Patent Publication Number: US-2019187591-A1

Title: Image forming apparatus

Description:
TECHNICAL FIELD 
     The present invention relates to an electrophotographic image forming apparatus for forming an image with a liquid developer. 
     BACKGROUND ART 
     Conventionally, the image forming apparatus for forming the image with the liquid developer containing toner and a carrier liquid has been known. The liquid developer is accommodated in a mixer and is supplied from the mixer to a developing device, and is subjected to development. Then, toner for supply is accommodated in a toner tank and a carrier liquid for supply is accommodated in a carrier tank, respectively, and the toner for supply and the carrier liquid for supply are supplied from the respective tanks to the mixer. The mixer mixes and disperses the toner in the carrier liquid and generates the liquid developer. In such an image forming apparatus, the liquid developer which is not used in the development is collected and recycled. In recycling of the liquid developer, toner which is a dispersoid in the liquid developer and the carrier liquid which is a dispersion medium in the liquid developer are separated, and the separated carrier liquid is sent to the carrier tank and is used again (Japanese Laid-Open Patent Application 2008-242436). 
     However, in the case where the liquid developer is repetitively recycled, with application of a high voltage, volume resistivity of the carrier liquid after separation lowers depending on an increase in amount of a charge control agent ionized from the toner in the carrier liquid after the separation (deterioration of the carrier liquid). When the carrier liquid lowered in volume resistivity (hereinafter simply referred to as resistance) is supplied to the mixer, the resistance of the liquid developer lowers. Then, when the liquid developer lowered in resistance is subjected to development, an image defect can be generated. Therefore, conventionally, the resistance of the carrier tank is detected using a resistance sensor and the carrier liquid for supply high in resistance is supplied on the basis of a detection value of the resistance sensor, and thus the resistance of the liquid developer was maintained in a predetermined range. 
     Problem to be Solved by the Invention 
     As described above, the resistance of the carrier liquid is largely influenced by an amount of the charge control agent ionized from the toner. However, in the carrier liquid, in addition to the charge control agent, another substance, capable of fluctuating the resistance, such as a toner dispersing agent is contained. For that reason, conventionally, even when the carrier liquid for supply is supplied to the carrier tank on the basis of the detection value of the resistance sensor influence by the substance in addition to the charge control agent, the resistance of the carrier liquid cannot be improved, and as a result, it was difficult to maintain the resistance of the liquid developer in a predetermined range. 
     The present invention has been accomplished in view of the above-described problem, and aims at providing an image forming apparatus in which in a constitution re-using the carrier liquid, the volume resistivity of the carrier liquid is acquired by calculation without using the resistance sensor and supply control of the carrier liquid for supply is carried out on the basis of this. 
     Means for Solving the Problem 
     According to an aspect of the present invention, there is provided an image forming apparatus comprising: an image forming portion for forming an image with a liquid developer containing toner and a carrier liquid; a separating device for separating the liquid developer collected from the image forming portion into the toner and the carrier liquid under application of a voltage; a toner container for accommodating toner for supply; a carrier container for accommodating the carrier liquid separated by the separating device; a mixing device for mixing the carrier liquid supplied from the carrier container with the toner for supply supplied from the toner container; a supplying device for supplying, to the carrier container, a carrier liquid for supply having a resistance value higher than a predetermined resistance value; a first supplying portion for supplying the liquid developer from the mixing device to the image forming portion; a second supplying portion for supplying the carrier liquid from the separating device to the carrier container; a calculating portion for calculating a value relating to volume resistivity of the carrier liquid in the carrier container on the basis of a supplying operation of the second supplying portion; and a controller for causing the supplying device to supply the carrier liquid for supply therefrom to the carrier container in order to adjust the volume resistivity of the carrier liquid in the carrier container on the basis of the value relating to the volume resistivity of the carrier liquid acquired by the calculating portion. 
     According to another aspect of the present invention, there is provided an image forming apparatus comprising: an image forming portion for forming an image with a liquid developer containing toner and a carrier liquid; a separating device for separating the liquid developer collected from the image forming portion into the toner and the carrier liquid under application of a voltage; a toner container for accommodating toner for supply; a carrier container for accommodating the carrier liquid separated by the separating device; a mixing device for mixing the carrier liquid supplied from the carrier container with the toner for supply supplied from the toner container; a supplying device for supplying, to the mixing device, a carrier liquid for supply; a first supplying portion for supplying the liquid developer from the mixing device to the image forming portion; a second supplying portion for supplying the carrier liquid from the separating device to the carrier container; a calculating portion for calculating a value relating to volume resistivity of the carrier liquid in the carrier container on the basis of a supplying operation of the second supplying portion; and a controller for causing the supplying device to supply the carrier liquid for supply therefrom to the mixing device in order to adjust the volume resistivity of the carrier liquid in the carrier container on the basis of the value relating to the volume resistivity of the carrier liquid acquired by the calculating portion. 
     Effect of the Invention 
     According to the present invention, in the constitution re-using the carrier liquid, the volume resistivity of the carrier liquid depending on the number of times of drive of the second supplying portion is acquired by calculation and supply control of the carrier liquid for supply is carried out on the basis of this, and thus the volume resistivity of the liquid developer is easily maintained in a predetermined range. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic view showing a structure of an image forming apparatus according to First Embodiment. 
         FIG. 2  is a schematic view showing a feeding path of a liquid developer in the image forming apparatus according to First Embodiment. 
         FIG. 3  is a control block diagram showing a supply control system of a carrier liquid for supply. 
         FIG. 4  is a flowchart showing a supply control process of the carrier liquid for supply. 
         FIG. 5  is a flowchart showing a process of calculating volume resistivity of a carrier liquid. 
         FIG. 6  is a view for illustrating a calculating method of the volume resistivity of the carrier liquid depending on the number of times of passing of the carrier liquid through a separation and extraction device. 
         FIG. 7  is a graph showing a carrier liquid amount for each of numbers of times of the passing of the carrier liquid through the separation and extraction device. 
         FIG. 8  is a view for illustrating a calculating method of the volume resistivity of the carrier liquid depending on the number of times of passing of the carrier liquid through the separation and extraction device and a developing device. 
         FIG. 9  is a graph showing a carrier liquid amount for each of numbers of times of the passing of the carrier liquid through the separation and extraction device and the developing device. 
         FIG. 10  is a schematic view showing a feeding path of a liquid developer in an image forming apparatus according to Second Embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     First Embodiment 
     First embodiment of the present invention will be described using  FIGS. 1-7 . First, a general structure of an image forming apparatus in this embodiment will be described using  FIG. 1 . 
     (Image Forming Apparatus) 
     An image forming apparatus  100  in this embodiment is a digital printer of an electrophotographic type in which a toner image is formed on a recording material S (a sheet, a sheet material such as an OHP sheet and so on). The image forming apparatus  100  is operated on the basis an image signal, and a toner image formed by an image forming portion  12  is transferred onto the sheet as the recording material successively fed from each of cassettes  11   a ,  11   b  and then is fixed on the recording material S, so that an image is obtained. The image signal is sent from an external terminal such as an unshown scanner or an unshown personal computer to the image forming apparatus  100 . 
     The image forming portion  12  includes a photosensitive drum  13  as an image bearing member, a charger  14 , a laser exposure device  15 , a developing device  16  and a drum cleaner  19 . A surface of the photosensitive drum  13  electrically charged by the charger  14  is irradiated with laser light E from the laser exposure device  15  depending on the first signal, so that an electrostatic latent image is formed on the photosensitive drum  13 . This electrostatic latent image is developed as a toner image by the developing device  16 . In this embodiment, in the developing device  16 , a liquid developer D in which powdery toner which is a dispersoid is dispersed in a carrier liquid which is a dispersion medium is accommodated, and development is effected using this liquid developer D. 
     The liquid developer D is generated by mixing and dispersing toner T in a carrier liquid C in a predetermined ratio in a mixer  31  as a mixing device, and then is supplied to the developing device  16 . The carrier liquid C is accommodated in a carrier tank  32  as a carrier container, and the toner T for supply is accommodated in a toner tank  33  as a toner container. Then, depending on a mixed state of the carrier liquid C and the toner T in the mixer  31 , the carrier liquid C or the toner T is supplied from an associated tank toward the mixer  31 . In the mixer  31 , a stirring blade driven by an unshown motor is accommodated, and the developer liquid D is mixed with the carrier liquid C or the toner T by being stirred, so that the toner is dispersed in the carrier liquid. 
     The liquid developer supplied from the mixer  31  to the developing device  16  is coated (supplied) on a developing roller  18  by a coating roller  17  in a supplying section  16   a  of the developing device  16  and is used for development. The developing roller  18  carries and feeds the liquid developer D on a surface thereof, and develops with the toner the electrostatic latent image formed on the photosensitive drum  13  (image bearing member). The toner T and the carrier liquid C which remain on the developing roller  18  after the development is collected in a collecting section  16   b  of the developing device  16 . Here, each of coating of the liquid developer from the coating roller  17  onto the developing roller  18  and the development of the electrostatic latent image on the photosensitive drum  13  by the developing roller  18  is made using an electric field. 
     The toner image formed on the photosensitive drum  13  is transferred onto an intermediary transfer roller  20  using the electric field, and then is fed to a nip formed by the intermediary transfer roller  20  and a transfer roller  21 . The toner T and the carrier liquid C which remain on the photosensitive drum  13  after the toner image transfer onto the intermediary transfer roller  20  are collected by the drum cleaner  19 . Incidentally, at least one of the intermediary transfer roller  20  and the transfer roller  21  may also be an endless belt. 
     The recording material S accommodated in each of the cassettes  11   a ,  11   b  is fed toward a registration feeding portion  23  by an associated feeding portion  22   a  or  22   b  constituted by feeding rollers. The registration feeding portion  23  feeds the recording material S to the nip between the intermediary transfer roller  20  and the transfer roller  21  by being timed to the toner image transferred on the intermediary transfer roller  20 . 
     In the nip between the intermediary transfer roller  20  and the transfer roller  21 , the toner image is transferred onto the recording material S passing through the nip, and the recording material S on which the toner image is transferred is fed to a fixing device  25  by a feeding belt  24 , so that the toner image transferred on the recording material S is fixed. The recording material S on which the toner image is fixed is discharged to an outside of the image forming apparatus, so that an image forming step is completed. 
     The intermediary transfer roller  20  and the transfer roller  21  are provided with an intermediary transfer roller cleaner  26  and a transfer roller cleaner  27 , respectively, for collecting the toner T and the carrier liquid C which remain on the associated roller. 
     (Liquid Developer) 
     Next, the liquid developer develop will be described. As the liquid developer D, a conventionally used liquid developer may also be used, but in this embodiment, an ultraviolet-curable liquid developer D is used and will be described below. 
     The liquid developer D is an ultraviolet-curable liquid developer which contains a cation-polymerizable liquid monomer, a photo-polymerization initiator and toner particles insoluble in the cation-polymerizable liquid monomer. The cation-polymerizable liquid monomer is vinyl ether compound, and the photo-polymerization initiator is a compound represented by the following formula (Chem 1). 
     
       
         
         
             
             
         
       
     
     Specifically, first, the toner particles include a colorant and a toner resin material in which the colorant is incorporated. Together with the toner resin material and the colorant, another material such as a charge control agent may also be contained. As a manufacturing method of the toner particles, a well-known technique such as a coacervation in which the colorant is dispersed and a resin material is gradually polymerized so that the colorant is incorporated in the polymer or an internal pulverization method in which a resin material or the like is melted and the colorant is incorporated in the melted resin material may also be used. As the toner resin material, epoxy resin, styrene-acrylic resin or the like is used. The colorant may be a general-purpose organic or inorganic colorant. In the manufacturing method, in order to enhance a toner dispersing property, a dispersant is used but a synergist can also be used. 
     Next, a curable liquid which is the carrier liquid is constituted by the charge control agent for imparting electric charges to the toner surface, a photo-polymerization agent (initiator) for generating acid by ultraviolet (UV) irradiation and a monomer bondable by the acid. The monomer is a vinyl ether compound which is polymerizable by a cationic polymerization reaction. Separately from the photo-polymerization initiator, a sensitizer may also be contained. By photo-polymerization, a storage property lowers, and therefore a cationic polymerization inhibitor may also be added in an amount of 10-5000 ppm. In addition, a charge control aid, another additive or the like may also be used in some cases. 
     The UV curing agent (monomer) of the developer is a mixture of about 10% (weight %) of a monofunctional monomer having one vinyl ether group represented by a chemical formula (Chem 2 below) and about 90% (weight %) of difunctional monomer having two vinyl ether groups (represented by a chemical formula (Chem 3 below). 
     
       
         
         
             
             
         
       
     
     As the photo-polymerization initiator, 0.1% of a compound represented by (Chem 4) below is mixed. By using this photo-polymerization initiator, different from the case where an ionic photo-acid generator, a high-resistance liquid developer is obtained while enabling satisfactory fixing. 
     
       
         
         
             
             
         
       
     
     Incidentally, a cationic polymerizable liquid monomer may desirably be a compound selected from the group consisting of dichloropendadiene vinyl ether, cyclohexanedimethanol divinyl ether, tricyclodecane vinyl ether, trimethylolpropane trivinyl ether, 2-ethyl-1,3-hexamediol divinyl ether, 2,4-diethyl-1,5-pentanediol divinyl ether, 2-butyl-2-ethyl-1,3-propanediol divinyl ether, neopentylglycol divinyl ether, pentaerythritol tetravinyl ether, and 1,2-decanediol divinyl ether. 
     As the charge control agent, a well-known compound can be used. As a specific example, it is possible to use fats and oils such as linseed oil and soybean oil; alkyd resin; halogen polymer; oxidative condensates such as aromatic polycarboxylic acid, acidic group-containing water-soluble dye and aromatic polyamine; metallic soaps such as cobalt naphthenate, nickel naphthenate, iron naphthenate, zinc naphthenate, cobalt octylate, nickel octylate, zinc octylate, cobalt dodecylate, nickel dodecylate, zinc dodecylate, aluminum stearate, and cobalt 2-ethylhexylate; sulfonic acid metal salts such as petroleum acid metal salt and metal salt of sulfosuccinic acid; phospholipid such as lectithin; salicylic acid metal salt such as t-butylsalicylic acid metal complex; polyvinyl pyrrolidone resin; polyamide resin; sulfonic acid-containing resin; and hydroxybenzoic acid derivative. 
     (Feeding of Liquid Developer) 
     Next, feeding of the liquid developer D in this embodiment will be described using  FIG. 2 . A transporting pipe from the carrier tank  32  to the mixer  31  and a transporting pipe from the toner tank  33  to the mixer  31  are provided with a carrier supplying pump  41  and a toner supplying pump  42 , respectively, and a supply amount of the carrier liquid C to the mixer  31  and a supply amount of the toner T to the mixer  31  are adjusted. From the mixer  31 , the liquid developer D necessary for the development is supplied to the developing device  16  by a developer supplying pump  44  as a first supplying portion. The developing device  16  is provided with a developer amount detecting device  160 , and the developer amount detecting device  160  detects an amount of the liquid developer D in the developing device  16 . Supply of the liquid developer D to the developing device  16  is carried out so that a detection value of the developer amount detecting device  160  is not less than a predetermined value (for example 200 ml). Then, the liquid developer D which remains on the developing roller  18  after the development and which is collected into a collecting section  16   b  of the developing device  16  is returned to the mixer  31  by a circulating pump  43  as a returning portion, and is used again. Incidentally, the liquid developer D collected into the collecting section  16   b  of the developing device  16  may also be fed to the separation and extraction device  34 . 
     As described above, the toner T and the carrier liquid C which are collected by the drum cleaner  19 , the intermediary transfer roller cleaner  26  and the transfer roller cleaner  27  are fed to the separation and extraction device  34  as a separating device by pumps  48 ,  49  and  50 , respectively. The separation and extraction device  34  is separates the toner T and the carrier liquid C by an electrolytic parting system, and makes the carrier liquid re-usable. 
     The separation and extraction device  34  separates the liquid developer into the re-usable carrier liquid and waste fluid W containing impurities such as the toner and paper powder. The re-usable carrier liquid separated by the separation and extraction device  34  is fed to the carrier tank  32  by a separation and collection pump  45  as a second supplying portion. On the other hand, the separated waste fluid W is fed to a waste fluid collecting container  35  by a pump  47  provided to a transporting pipe. 
     In the carrier tank  32 , a float sensor  320  as a liquid amount detecting portion for detecting a liquid amount of the carrier liquid in the carrier tank  32  is provided. In this embodiment, the carrier tank  32  is provided with only the float sensor  320  but is not provided with a resistance sensor for detecting the volume resistivity (resistance) of the carrier liquid. The float sensor  320  detects a position (liquid level) of a float floated on a liquid surface, and thus detects the liquid amount in the carrier tank  32 . As the float sensor  320 , for example, a float sensor in which a float provided with a magnet and a reed switch are provided and a position of the float is detected by the reed switch is used. Incidentally, the liquid amount detecting portion is not limited to the float sensor  320 . 
     [Supply of Carrier Liquid] 
     In this embodiment, a supplying device  36 A for supplying the carrier liquid for supply is provided. The supply of the carrier liquid for supply by the supplying device  36 A is controlled by a controller  200  (see  FIG. 1 ) as a controller. The supplying device  36 A includes a supplying carrier tank  36  and a supplying pump  51  provided to a communicating pipe communicating the supplying carrier tank  36  with the carrier tank  32 . In the supplying carrier tank  36 , the carrier liquid for supply having relatively high resistance of not less than 1.0E+14 Ωcm in resistance is accommodated. This carrier liquid for supply is higher in resistance than the carrier liquid which is separated and extracted by the separation and extraction device  34  and which is sent to the carrier tank  32 , and is higher in resistance than the carrier liquid used at the image forming portion  12 . 
     The supplying device  36 A is capable of supplying the carrier liquid for supply on the basis of the liquid amount of the carrier liquid in the carrier tank  32  (in the carrier container). Specifically, in the case where the liquid amount of the carrier liquid in the carrier tank  32  is detected as being a predetermined value or less by the float sensor  320 , the supplying pump  51  is driven, so that the carrier liquid for supply is supplied from the supplying carrier tank  36  to the carrier tank  32 . 
     Further, the supplying device  36 A is capable of supplying the carrier liquid for supply on the basis of the resistance of the carrier liquid in the carrier tank  32 . In the case of this embodiment, the resistance of the carrier liquid in the carrier tank  32  is acquired by calculation, and in the case where the resistance of this carrier liquid is lower than the predetermined value, the supplying pump  51  is driven, so that the carrier liquid for supply is supplied from the supplying carrier tank  36  to the carrier tank  32 . 
     [With Regard to Deterioration of Carrier Liquid] 
     On the surface of the toner in the liquid developer, the charge control agent of a polarity opposite to a polarity of a surface potential of the toner exists. Further, as regards the liquid developer subjected to development by the developing device  16 , the toner and the charge control agent are ionized in response to application of a high voltage during the development. Most of the toner in the liquid developer is consumed with the development, but the charge control agent is little consumed, and therefore, the charge control agent is liable to remain in the liquid developer. The resistance of this charge control agent is for example about 1.0E+9 Ωcm, and therefore, the liquid developer repetitively used is lowered in resistance compared with the liquid developer before repetitively used. Thus, when the liquid developer (deteriorated liquid developer) containing a large amount of the ionized charge control agent is used again as it is, the image defect is liable to generate. 
     As described above, the liquid developer collected by the drum cleaner  19 , the intermediary transfer roller cleaner  26  and the transfer roller cleaner  27  is separated into the carrier liquid and the waste fluid by the separation and extraction device  34 . In the separation and extraction device  34 , when the liquid developer is separated into the carrier liquid and the waste fluid, the high voltage is applied to the liquid developer. That is, also during the recycling of the liquid developer, the toner and the charge control agent are ionized. Then, even when the liquid developer is separated into the carrier liquid and the waste fluid, the charge control agent remains in the carrier liquid. Therefore, the charge control agent increases in amount in the carrier liquid separated by the separation and extraction device  34 , and correspondingly thereto, the resistance of the carrier liquid in the carrier tank  32  lowers. 
     The resistance of the carrier liquid in the carrier tank  32  can be increased only by the above-described supply of the carrier liquid for supply. By the supply of the carrier liquid for supply, a relative amount occupied by the charge control agent in the carrier liquid decreases, so that the resistance of the carrier liquid increases. 
     Incidentally, conventionally, in order to improve the resistance of the carrier liquid, the carrier tank  32  was provided with a resistance sensor, and in the case where a detection value (sensor value) of the resistance sensor was smaller than a predetermined value, the supplying device  36 A was controlled, and thus supply of the carrier liquid for supply was carried out. The resistance sensor detects an electric resistance at that time by providing a pair of electrodes in the liquid developer and by causing a current to pass through the electrodes, for example. Therefore, a detection value of the resistance sensor can fluctuate by the influence of not only the charge control agent in the carrier liquid but also another substance such as the toner dispersant. However, the resistance sensor detects only the resistance of an entirety of the carrier liquid and cannot detect an amount of the charge control agent contained in the carrier liquid and an amount of another substance such as the toner dispersant. For that reason, even when sensor amounts are the same, amounts of the charge control agents contained in the carrier liquids are not always the same. Although the amounts of the charge control agents contained in the carrier liquids may be not the same when the supply of the carrier liquid for supply is carried out on the basis of the sensor values, a variation (error) can occur in resistance of the carrier liquids after the supply of the carrier liquid for supply. Thus, in the case where the resistance sensor is used, a change in resistance depending on the amount of the charge control agent contained in the carrier liquid cannot be properly grasped. For that reason, the carrier liquid for supply is supplied, and even when the sensor value exceeds the predetermined value, the resistance of the liquid developer in the mixer  31  to which the carrier liquid is supplied from the carrier tank  32  was not improved, so that the image defect continuously generated in some instances. 
     In this embodiment, in view of the above point, the resistance of the carrier liquid in the carrier tank  32  was acquired by calculation without using the resistance sensor, and the supplying device  36 A was controlled on the basis of this, so that supply of the carrier liquid for supply was enabled. In the following, supply control of the carrier liquid for supply will be described with reference to  FIG. 3  to  FIG. 6  while appropriately making reference to  FIG. 1  and  FIG. 2 . 
     [Controller] 
     The image forming apparatus  100  of this embodiment includes the controller  200  as the controller. With the controller  200 , as shown in  FIG. 3 , the memory  201 , the separation and extraction device  34 , the circulating pump  43 , the developer supplying pump  44 , the separation and collection pump  45 , the supplying pump  51  and the like are connected. Incidentally, with the controller  200 , in addition to the illustrated members, various devices and various sensors, such as the image forming portion  12 , the float sensor  320 , another pump, motor, high voltage source and the like are connected, but are omitted from illustration and description in this embodiment. 
     The controller  200  is for example a CPU (Central Processing Unit) or the like for carrying out various pieces of control of the image forming apparatus  100 , such as an image forming operation. The memory  201  is a storing portion such as an ROM, an RAM or a hard disk device. In the memory  201 , various control programs, data and the like for controlling the image forming apparatus  100  are stored. The controller  200  executes an image forming job (image forming program) stored in the memory  201  and causes the image forming apparatus  100  to carry out image formation. Further, the controller  200  executes a supply control process (see  FIGS. 4 and 5  described later) of the carrier liquid for supply stored in the memory  201  and causes the image forming apparatus  100  (specifically the supplying device  36 A) to perform the supply of the carrier liquid for supply. In the case of this embodiment, the controller  200  causes the supplying device  34 A to operate in the case where the number of times per unit time of drive of the separation and collection pump  45  is large. Incidentally, the memory  201  is capable of temporarily storing a calculation process result or the like with execution of the various control programs. 
     Here, the image forming job is a series of operations from a start of the image formation until the image forming operation is completed, on the basis of a print signal for forming the image on the recording material S. That is, the image forming job is a series of operations from a start of a preparatory operation (so-called a pre-rotation operation) required for carrying out the image formation until a preparatory operation (so-called a post-rotation) required for ending the image formation toner the image forming step. Specifically, the image forming job refers to the operations from the time of the pre-rotation (preparatory operation before the image formation) after receiving the print signal (input of the image forming job) to the post-rotation (operation after the image formation), and includes an image forming period and a sheet interval. 
     The controller  200  can be largely divided into a carrier supply discriminating portion  202 , a pump driver  203  and a calculating portion  300 . The carrier supply discriminating portion  202  discriminates whether or not the carrier liquid for supply should be supplied to the carrier tank  32  on the basis of the resistance of the carrier liquid in the carrier tank  32 . The controller  200  controls the supplying pump  51  on the basis of this discrimination. The controller  200  controls the supplying pump  51 , the circulating pump  43 , the developer supplying pump  44 , the separation and collection pump  45  and further another pump through the pump driver  203 . In the case of this embodiment, the controller  200  counts the number of times of drive of each of the pumps and causes the memory  201  to store counted values. 
     The calculating portion  300  as a calculating portion is divided into a deterioration degree distribution calculating portion  301  and a resistance calculating portion  302 . In this embodiment, as the resistance of the carrier liquid used when the carrier supply discriminating portion  202  discriminates whether or not the carrier liquid for supply should be supplied, resistance acquired by the calculating portion  300  is used. Although description will be made specifically later, the resistance calculating portion  302  acquires the resistance of the carrier liquid in the carrier tank  32  on the basis of a “liquid amount of the carrier liquid for each of numbers of times of passing of the carrier liquid through the separation and extraction device  34 ” and “resistance of the carrier liquid for each of numbers of times of passing of the carrier liquid through the separation and extraction device  34 ”. The above-described “liquid amount (of the carrier liquid) for each of numbers of times of passing” is calculated by the deterioration degree distribution calculating portion  301  and is stored in the memory  201 . On the other hand, as regards the above-described “resistance (of the carrier liquid) for each of numbers of times of passing”, the resistance of the carrier liquid after passing through the separation and extraction device  34  is stored in the memory  201  in advance for each of numbers of times of the passing. This is acquired by an experiment. 
     [Supply Control Process] 
       FIG. 4  shows a supply control process of the carrier liquid for supply executed by the controller  200 . This process is repetitively executed, for example, for each 100 milliseconds so long as the image forming job is carried out. As shown in  FIG. 4 , the controller  200  detects the presence or absence of execution of the image forming job (S 1 ). Then, the controller  200  executes process of a “carrier liquid resistance calculating process” (S 2 ) and later in synchronism with the execution of the image forming job, i.e., during the operation of the image forming apparatus  100 . As described later (see  FIG. 5 ), in the “carrier liquid resistance calculating process”, every drive of the separation and collection pump  45  during the execution of the image forming job, the resistance of the carrier liquid in the carrier tank  32  is acquired by calculation. “Carrier liquid resistance calculating process” 
     (S 2  of  FIG. 4 ) will be described using  FIG. 5 . The deterioration degree distribution calculating portion  301  counts, every drive of the separation and collection pump  45 , the number of times of drive of the separation and collection pump  45  on the basis of a pump driving signal acquired from the pump driver  203  and causes the memory  201  to store counted values (S 21 ). In this embodiment, the case where the separation and collection pump  45  feed a predetermined amount of the carrier liquid to the carrier tank  32  is counted as one time of drive of the separation and collection pump  45 . Further, the deterioration degree distribution calculating portion  301  acquires the liquid amount of the carrier liquid in the carrier tank  32  from the float sensor  320  (S 22 ). Then, the deterioration degree distribution calculating portion  301  calculates, every one drive of the separation and collection pump  45  (every one passing of the carrier liquid through the separation and extraction device  34 ), the “liquid amount (of the carrier liquid) for each of numbers of times of passing” in which the carrier liquid in the carrier tank  32  passes through the separation and extraction device  34 . For example, the deterioration degree distribution calculating portion  301  calculates a “liquid amount by passing of one time” in the case where the separation and collection pump  45  is driven one time, calculates the “liquid amount by passing of one time” and “liquid amount by passing of two times” in the case where the separation and collection pump  45  is driven two times, and calculates the “liquid amount by passing of one time”, the “liquid amount by passing of two times” and a “liquid amount by passing of three times” in the case where the separation and collection pump  45  is driven three times. As described above, in the case, the “number of times of passing (number of passing times)” of the carrier liquid through the separation and extraction device  34  is grasped by the number of times of passing of the carrier liquid through the separation and collection pump  45 . 
     [Calculation of Liquid Amount for Each Number of Times of Passing] 
     A calculating method of the “liquid amount for each number of times of passing” will be described by a calculation mold. As a calculation model, a matrix C with one row and n columns, in which the liquid amount of the carrier liquid in the carrier tank  32  is assigned is used. At first row and first column of the matrix C, as a “liquid amount by passing of no time (in an initial state of no passing” in which the carrier liquid does not pass through the separation and collection pump  45  even one time, an entire amount of the carrier liquid amount in the carrier tank  32  is assigned. Then, every time when the separation and collection pump  45  is driven one time (every time when the carrier liquid passes through the separation and extraction device  34  one time, the “liquid amount for each number of times of passing” is successively assigned for elements moving the columns. For example, when the separation and collection pump  45  is driven two times, the “liquid amount by passing of no time” for the first row and first column, the “liquid amount by passing of one time” for the first row and second column and the “liquid amount by passing of two times” for the first row and third column and successively assigned. The sum of the elements of the matrix C is coincident with a total liquid amount of the carrier liquid in the carrier tank  32 . Incidentally, the liquid amount of the carrier liquid may preferably be calculated using a volume (ml or cc) rather than a weight from a viewpoint of decreasing a calculation load. 
     This will be specifically described using  FIG. 6 . In this embodiment, the case where the separation and collection pump  45  is driven two times will be described. Incidentally, as a calculation model, the liquid amount of the carrier liquid flowing from the separation and extraction device  34  with single drive of the separation and collection pump  45  and the liquid amount of the carrier liquid contained in the liquid developer flowing into the separation and extraction device  34  by the pumps  48 ,  49  and  50  at that time are equal to each other. That is, the carrier liquid amount does not increase and decrease before and after the drive of the separation and collection pump  45 . Further, the liquid amount (feeding amount) of the carrier liquid fed by the single drive of the separation and collection pump  45  is 50 ml, and the liquid amount of the carrier liquid contained in the carrier tank  32  is 100 ml. Of course, these numerical values are an example for explanation and are not limited thereto. 
     The “liquid amount by passing of no time”, the “liquid amount by passing of one time” and the “liquid amount by passing of two times” are represented by C 10 , C 11  and C 12 , respectively. In the case where the separation and collection pump  45  is not driven even once, the respective elements of the matrix C can be represented by formula 1 to formula 3. In this embodiment, the matrix C is “100, 0, 0” (after passing of no time (during initial state) “AFTER NO PASSING (INITIAL)” of  FIG. 6 ). 
         C [1,1]= C 10=100  formula 1
 
         C [1,2]= C 11=0  formula 2
 
         C [1,3]= C 12=0  formula 3
 
     By the first drive of the separation and collection pump  45 , the respective elements of the matrix C changes depending on calculation of formula 4 to formula 6. The formula 4 to 6 represent, of a liquid amount R (feeding amount of the separation and collection pump  45 ) of the carrier liquid passing through the separation and extraction device  34  depending on the single drive of the separation and collection pump  45 , the “liquid amount by passing of no time”, the “liquid amount by passing of one time” and the “liquid amount by passing of two times” as Q 10 , Q 11  and Q 12 . The liquid amounts Q 10  to Q 12  constitute a matrix Q “50, 0, 0”. The above Q 10  to Q 12  are assigned to first row and first column to first row and third column as shown in  FIG. 6 . 
         Q 10= R×C 10/( C 10+ C 11+ C 12)=50×100/100=50   formula 4
 
         Q 11= R×C 11/( C 10+ C 11+ C 12)=50×0/100=0   formula 5
 
         Q 12= R×C 12/( C 10+ C 11+ C 12)=50×0/100=0   formula 6
 
     Then, with first passing of the carrier liquid through the separation and extraction device  34 , the respective elements of the matrix Q “50, 0, 0” are moved row by row, so that a matrix Q “0, 50, 0” is provided. This is accommodated again in the carrier tank  32 , so that the respective elements of the matrix C after the single drive of the separation and collection pump  45  can be represented by formula 7 to formula 9. 
         C [1,1]= C 10− Q 10=100−50=50  formula 7
 
         C [1,2]= C 11− Q 11+ Q 10=0−0+50=50   formula 8
 
         C [1,3]= C 12− Q 12+ Q 11=0−0+0=0  formula 9
 
     The matrix C “50, 50, 0” after the single drive of the separation and collection pump  45  (after passing of one time “AFTER 1ST-PASSING” of  FIG. 6 ) represents that of the carrier liquid in the carrier tank  32 , the “liquid amount by passing of no time” is 50 ml, the “liquid amount by passing of one time” is 50 ml, and the “liquid amount by passing of two times” is 0 ml. That is, when the separation and collection pump  45  is driven one time, 50 ml of the carrier liquid which has not been fed to the separation and extraction device  34  remains as the “liquid amount by passing of no time” in the carrier tank  32 , and 50 ml of the carrier liquid fed to the separation and extraction device  34  is accommodated again as the “liquid amount by passing of one time” in the carrier tank  32 . 
     Although description will be omitted, the respective elements of the matrix C after the second drive of the separation and collection pump  45  are similarly represented by formula 11 to formula 13 (matrix C “25, 50, 25”, after passing of two times, “AFTER 2ND-PASSING” of  FIG. 6 ). 
         C [1,1]= C 10− Q 10=50−25=25  formula 11
 
         C [1,2]= C 11− Q 11+ Q 10=50−25+25=50   formula 12
 
         C [1,3]= C 12− Q 12+ Q 11=0−0+25=25   formula 13
 
     Here, Q 10  to Q 12  are acquired by the following formula 14 to formula 16. 
         Q 10= R×C 10/( C 10+ C 11+ C 12)=50×50/100=25   formula 14
 
         Q 11= R×C 11/( C 10+ C 11+ C 12)=50×50/100=25   formula 15
 
         Q 12= R×C 12/( C 10+ C 11+ C 12)=50×0/100=0   formula 16
 
     The matrix C “25, 50, 25” represents, as a breakdown of the carrier liquid in the carrier tank  32 , that the “liquid amount by passing of no time” is 25 ml, the “liquid amount by passing of one time” is 50 ml, and the “liquid amount by passing of two times” is 25 ml. That is, during the second drive of the separation and collection pump  45 , of 100 ml of the carrier liquid containing 50 ml which is the “liquid amount by passing of no time” and 50 ml which is the “liquid amount by passing of one time”, 50 ml of the carrier liquid is fed. In the carrier tank  32 , the “liquid amount by passing of no time” of the carrier liquid and the “liquid amount by passing of one time” of the carrier liquid exist in mixture, so that of 50 ml of the carrier liquid to be fed, 25 ml is the “liquid amount by passing of no time” and remaining 25 ml is the “liquid amount by passing of one time” (matrix Q “25, 25, 0”). If so, also as regards 50 ml of the carrier liquid remaining in the carrier tank  32 , the “liquid amount by passing of no time” is 25 ml and the “liquid amount by passing of one time” is 25 ml (matrix C “25, 25, 0”). 
     The carrier liquid in 50 ml passes through the separation and extraction device  34 , so that the “liquid amount by passing of one time” is 25 ml and the “liquid amount by passing of two times” is 25 ml, and the carrier liquid returns to the carrier tank  32  (matrix Q “0, 25, 25”). Further, as described above, in the carrier tank  32 , 25 ml which is the “liquid amount by passing of no time” of the carrier liquid and 25 ml which is the “liquid amount by passing of one time” of the carrier liquid remain. Therefore, in the carrier tank  32  after the second drive of the separation and collection pump  45 , the carrier liquid in which 25 ml which is the “liquid amount by passing of no time” of the carrier liquid, 50 ml which is the “liquid amount by passing of one time” of the carrier liquid and 25 ml which is the “liquid amount by passing of two times” of the carrier liquid exist in mixture is accommodated (matrix C “25, 50, 25”). 
     In the above-described manner, calculation of the “liquid amount for each number of times of passing” of the carrier liquid contained in the carrier liquid in the carrier tank  32  is performed every time when the separation and collection pump  45  is driven once (every time when the carrier liquid passes through the separation and extraction device  34  once). In  FIG. 7 , an example of the “liquid amount for each number of times of passing (NUMBER OF PASSING TIMES (TIMES))” in the case where the separation and collection pump  45  is driven twenty times is shown. 
     The “liquid amount for each number of times of passing” shown in  FIG. 7  represents as a whole a distribution such that how many amount of the carrier liquid which has passed through the separation and extraction device  34  what times exists in the carrier tank  32 . As has already been described above, also when the liquid developer is separated into the carrier liquid and the waste fluid by the separation and extraction device  34 , the relative amount occupied by the charge control agent in the carrier liquid increases (the carrier liquid deteriorates). That is, with a larger number of times of drive (number of times of passing) of the separation and collection pump  45 , the carrier liquid is more conspicuous in deterioration. As can be understood from  FIG. 7 , in the case where the carrier liquid is passed through the separation and extraction device  34 , a proportion occupied by the deteriorated carrier liquid decreases with four times as a peak. 
     [Calculation of Resistance of Carrier Liquid] 
     Returning to  FIG. 5 , the resistance calculating portion  302  acquires the resistance of the carrier liquid in the carrier tank  32  with the “liquid amount of each number of times of passing” calculated by the deterioration degree distribution calculating portion  301  (S 23 ). The resistance of the carrier liquid under application of a high voltage has already been stored in advance in the memory  201  for each of numbers of times of passing of the carrier liquid through the separation and extraction device  34 . The resistance of the carrier liquid is proportional to the number of times of passing of the carrier liquid through the separation and extraction device  34  and is lowered to for example 1/2 of the resistance of the carrier liquid before passing of the carrier liquid for each (single) passing. Specifically, in the case where the resistance of the carrier liquid which has passed through the separation and extraction device  34  no time is “1.0E+14 Ωcm”, the resistance after single passing is “0.5E+14 Ωcm”, and the resistance after passing of two times is “0.25E+14 Ωcm”. Accordingly, as described above, the “liquid amount for each number of times of passing” is for example represented by the above-described formula 11 to formula 13 (matrix C “25, 50, 25” of  FIG. 6 ), the resistance of the carrier liquid is acquired by formula 17 shown below. 
       (1.0 E+ 14×25+0.5 E+ 14×50+0.25 E+ 14×15)/(25+50+25)=0.5625 E+ 14  formula 17
 
     Returning to  FIG. 4 , the controller  200  executes a “carrier liquid resistance calculating process” (S 2 ), and thereafter discriminates whether or not the calculated resistance (resistance calculation result) of the carrier liquid is smaller than a predetermined value (for example, 1.0E+11 Ωcm) (S 3 ). In the case where the controller  200  discriminated that the resistance calculation result is smaller than the predetermined value (YES of S 3 ), the controller  200  causes the supplying pump  51  to be driven for a predetermined time in order to supply a predetermined amount of the carrier liquid for supply (S 4 ). That is, in this case, small resistance of the carrier liquid means that the carrier liquid is large in amount of the charge control agent, so that in order to reduce the relative amount occupied by the charge control agent in the carrier liquid, the controller  200  carries out control of supplying the carrier liquid for supply. Thereafter, the controller  200  ends this supply control process. 
     On the other hand, in the case where the controller  200  discriminated that the resistance calculation result is the predetermined value or more (NO of S 3 ), on the basis of a detection result of the float sensor  320 , the controller  200  discriminates whether or not the liquid amount of the carrier liquid in the carrier tank  32  is not more than a predetermined value (for example, five litters) (S 5 ). In the case where the controller  200  discriminated that the liquid amount of the carrier liquid is larger than the predetermined value (NO of S 5 ), the controller  200  ends this supply control process. In this case, the carrier liquid has sufficiently high resistance, i.e., a good carrier liquid small in amount of the charge control agent, and also the liquid amount is sufficiently ensured, so that the carrier liquid for supply is not supplied. In the case where the controller  200  discriminated that the liquid amount of the carrier liquid is the predetermined value or less (YES of S 5 ), the controller  200  causes the supplying pump  51  to be driven for a predetermined time in order to supply a predetermined amount of the carrier liquid for supply (S 4 ). Thereafter, the controller  200  ends this supply control process. 
     As described above, in this embodiment, the resistance of the carrier liquid used when the carrier supply discriminating portion  202  discriminates whether or not the carrier liquid for supply should be supplied is acquired by calculation. Further, the resistance of the carrier liquid is acquired on the basis of a “liquid amount of the carrier liquid for each of numbers of times of passing of the carrier liquid through the separation and extraction device  34 ” and “resistance of the carrier liquid for each of numbers of times of passing of the carrier liquid through the separation and extraction device  34 ”. According to this, in the resistance acquired by calculation, a fluctuation in resistance due to the ionized charge control agent contained in the carrier liquid is reflected. Therefore, compared with the case where the resistance sensor is used, a variation (error) in resistance of the carrier liquid after the carrier liquid for supply is supplied does not readily occur. Accordingly, supply control of the carrier liquid for supply is carried out on the basis of the resistance acquired by calculation, whereby the resistance of the liquid developer can be maintained in a predetermined range. When the resistance of the liquid developer can be maintained in the predetermined range, the image defect does not readily generate. 
     Incidentally, implementation of ionization of the charge control agent was made not only during separation and extraction of the carrier liquid but also during development has already been described. Further, in the developing device  16 , of the liquid developer supplied from the mixer  31  by the developer supplying pump  44 , the liquid developer which was not used for the development is returned to the mixer  31  by the circulating pump  43  and thereafter is used again. Accordingly, the carrier liquid contained in the liquid developer is deteriorated every time when the circulating pump  43  is driven once. In view of this point, when calculation is performed in consideration of the deterioration of the carrier liquid in the developing device  16  in addition to the above-described deterioration of the carrier liquid in the separation and extraction device  34 , it is possible to acquire more proper resistance of the carrier liquid. 
     A calculating method of the resistance of the carrier liquid in consideration of the above-described deterioration of the carrier liquid in the separation and extraction device  34  and the deterioration of the carrier liquid in the developing device  16  will be specifically described by a calculation model. In this embodiment, using  FIG. 8 , the case where each of the separation and collection pump  45  and the circulating pump  43  is driven once will be described. In this embodiment, the case where the circulating pump  43  returns a predetermined amount of the liquid developer into the mixer  31  is counted as one time of drive of the circulating pump  43 . 
     Incidentally, similarly as the above-described First Embodiment, the carrier liquid amount does not increase and decrease before and after the drive of the separation and collection pump  45 , and the liquid amount of the carrier liquid fed by single drive of the separation and collection pump  45  is 50 ml and the liquid amount of the carrier liquid accommodated in the carrier tank  32  is 100 ml. Further, the liquid amount of the carrier liquid supplied from the mixer  31  to the developing device  16  by single drive of the developer supplying pump  44  and the liquid amount of the carrier liquid returned from the developing device  16  to the mixer  31  by the circulating pump  43  at that time are equal to each other. That is, the carrier liquid amount does not increase and decrease before and after the drive of the circulating pump  43 . Further, the liquid amount of the carrier liquid fed by the single drive of each of the developer supplying pump  44  and the circulating pump  43  is 20 ml. 
     As shown in  FIG. 8 , as a calculation model, a matrix C with m rows and n columns, in which the liquid amount of the carrier liquid in the carrier tank  32  is assigned is used (In  FIG. 8 , only two rows and three columns are shown). At first row and first column of the matrix C, as a “liquid amount by passing of no time” in which the carrier liquid does not pass through the separation and collection pump  45  even one time, an entire amount of the carrier liquid amount in the carrier tank  32  is assigned. Then, every time when the separation and collection pump  45  is driven one time (every time when the carrier liquid passes through the separation and extraction device  34  one time, the “liquid amount for each number of times of passing” is successively assigned for elements moving the columns. This has already been described above and will be omitted from description here. After the separation and collection pump  45  is driven once, a matrix C “50, 50, 0” is provided (after single passing of the carrier liquid through the separation and extraction device “AFTER 1ST-PASSING OF SRRTN &amp; EXTRCTN DEVICE” of  FIG. 8 ). 
     Then, every time when the circulating pump  43  is driven once (every time when the carrier liquid passes through the developing device  16  once), a “liquid amount of each number of times of passing” of the carrier liquid which passed through the developing device  16  is successively assigned for an element moving an associated row. That is, a “liquid amount in which carrier liquid passed one time through developing device  16 ” is assigned for second row during drive of one time of the circulating pump  43 , a “liquid amount in which carrier liquid passed two times through developing device  16 ” is assigned for second row during drive of two times of the circulating pump  43 , and a “liquid amount in which carrier liquid passed three times through developing device  16 ” is assigned for third row during drive of three times of the circulating pump  43 . 
     As shown in  FIG. 8 , in the case where the circulating pump  43  is driven once after the single drive of the separation and collection pump  45 , the matrix C is such that the first row is “40, 40, 0” and the second row is “10, 10, 0” (after single passing of the carrier liquid through the developing device “AFTER 1ST-PASSING OF DEVELOPING DEVICE” of  FIG. 8 ). In  FIG. 8 , first row and first column represents a “liquid amount in which carrier liquid passed no time through separation and extraction device  34 ” and first row and second column represent a “liquid amount in which carrier liquid passed one time through separation and extraction device  34 ”. In  FIG. 8 , second row and first column represent a “liquid amount in which carrier liquid passed no time through separation and extraction device  34  and passed one time through developing device  16 ” and second row and second column represents a “liquid amount in which carrier liquid passed one time through separation and extraction device  34  and passed one time through developing device  16 ”. 
     In the above-described manner, calculation of the “liquid amount for each number of times of passing” of the carrier liquid contained in the carrier liquid in the carrier tank  32  is performed every time when each of the separation and collection pump  45  and the circulating pump  43  is driven once. In  FIG. 9 , an example of the “liquid amount for each number of times of passing (NUMBER OF PASSING TIMES (TIMES))” in the case where each of the separation and collection pump  45  and the circulating pump  43  is driven twenty times is shown. 
     The “liquid amount for each number of times of passing” shown in  FIG. 9  represents as a whole a distribution such that how many amount of the carrier liquid which has passed through each of the separation and extraction device  34  and the developing device  16  what times exists in the carrier tank  32 . As can be understood from  FIG. 9 , in the case where the carrier liquid is passed through the developing device  16 , after eight times, compared with the case where the carrier liquid is passed through the separation and extraction device  34 , a proportion occupied by the deteriorated carrier liquid increases remarkably. This is because the toner is consumed in the developing device  16  and compared with the separation and extraction device  34 , a high-voltage application time is long and correspondingly the ionized charge control agent generates in a large amount. 
     Further, the resistance of the carrier liquid is calculated using the resistance assigned in advance for each of elements of the matrix C and the “liquid amount for each number of times of passing” of the above-described matrix C. The resistance of the carrier liquid for each number of times of passing of the carrier liquid through the separation and extraction device  34  and for each number of times of passing of the carrier liquid through the developing device  16  is already been stored in the memory  201 . The resistance of the carrier liquid is proportional to the number of times of passing of the carrier liquid through the developing device  16  and lowers to for example 1/4 of the resistance of the carrier liquid before the passing for each single passing. The resistance of the carrier liquid at each of the elements of the matrix C shown in  FIG. 8  is for example such that first row and first column to first row and third column are successively “1.0E+14 Ωcm”, “0.5E+14 Ωcm” and “0.025E+14 Ωcm”. Further, second row and first column to second row and third column are successively “0.025E+14 Ωcm”, “0.125E+14 Ωcm” and “0.0625E+14 Ωcm”. The controller  200  calculates the resistance of the carrier liquid on the basis of the “liquid amount for each number of times of passing” and these values of the resistance. 
     As described above, also in this case, the resistance of the carrier liquid used when whether or not the carrier liquid for supply should be supplied is discriminated is acquired by the calculation. However, when the resistance is calculated, not only the ionization of the charge control agent by the separation and extraction device  34  but also the influence of the ionization of the charge control agent by the developing device  16  are taken into consideration, so that a fluctuation in resistance due to the ionized charge control agent contained in the carrier liquid was reflected in the calculation. According to this, it is possible to acquire more proper resistance of the carrier liquid. 
     Second Embodiment 
     Second Embodiment of the present invention will be described using  FIG. 10 . In the above-described First Embodiment, the carrier liquid for supply was supplied from the supplying device  36 A to the carrier tank  32 . On the other hand, in an image forming apparatus  100 A of Second Embodiment, the carrier liquid for supply is supplied from a supplying device  60 A to the mixer  31 . Other basic constitutions and actions are similar to those in First Embodiment, and therefore in the following, the same constitutions will be omitted from description or illustration or will be briefly described, and a portion different from First Embodiment will be principally described. 
     Also in the case of this embodiment, the separation and extraction device  34 , the carrier tank  32  for accommodating the carrier liquid separated by the separation and extraction device  34 , and the mixer  31  to which the carrier liquid is supplied from the carrier tank  32  are provided. Further, in this embodiment, the supplying device  60 A for supplying the carrier liquid for supply to the mixer  31  is provided. The supplying device  60 A includes a supplying carrier tank  60  and a supplying pump  61  provided to a communication pipe for establishing communication between the supplying carrier tank  60  and the mixer  31 . 
     The supplying device  60 A supplies the carrier liquid for supply on the basis of the resistance of the carrier liquid in the carrier tank  32 . Similarly as in the above-described First Embodiment, also in this embodiment, the resistance of the carrier liquid in the carrier tank  32  is acquired by calculation. Then, in the case where the resistance of the carrier liquid is lower than a predetermined value, the supplying pump  61  is driven, so that the carrier liquid for supply is supplied from the supplying carrier tank  60  to the mixer  31 . 
     Other Embodiments 
     Incidentally, in the case where the carrier liquid for supply is supplied, a supply amount may only be required to be added to the “liquid amount by passing of no time” at first row and first column of the matrix C. Therefore, by using the matrix C after the supply amount is added, calculation of the “liquid amount for each number of times of passing” is carried out as described above. When this is briefly described using  FIG. 6  as an example, in the case where for example, 20 ml of the carrier liquid for supply is supplied after two times of passing, a value of the matrix C at first row and first column is changed from “25” to “45” obtained by adding “20” which is the supply amount to “25”. 
     On the other hand, in the case where the carrier liquid is consumed during development, from each of the elements of the matrix Q, a liquid amount corresponding to an equally divided consumption amount may only be required to be subtracted. Therefore, by using the matrix Q after the consumption amount is subtracted, calculation of the “liquid amount for each number of times of passing” is carried out as described above. When this is briefly described using  FIG. 8  as an example, in the case where for example, 6 ml of the carrier liquid is consumed both values of the matrix Q at second row and first column and second row and second column are changed from “10” to “7” obtained by subtracting “3”, which is an equally divided consumption amount, from “10”. 
     Incidentally, in the case where the number of times of passing of the carrier liquid through the developing device  16  is taken into consideration during calculation of the resistance of the carrier liquid, calculation of the “liquid amount for each number of times of passing” of the carrier liquid through the developing device  16  was carried out every time when the circulating pump  43  is driven once, but the present invention is not limited thereto. For example, the calculation of the “liquid amount for each number of times of passing” of the carrier liquid through the developer supplying pump  44 , in place of the circulating pump  43 , may also be carried out every time when the developer supplying pump  44  is driven once. 
     INDUSTRIAL APPLICABILITY 
     According to the present invention, there is provided an image forming apparatus in which the volume resistivity of the carrier liquid is acquired by calculation and supply control of the carrier liquid for supply is carried out on the basis of this. 
     EXPLANATION OF SYMBOLS 
       12  . . . image forming portion,  13  . . . drum (image bearing member),  16  . . . developing device,  31  . . . mixing device (mixer),  32  . . . carrier container (carrier tank),  33  . . . toner container (toner tank),  34  . . . separating device (separation and extraction device),  36 A ( 60 A) . . . supplying device,  43  . . . returning portion (circulating pump),  44  . . . first supplying portion (developer supplying pump),  45  . . . second supplying portion (separation and collection pump),  100  ( 100 A) . . . image forming apparatus,  200  . . . controller (control portion),  300  . . . calculating portion (operation part),  320  . . . liquid amount detecting portion (float sensor)