumors, e.g. melanoma, soft tissue sarcomas, etc. [2]- [5]. In fact cell, membrane modifications due to the application of an electric field can improve the uptake of low permeate chemotherapeutic drugs in cancer cells. Electrical properties of tissues depend on cell size and density [6]- [8]. In recent literature the electrical resistivity of electroporated tissue has been modeled as a non-linear equation on electric field intensity [9]:

  )) ( tanh( 1 2 ) ( 1 0 1 1 1 0 1 th E k          E E     (1)
where  0 and  1 are the resistivity values before and after electroporation, E th the electric field threshold and k a fitting coefficient [9]. The threshold of electric field, E th that induces cell electroporation depends on the tissue type [10]. In this contribution a measurement set-up, designed to evaluate the tissue resistivity is investigated. This study is relevant in order to evaluate the electrical properties of different type of tumor. This information can be used to tune the clinical technique for different tumors that are currently treated by ECT (e.g. melanoma).

The method

The measurements of resistance have been done by the classical four point method [11], [START_REF]IEEE Guide for Measuring Earth Resistivity, Ground Impedance, and Earth Surface Potentials of a Ground System Part 1: Normal Measurements[END_REF]. The same method has been used also by other authors in order to characterize the biological tissue resistivity [START_REF] Wang | [END_REF]- [15]. Considering Fig. 1 where four electrodes are implanted at a distance d in the material to characterize. The two external electrodes, implanted at a depth L, are supplied by an electrical current, whereas the two internal electrodes are connected to a voltmeter to evaluate the voltage difference. The optimal value of L has been determined by numerical computations. Given the electrodes distance, d, and the voltage, V m , and current, I m , the measured resistivity is given by:

d I V m m   2  (2)
The first sensor has been realized by modifying the linear standard electrode used in ECT in which needles with a diameter, D el , of 0.7 mm are posed at inter-needle distance, d, of 2.5 mm. The length of external electrode has been studied using a Finite Element model.

FEM design

Model geometry is a parallelepiped (e.g. sizes 3×2×2.5 cm) with four cylinders that simulate the positions of the stainless steel needles, 0.7 mm diameter, represented in Fig 3 . The parallelepiped describes a region made of a homogeneous material with a known resistivity (e.g. 60 m). The external electrodes are made of stainless steel, whereas the cylinders, that represent voltage probes, are of the same material of the parallelepiped. In fact, it is supposed that they do not significantly perturb the current distribution since there are connected to the voltmeter that works as an open circuit. The external electrodes are supplied by imposing a constant voltage difference on the external electrodes. The correspondent electrical current has been evaluated by solving a static conduction problem. The following boundary value problem is solved on electric scalar potential, V [16]- [START_REF] Barba | Field models in electricity and magnetism[END_REF] in order to evaluate the electric field distribution:

0     V  inside the parallepiped 0    n V on external boundary (3)
imposing a constant electric potential, V, on the two electrodes and a floating potential on the model boundary.

Given the electric field distribution in the tissue, the voltage difference between the internal electrodes has been evaluated. Using (2) the resistivity has been derived. Table 1 reports the results obtained varying the length L of the external electrode and the electrode diameter, D_el with an electrode distance d equal to 2.5 mm.. The length of the internal voltage electrode is 0.5 mm; anyway, this length is not mandatory since these electrodes measure the voltage in the area between the external electrodes without perturbing the electric field distribution. The voltage difference is measured between the center of electrodes, V m1 and V m2 , at a depth of 0.1 mm from the electrode surface. I m is the applied current through the electrodes E 1 and E 2 in Fig. 1 (c). Finally, the resistivity  is evaluated with ( 2). Since the electric potential is not constant on the regions that describe the internal needles a resistivity interval, , has been evaluated considering the voltage variation on the electrode surface. For each electrode the voltage has been also evaluated in two pairs of points on needles surface, as shown in Fig 1(c). Considering the resistivity evaluated from these two voltage differences, V m1A and V m2B ,  + , or, V m1B and V m2A ,  -, in Fig 1(c), the interval of resistivity, , that is ( + - -)/2 has been computed. From data in Table 1 it appears that the electrodes with a diameter of 0.7 mm and an inter-electrode distance d equals to 2.5 mm with an electrode length between 0.5 and 2 mm give a better evaluation of the actual resistivity that has been fixed equal to 60 m (gray rows in Table 1). A lower electrode diameter underestimates the resistivity as well as longer electrodes.

A V d d d L Voltage difference 2,5 mm A V m1 V m2 V m1A V m1B V m2A V m2B E 1 E 2 (a) (b) (c)
Table 1 Results of FEM simulations

L [mm] D el [mm] d [mm] V m1 [V] V m2 [V] I m [A]  [m]  [m] 0.2 0.

Prototype and validation

From FEM results some prototypes of resistivity sensors have been constructed (example in Fig. 2 (a)). Size data are summarized in Table 2.

The first validation of the measurement device has been provided by measuring the resistivity of NaCl solution at 0.9%. The resistivity values have been measured with the new device and using the electrical conductivity meter HI8883 by Hanna Instruments, calibrated at 20 °C using the standard solution 'Crison conductivity standard 9710' (14,13 mSm -1 @ 25°C). The measured conductivity of the solution is 13.7 mSm -1 (resistivity 73 m). Results of these preliminary measurements are presented in Table 2. The sensors that give a more accurate evaluation of the resistivity are the ones with electrodes length of 1.5 or 2 mm. Longer electrodes, like L=2.5, overestimate the resistivity, whereas smaller electrodes underestimate this value. From these measurements it results that the probe S#2 and S#3 give an estimation of the resistivity close to the real one, as measured by electrical conductivity meter.

Potato tissue resistivity

The sensor S#2 has been tested to measure the resistivity of potato tissues. In this case the resistivity of potato tissue has been evaluated using the device in Fig. 2 (b). It is composed by two stainless steel contact with variable distance where the tissue sample can be positioned. A direct voltage has been applied by means of a DC voltage supply (GW GPR 1810H by Instek) and the corresponding electrical currents and applied voltages have been measured using a data logger (HP34970A, by HP). From the size of potato sample, measured using a vernier caliper, the resistivity, , has been derived from the resistance value, R, measured at the contacts:

h A R   (4)
where A is the area of the sample in contact with metal strip and h is the distance between metal contacts. From these measurements the range of the expected resistivity has been determined and measurement data are in Table 3.

Table 3 measurements of the potato resistivity using the device in Fig. 4. For resistivity and conductivity the sampling standard deviation is presented in bracket.

V [V] I [A] A [m2] h [m] d [mm]  [m]

 [Sm -1 ] Fig. 2 ( Some measurements of resistivity have been carried out also with the sensor (S#3), with the same instrumentation described before. Results are reported in Table 3. It appears that the estimated resistivity (or conductivity) using the two methods are comparable. The data identified with 'Sample A' are derived by the same potato tuber. Finally data in Table 4 report the resistivity of electropored and not-electropored potato tissue. The electroporation has been induced by placing a piece of potato tissue (with a thickness of approximately 1 cm) in the device shown in Fig. 2 (b) and applying a suitable constant voltage difference for few seconds with the DC power supply TDK-Lambda (GEN 1500 W). The electroporation occurrence is evaluated by observing the color of the sample after 24 h: if the tissue is dark the electroporation occurred [START_REF] Castiello | [END_REF]- [22]. An example of electroporated and not electroporated sample is in Fig. 2 (c). For all the samples, the resistivity has been evaluated before and after the application of electric currents and reported in Table 4. A difference in measured value of resistivity can be observed between electropored and not-electropored in all the samples. Difference in resistance values of not-electropored tissue can be due to water content and microscopic characteristic of tissue (e.g. root start).

Conclusion

The paper presents the design of a probe to measure resistivity of biological tissue. Experimental tests have been carried out to assess the measurements reliability by using a conductivity meter. Further measurements have been carried out on electroporated and not-electroporated potato tissue.

Fig 1 (

 1 Fig 1 (a) schematic of the measurements set-up, (b) geometry of FEM model and (c) evaluation points for voltage measurements.

  a) Sensor prototype, (a) measurements set-up for potato sample and (c) not-electroporated (Not-EP) and electroporated (EP) potato tissue.

Table 2 :

 2 evaluation of the electrical conductivity of a NaCl solution using the sensor.

		L [mm]	D el [mm]	d [mm]	V [V]	I [A]	d [mm]	 [Sm -1 ]	dev_st()	 [m]
	S#1	0.1	2.5	0.7	2.57	0.029	2.5	0.0072	0.0002	138.37
	S#2	1.5	2.5	0.7	2.71	0.058	2.5	0.0139	0.0031	75.19
	S#3	2	2.5	0.7	3.27	0.067	2.5	0.0134	0.0021	76.44
	S#4	2.5	2.5	0.7	2.94	0.068	2.5	0.0150	0.0012	69.40

Table 4

 4 measurements of the potato resistivity using the device in Fig.2(a) of electropored and not-electropored tissue (standard deviation in bracket).

		 [m] -not-EP	 [m] -EP	Thickness [mm]	Applied voltage [V]	E [V/cm]
	sample 1	19.92 ( 3.39)	14.49 ( 1.03)	9.60	37.50	39.06
	sample 2	21.64 ( 1.99)	12.46 ( 0.30)	9.20	42.00	45.65
	sample 3	14.83 ( 3.21)	7.60	( 0.41)	9.60	37.50	39.06
	sample 4	18.83 ( 0.55)	11.02 ( 0.22)	9.40	37.50	39.89