JP5273591B2 - Coating drying simulation method - Google Patents
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- JP5273591B2 JP5273591B2 JP2009054112A JP2009054112A JP5273591B2 JP 5273591 B2 JP5273591 B2 JP 5273591B2 JP 2009054112 A JP2009054112 A JP 2009054112A JP 2009054112 A JP2009054112 A JP 2009054112A JP 5273591 B2 JP5273591 B2 JP 5273591B2
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- 239000011248 coating agent Substances 0.000 title claims abstract description 161
- 238000000576 coating method Methods 0.000 title claims abstract description 161
- 238000001035 drying Methods 0.000 title claims abstract description 109
- 238000000034 method Methods 0.000 title claims abstract description 39
- 238000004088 simulation Methods 0.000 title claims abstract description 33
- 239000002904 solvent Substances 0.000 claims abstract description 125
- 239000007788 liquid Substances 0.000 claims abstract description 69
- 229920000642 polymer Polymers 0.000 claims abstract description 63
- 238000009792 diffusion process Methods 0.000 claims abstract description 47
- 238000012546 transfer Methods 0.000 claims abstract description 43
- 230000004907 flux Effects 0.000 claims abstract description 9
- 239000003960 organic solvent Substances 0.000 claims description 18
- 229920002799 BoPET Polymers 0.000 claims description 7
- 239000013557 residual solvent Substances 0.000 claims description 6
- 238000000935 solvent evaporation Methods 0.000 claims description 5
- 238000005187 foaming Methods 0.000 claims description 4
- 230000000704 physical effect Effects 0.000 claims description 3
- 238000005259 measurement Methods 0.000 claims description 2
- 239000000463 material Substances 0.000 abstract description 13
- 238000004364 calculation method Methods 0.000 description 28
- 239000000758 substrate Substances 0.000 description 27
- 239000000306 component Substances 0.000 description 15
- YXFVVABEGXRONW-UHFFFAOYSA-N Toluene Chemical compound CC1=CC=CC=C1 YXFVVABEGXRONW-UHFFFAOYSA-N 0.000 description 9
- 239000007888 film coating Substances 0.000 description 5
- 238000009501 film coating Methods 0.000 description 5
- ZWEHNKRNPOVVGH-UHFFFAOYSA-N 2-Butanone Chemical compound CCC(C)=O ZWEHNKRNPOVVGH-UHFFFAOYSA-N 0.000 description 3
- XEKOWRVHYACXOJ-UHFFFAOYSA-N Ethyl acetate Chemical compound CCOC(C)=O XEKOWRVHYACXOJ-UHFFFAOYSA-N 0.000 description 3
- 230000004913 activation Effects 0.000 description 3
- 238000004422 calculation algorithm Methods 0.000 description 3
- 230000008859 change Effects 0.000 description 3
- 230000000694 effects Effects 0.000 description 3
- 239000007787 solid Substances 0.000 description 3
- CSCPPACGZOOCGX-UHFFFAOYSA-N Acetone Chemical compound CC(C)=O CSCPPACGZOOCGX-UHFFFAOYSA-N 0.000 description 2
- 238000002940 Newton-Raphson method Methods 0.000 description 2
- 230000007547 defect Effects 0.000 description 2
- 238000006073 displacement reaction Methods 0.000 description 2
- 238000002474 experimental method Methods 0.000 description 2
- 238000007726 management method Methods 0.000 description 2
- 229920002433 Vinyl chloride-vinyl acetate copolymer Polymers 0.000 description 1
- 238000003889 chemical engineering Methods 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 239000003795 chemical substances by application Substances 0.000 description 1
- 238000012937 correction Methods 0.000 description 1
- 238000013500 data storage Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000010981 drying operation Methods 0.000 description 1
- 239000003822 epoxy resin Substances 0.000 description 1
- 239000006260 foam Substances 0.000 description 1
- 230000006870 function Effects 0.000 description 1
- 230000003993 interaction Effects 0.000 description 1
- 229920000647 polyepoxide Polymers 0.000 description 1
- 239000000126 substance Substances 0.000 description 1
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- Application Of Or Painting With Fluid Materials (AREA)
Abstract
Description
本発明は、溶剤とポリマを含む塗液を塗布した基材を乾燥させる塗工乾燥機に用いるのに好適な塗工乾燥シミュレーション方法に関する。 The present invention relates to a coating / drying simulation method suitable for use in a coating dryer that dries a substrate coated with a coating liquid containing a solvent and a polymer.
フィルム塗工製品は、コータ部で基材上に塗液を塗り、乾燥機で溶剤を除去することによって製造される。従来、フィルム塗工において塗工乾燥条件設定には、類似品種や類似製品厚みを参考に塗工乾燥条件を暫定的に決定し、その後、実機にて試し塗りを行い、微調整を行い塗工乾燥条件の最終決定を行っていた。そのため、通常で塗工条件ふりが１回で終了することは希で、数回に渡り行われる。また、製品の品質上ロバスト性が安定せず、溶剤の過乾燥や未乾燥による製品不良問題も希に起きている。 A film-coated product is produced by applying a coating solution on a substrate at a coater unit and removing the solvent with a dryer. Conventionally, the coating drying conditions in film coating are tentatively determined with reference to the thickness of similar varieties and similar products, and then trial coating is performed on the actual machine and fine adjustment is performed. The final determination of the drying conditions was made. For this reason, it is rare that the coating condition pretend is completed once, and it is performed several times. Moreover, the robustness is not stable in terms of product quality, and the problem of product defects due to over-drying or non-drying of the solvent rarely occurs.
しかしながら、塗工機の塗工乾燥条件設定には、乾燥温度、ノズル風速、乾燥炉排気量、塗工ライン速度の多数条件設定が必要である。一方、残溶剤量、乾燥炉内ガス濃度管理、規格温度、製品膜厚、製品特性、溶剤の発泡管理の多数制約条件も考慮する必要がある。 However, setting of the coating drying conditions of the coating machine requires setting of a number of conditions such as the drying temperature, the nozzle wind speed, the drying furnace displacement, and the coating line speed. On the other hand, it is also necessary to consider many constraints on the amount of residual solvent, gas concentration management in the drying furnace, standard temperature, product film thickness, product characteristics, and solvent foam management.
乾燥シミュレーションシステムとして、非特許文献１にフィルム塗工の乾燥シミュレータが開示されている。非特許文献１には、単一溶剤とポリマで構成される二成分系塗液（アセトン系塗液又はトルエン系塗液（有機溶剤系塗液））のシミュレーションが記載されている。 As a drying simulation system, Non-Patent Document 1 discloses a film coating drying simulator. Non-Patent Document 1 describes a simulation of a two-component coating liquid (acetone-based coating liquid or toluene-based coating liquid (organic solvent-based coating liquid)) composed of a single solvent and a polymer.
また、非特許文献２に塗工製品の乾燥シミュレーション方法が開示されている。非特許文献２の乾燥シミュレーション方法は、膜内に形成される濃度分布、温度分布を考慮していない点や、製品膜厚、乾燥温度、ノズル風速、塗工ライン速度に対して、設定基準を定めて設定基準での乾燥特性曲線を算出し、乾燥速度を算出するためのパラメータフィッティングを行い、乾燥速度を算出している。実験で用いた塗工液は、塩化ビニル酢酸ビニルコポリマー、メチルエチルケトン（有機溶剤１）、及びトルエン（有機溶剤２）を成分とするものである。 Non-Patent Document 2 discloses a drying simulation method for coated products. The drying simulation method of Non-Patent Document 2 sets the standard for the point that does not consider the concentration distribution and temperature distribution formed in the film, the product film thickness, the drying temperature, the nozzle wind speed, and the coating line speed. A drying characteristic curve based on a set standard is calculated, parameter fitting for calculating the drying speed is performed, and the drying speed is calculated. The coating liquid used in the experiment contains vinyl chloride vinyl acetate copolymer, methyl ethyl ketone (organic solvent 1), and toluene (organic solvent 2) as components.
また、非特許文献３には、単一溶剤とポリマで構成される二成分系塗液において、Ｒｅｇｕｌａｒ Ｒｅｇｉｍｅ理論及び流束比較法を用いて溶剤拡散係数を求める方法が記載されている。 Non-Patent Document 3 describes a method of obtaining a solvent diffusion coefficient using a Regular Regime theory and a flux comparison method in a two-component coating liquid composed of a single solvent and a polymer.
実際のフィルム塗工製品において、二溶剤とポリマで構成される三成分系塗液がしばしば使用される。しかしながら、非特許文献１には、単一溶剤とポリマで構成される二成分系塗液のシミュレーションが記載されているだけであるので、非特許文献１及び非特許文献３のシミュレーションをそのまま三成分系塗液に適用することはできない。 In an actual film coating product, a three-component coating liquid composed of two solvents and a polymer is often used. However, since Non-Patent Document 1 only describes a simulation of a two-component coating liquid composed of a single solvent and a polymer, the simulations of Non-Patent Document 1 and Non-Patent Document 3 are used as they are. It cannot be applied to system coating liquids.
また、引用文献２に記載されているシミュレーション方法では、実際の塗工における設定が設定基準から大きく外れてしまうと、計算精度を保つことが困難になる。 Moreover, in the simulation method described in the cited document 2, it is difficult to maintain the calculation accuracy if the setting in actual coating greatly deviates from the setting standard.
そこで、本発明は、膜内に形成される溶剤濃度分布、塗液温度分布を考慮し、かつ、溶剤２成分とポリマ１成分で構成される三成分系塗液を塗布した基材を乾燥させる塗工乾燥機に用いるのに好適な塗工乾燥シミュレーション方法を提供することを目的とする。 Therefore, the present invention takes into consideration the solvent concentration distribution and the coating liquid temperature distribution formed in the film, and dries the substrate coated with the three-component coating liquid composed of two components of the solvent and one component of the polymer. An object of the present invention is to provide a coating drying simulation method suitable for use in a coating dryer.
上記課題を解決するために鋭意検討の結果、塗液の溶剤乾燥速度の実測値からＲｅｇｕｌａｒ Ｒｅｇｉｍｅ理論及び流束比較法を用いて溶剤拡散係数を導出することを利用して、計算精度が向上することを見出し、発明の完成に至った。 As a result of intensive studies to solve the above problems, the calculation accuracy is improved by deriving the solvent diffusion coefficient from the measured value of the solvent drying speed of the coating liquid using the Regular Regime theory and the flux comparison method. We found out that the invention was completed.
上記目的を達成するために、本発明は、２成分の溶剤と１成分のポリマを含む塗液を塗布した基材を連続したｎ個（ｎは正の整数）のゾーンに分けられている塗工乾燥炉を用いて乾燥する場合の塗工乾燥シミュレーション方法であって、溶剤とポリマを含む塗液の溶剤乾燥速度を実測値で求め、溶剤拡散係数の温度依存性がアレニウス型であることを前提として当該溶剤乾燥速度からレギュラーレジーム理論（Ｒｅｇｕｌａｒ Ｒｅｇｉｍｅ理論）及び流束比較法を用いて溶剤拡散係数を導出し、溶剤とポリマを含む塗液中に含まれる溶剤の溶剤蒸気圧をＦｌｏｒｙ−Ｈｕｇｇｉｎｓ理論から算出し、各乾燥炉ゾーン能力より物質移動係数を算出し、乾燥炉能力から溶剤とポリマを含む塗液及び該塗液が塗布された基材の伝熱係数を算出し、溶剤拡散係数、溶剤蒸気圧、物質移動係数を用いて、各溶剤とポリマを含む塗液内に含まれる溶剤濃度分布を１次元非定常拡散方程式により算出し、溶剤とポリマを含む塗液及び該塗液が塗布された基材の物性値より定まる熱伝導度及び温度伝導率、及び前記伝達係数を用いて、基材に塗布された溶剤とポリマを含む塗液（塗膜）内、及び該塗液が塗布された基材内の温度分布を１次元非定常熱伝導方程式により算出し、溶剤濃度計算値より単位換算をすることにより塗液中残溶剤率をシミュレーションすることを特徴としている。 In order to achieve the above object, the present invention provides a coating in which a base material coated with a coating solution containing a two-component solvent and a one-component polymer is divided into n consecutive zones (n is a positive integer). This is a method for simulating the coating drying when drying using an industrial drying furnace. The solvent drying rate of the coating liquid containing the solvent and polymer is obtained by actual measurement, and the temperature dependence of the solvent diffusion coefficient is Arrhenius type. As a premise, the solvent diffusion coefficient is derived from the solvent drying speed using the regular regime theory and the flux comparison method, and the solvent vapor pressure of the solvent contained in the coating liquid containing the solvent and the polymer is determined as Flory-Huggins. Calculate from theory, calculate the mass transfer coefficient from each drying furnace zone capacity, calculate the coating liquid containing solvent and polymer from the drying furnace capacity and the heat transfer coefficient of the substrate coated with the coating liquid, Using the agent diffusion coefficient, solvent vapor pressure, and mass transfer coefficient, the solvent concentration distribution contained in the coating liquid containing each solvent and polymer is calculated by a one-dimensional unsteady diffusion equation. Using the thermal conductivity and temperature conductivity determined from the physical properties of the substrate on which the coating solution is applied, and the transfer coefficient, the coating solution (coating film) containing the solvent and polymer applied to the substrate, and the The temperature distribution in the base material coated with the coating liquid is calculated by a one-dimensional unsteady heat conduction equation, and the residual solvent ratio in the coating liquid is simulated by converting the unit from the calculated value of the solvent concentration.
このように構成された本発明によるシミュレーション方法によれば、実験から得た乾燥速度からＲｅｇｕｌａｒ Ｒｅｇｉｍｅ理論、流束比較法を用いて、乾燥速度を導出しているため、製品膜厚、乾燥温度、ノズル風速、塗工ライン速度が変化しても、フィッティングを行う必要もなく、計算精度を保つことが可能である。 According to the simulation method of the present invention configured as described above, the drying speed is derived from the drying speed obtained from the experiment using the Regular Regime theory and the flux comparison method, so that the product film thickness, the drying temperature, Even if the nozzle wind speed and coating line speed change, it is not necessary to perform fitting, and calculation accuracy can be maintained.
本発明の実施形態において、溶剤とポリマを含む塗液を塗布する基材が、ＰＥＴフィルムであることが好ましい。 In the embodiment of the present invention, the substrate on which the coating liquid containing a solvent and a polymer is applied is preferably a PET film.
また、本発明の実施形態において、さらに、塗工乾燥シミュレーション方法からシミュレートされる溶剤とポリマを含む塗液内温度分布及び塗液内濃度分布に基づき、Ｆｌｏｒｙ−Ｈｕｇｇｉｎｓ理論より溶剤とポリマを含む塗液内溶剤蒸気圧を算出し、大気圧と比較することにより、溶剤とポリマを含む塗液内の発泡有無をシミュレートすることが好ましい。 Further, in the embodiment of the present invention, based on the Flory-Huggins theory, the solvent and the polymer are further included based on the temperature distribution and the concentration distribution in the coating liquid including the solvent and the polymer simulated by the coating drying simulation method. It is preferable to simulate the presence or absence of foaming in the coating liquid containing the solvent and the polymer by calculating the solvent vapor pressure in the coating liquid and comparing it with the atmospheric pressure.
この方法では、気泡不良を低減することができる。 With this method, bubble defects can be reduced.
また、本発明の実施形態において、更に、溶剤とポリマを含む塗液の表面濃度から、溶剤とポリマを含む塗液の表面皮バリの有無をシミュレーションすることが好ましい。 In the embodiment of the present invention, it is further preferable to simulate the presence or absence of surface burr of the coating liquid containing the solvent and the polymer from the surface concentration of the coating liquid containing the solvent and the polymer.
この方法では、乾燥速度を向上するために必要な乾燥条件最適化することができる。 In this method, it is possible to optimize the drying conditions necessary to improve the drying speed.
また、本発明の実施形態において、更に、各乾燥炉ゾーン内において溶剤とポリマを含む塗液内からの溶剤蒸発量を算出し、各乾燥炉ゾーン体積と比較することにより、各乾燥炉ゾーン内ガス濃度をシミュレーションすることが好ましい。 Further, in the embodiment of the present invention, the amount of solvent evaporation from the coating liquid containing the solvent and the polymer is calculated in each drying furnace zone, and is compared with the volume of each drying furnace zone to thereby calculate the inside of each drying furnace zone. It is preferable to simulate the gas concentration.
この方法では、各乾燥炉ゾーン内ガス濃度を均等に分散させることで、乾燥速度を向上させることができる。 In this method, the drying rate can be improved by uniformly dispersing the gas concentration in each drying furnace zone.
本発明により、溶剤濃度分布、塗液温度分布を考慮し、かつ、溶剤２成分とポリマ１成分で構成される三成分系塗液を塗布した基材を乾燥させる塗工乾燥機に用いるのに好適な塗工乾燥シミュレーション方法を提供することができる。 According to the present invention, it is used for a coating drier for drying a substrate on which a ternary coating liquid composed of two components of a solvent and one component of a polymer is applied in consideration of a solvent concentration distribution and a coating liquid temperature distribution. A suitable coating drying simulation method can be provided.
以下、図面を参照して本発明の実施形態を説明する。図１は、本発明の塗工乾燥シミュレーションシステムが用いられる塗工乾燥機の全体構成の一例を示す概略図である。コータ部で基材上に溶剤とポリマを含む塗液を塗り、溶剤とポリマを含む塗液を塗布された基材は乾燥炉内に搬入され、乾燥炉ゾーン内で溶剤とポリマを含む塗液に含まれる溶剤が除去されて、乾燥炉外へ搬出される。なお、図４において、速度をｖで表示しているが、本明細書においてｕ0と表示することもある。 Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a schematic diagram showing an example of the overall configuration of a coating dryer in which the coating / drying simulation system of the present invention is used. A coating liquid containing a solvent and a polymer is applied onto the base material at the coater unit, and the base material coated with the coating liquid containing the solvent and the polymer is carried into the drying furnace, and the coating liquid containing the solvent and the polymer in the drying furnace zone. The solvent contained in is removed and transported out of the drying furnace. In FIG. 4, the speed is indicated by v, but may be indicated as u 0 in this specification.
乾燥機は、溶剤を高温下で蒸発させるので、本発明のシミュレーション方法において、塗膜及び基材内の熱移動と、塗膜内の物質移動を同時に取り扱う。熱移動は、溶剤及び基材の温度分布として把握することができ、本実施形態では、塗膜厚さ方向の温度分布（図２に示す「伝熱モデル」)を考える。物質移動は、溶剤が移動することにより生じる溶剤の濃度分布として把握することができ、本実施形態では、塗膜厚さ方向の溶剤濃度分布（図３に示す「拡散モデル」）を考える。 Since the dryer evaporates the solvent at a high temperature, in the simulation method of the present invention, heat transfer in the coating film and the substrate and mass transfer in the coating film are simultaneously handled. The heat transfer can be grasped as the temperature distribution of the solvent and the base material, and in this embodiment, the temperature distribution in the coating film thickness direction (“heat transfer model” shown in FIG. 2) is considered. The mass transfer can be grasped as a solvent concentration distribution generated by the movement of the solvent, and in this embodiment, a solvent concentration distribution in the thickness direction of the coating film (“diffusion model” shown in FIG. 3) is considered.
〔伝熱モデル〕
図２は、本実施形態で考える伝熱モデルである。この伝熱モデルにおいて、塗膜の厚さ方向にｚ軸をとり、塗膜が空気と接する表面の座標を０とし、塗膜と基材が接する表面の座標をｈとし、基材と空気が接する表面の座標をｂとする。この伝熱モデルにおいて、塗膜内の温度分布、及び、基材内の温度分布を算出するために、１次元非定常熱伝導方程式を適用する。
[Heat transfer model]
FIG. 2 shows a heat transfer model considered in this embodiment. In this heat transfer model, the z-axis is taken in the thickness direction of the coating film, the coordinate of the surface where the coating film is in contact with air is 0, the coordinate of the surface where the coating film is in contact with the substrate is h, and the base material and air are Let b be the coordinates of the contacting surface. In this heat transfer model, a one-dimensional unsteady heat conduction equation is applied to calculate the temperature distribution in the coating film and the temperature distribution in the substrate.
塗膜内温度分布を算出するための１次元非定常熱伝導方程式（基礎式）、初期条件及び境界条件は、次の通りである。
（１）基礎式（塗膜伝熱）
(1) Basic formula (coating film heat transfer)
また、基材内温度分布を算出するための１次元非定常熱伝導方程式（基礎式）、初期条件及び境界条件は、次の通りである。
（４）基礎式（基材）
(4) Basic formula (base material)
各記号が表す量は次の通りである。
塗膜内計算位置：ｚ［ｍ］
塗膜厚み方向ｚ軸における座標位置（塗膜と基材の境界面）：ｈ［ｍ］
塗膜厚み方向ｚ軸における座標位置（基材底面）：ｂ［ｍ］
計算時間幅：ｔ［ｓ
塗膜内温度：Ｔ（ｚ）［Ｋ］（各ステップで計算）
基材内温度：Ｔ’（ｚ）［Ｋ］（各ステップで計算）
塗膜及び基材内初期温度：Ｔ0［Ｋ］（後掲の表参照）
溶剤蒸発潜熱：ΔＨ［Ｊ／ｋｇ］（後掲の表参照）
乾燥温度：Ｔｇ［Ｋ］（後掲の表参照）
塗膜の熱伝導度：λｌ［Ｊ／ｍ・ｓ・Ｋ］（後掲の表参照）
基材の熱伝導度：λｓ［Ｊ／ｍ・ｓ・Ｋ］（後掲の表参照）
溶剤乾燥速度：ｒ［ｋｇ／ｍ2・ｓ］（後述する拡散方程式の境界条件参照。２溶剤のうちの一方で近似する。各ステップで計算）
塗膜のレイノルズ数：Ｒｅ’
基材のレイノルズ数：Ｒｅ”
塗膜のプラントル数：Ｐｒ’
基材のプラントル数：Ｐｒ”
平均伝熱係数：ｈａｍ［Ｊ／ｍ2・ｓ・Ｋ］（後述・各ステップで計算）
The quantity represented by each symbol is as follows.
Calculation position in coating film: z [m]
Coordinate position on z axis of coating thickness direction (interface between coating film and substrate): h [m]
Coordinate position in the coating thickness direction z-axis (base of the substrate): b [m]
Calculation time width: t [s
Temperature in coating film: T (z) [K] (calculated at each step)
Base material temperature: T ′ (z) [K] (calculated at each step)
Initial temperature in coating film and substrate: T 0 [K] (see table below)
Solvent evaporation heat: ΔH [J / kg] (See the table below)
Drying temperature: Tg [K] (see table below)
Thermal conductivity of coating film: λl [J / m · s · K] (see table below)
Thermal conductivity of substrate: λs [J / m · s · K] (see table below)
Solvent drying rate: r [kg / m 2 · s] (Refer to the boundary conditions of the diffusion equation described later. Approximate one of the two solvents. Calculate at each step)
Reynolds number of coating film: Re '
Reynolds number of substrate: Re ”
Prandtl number of coating film: Pr '
Prandtl number of substrate: Pr "
Average heat transfer coefficient: ham [J / m 2 · s · K] (described later, calculated at each step)
これらの熱伝導方程式を計算するのに必要な平均伝熱係数ｈａは、乾燥機の構造によって決定され、これについては後述する。 The average heat transfer coefficient ha necessary to calculate these heat conduction equations is determined by the structure of the dryer, which will be described later.
〔拡散モデル〕
図３は、本実施形態で考える拡散モデルである。この拡散モデルにおいて、塗膜の厚さ方向にｚ’軸をとり、塗膜が基材と接する表面の座標を０とし、塗膜と空気が接する表面の座標をｓとする。この拡散モデルにおいて、塗膜内の溶剤濃度分布を算出するために、１次元非定常熱伝導方程式を適用する。
[Diffusion model]
FIG. 3 shows a diffusion model considered in this embodiment. In this diffusion model, the z ′ axis is taken in the thickness direction of the coating film, the coordinate of the surface where the coating film is in contact with the substrate is 0, and the coordinate of the surface where the coating film is in contact with air is s. In this diffusion model, a one-dimensional unsteady heat conduction equation is applied to calculate the solvent concentration distribution in the coating film.
塗膜内の溶剤濃度分布を算出するための１次元非定常拡散方程式（基礎式）、初期条件及び境界条件は、次の通りである。
（１）基礎式（拡散）
(1) Basic expression (diffusion)
各記号が表す量は次の通りである。
塗膜内計算位置：ｚ’［ｍ］
塗膜厚み方向ｚ’軸における座標位置（塗膜表面）：ｓ［ｍ］
塗膜内の濃度分布：Ｃ（ｚ’）［ｋｇ／ｍ３］（各ステップで計算）
塗膜内の初期濃度分布：Ｃ０［ｋｇ／ｍ３］
ポリマ−溶剤の溶剤拡散係数：Ｄ（ｚ’）［ｍ２／ｓ］（後述・各ステップで計算）
温度Ｔにおける溶剤蒸気圧（ポリマ濃度影響を含む）：Ｐ（Ｔ）［Ｐａ］（後述・各ステップで計算）
温度Ｔにおける溶剤蒸気圧（ポリマ濃度影響を含まず）：Ｐ’（Ｔ）［Ｐａ］（後述・各ステップで計算）
空気中の溶剤分圧：Ｐair［Ｐａ］（各ステップで計算）
平均物質移動係数：ｋｍ［ｍ／ｓ］（後述・各ステップで計算）
The quantity represented by each symbol is as follows.
Calculation position in coating film: z ′ [m]
Coordinate position (coating film surface) in the coating thickness direction z ′ axis: s [m]
Concentration distribution in coating film: C (z ′) [kg / m3] (calculated at each step)
Initial concentration distribution in coating film: C0 [kg / m3]
Solvent diffusion coefficient of polymer solvent: D (z ′) [m2 / s] (described later, calculated at each step)
Solvent vapor pressure at temperature T (including polymer concentration effect): P (T) [Pa] (calculated at each step described later)
Solvent vapor pressure at temperature T (not including polymer concentration effect): P ′ (T) [Pa] (calculated at each step described later)
Solvent partial pressure in air : P air [Pa] (calculated at each step)
Average mass transfer coefficient: km [m / s] (described later, calculated at each step)
この拡散方程式を計算するのに必要な平均物質移動係数ｋは、乾燥機の構造によって決定され、これについては後述する。また、上記拡散方程式を計算するのに必要な溶剤蒸気圧Ｐ（Ｔ）、Ｐ’（Ｔ）、及び溶剤拡散係数Ｄ（ｚ’）は、溶剤の物性によって決定され、これらについては後述する。 The average mass transfer coefficient k required to calculate this diffusion equation is determined by the structure of the dryer and will be described later. Further, the solvent vapor pressures P (T), P ′ (T) and the solvent diffusion coefficient D (z ′) necessary for calculating the diffusion equation are determined by the physical properties of the solvent, which will be described later.
〔平均伝熱係数〕
図４に示すように、本実施形態では、２次元平板垂直衝突噴流を考える。図４では、ｘ軸を基材の移動方向（又はその逆方向）にとり、隣接したノズルの中間点を原点とする。なお、図４において、速度をｕ0ではなく、ｖで表示している。
熱伝導方程式を計算するのに必要な平均伝熱係数ｈａｍを、次のように表す。
Ｈ≦４Ｂの場合
As shown in FIG. 4, in the present embodiment, a two-dimensional flat plate vertical collision jet is considered. In FIG. 4, the x-axis is taken in the direction of movement of the substrate (or the opposite direction), and the midpoint between adjacent nozzles is taken as the origin. In FIG. 4, the speed is indicated by v instead of u 0 .
The average heat transfer coefficient ham necessary for calculating the heat conduction equation is expressed as follows.
When H ≦ 4B
各記号が表す量は次の通りである。
平均伝熱係数：ｈａｍ［Ｊ／ｍ2・ｓ・Ｋ］（各ステップで計算）
空気の密度：ρ［ｋｇ／ｍ3］（温度を考慮して各ステップで計算）
ノズル風速：ｕ0［ｍ／ｓ］（後掲の表参照）
ノズルのスリット間隔：Ｂ［ｍ］（後掲の表及び図４参照）
空気の粘度：μ［Ｐａ・ｓ］（後掲の表参照）
空気の比熱：Ｃｐ［Ｊ／Ｋ・ｋｇ］
計算領域：Ｌ［ｍ］（図４参照）
ノズル−フィルム間距離：Ｈ［ｍ］（後掲の表及び図４参照）
空気の熱伝導度：λ［Ｊ／ｍ・ｓ・Ｋ］（温度を考慮して各ステップで計算）
The quantity represented by each symbol is as follows.
Average heat transfer coefficient: ham [J / m 2 · s · K] (calculated at each step)
Air density: ρ [kg / m 3 ] (calculated at each step considering temperature)
Nozzle wind speed: u 0 [m / s] (see table below)
Nozzle slit spacing: B [m] (see table below and FIG. 4)
Air viscosity: μ [Pa · s] (See table below)
Specific heat of air: Cp [J / K · kg]
Calculation area: L [m] (see FIG. 4)
Nozzle-film distance: H [m] (see the table below and FIG. 4)
Thermal conductivity of air: λ [J / m · s · K] (calculated at each step considering temperature)
Ｈ≦４Ｂの場合、平均伝熱係数ｈａｍは、概略的に、次のように求められる。
淀み点における２次元平板垂直衝突噴流の式を用いる。
ノズルのスリット間隔：Ｂ［ｍ］
空気の熱伝導度：λ［Ｊ／ｍ・ｓ・Ｋ］
溶剤−空気の気相拡散係数：Ｄｇ［ｍ2／ｓ］
空気の密度：ρ［ｋｇ／ｍ3］
ノズル風速：ｕ0［ｍ／ｓ］
空気の粘度：μ［Ｐａ・ｓ］
空気の比熱：Ｃｐ［Ｊ／Ｋ・ｋｇ］
これらの式から次の式が導かれる。
The formula of the two-dimensional vertical impinging jet at the stagnation point is used.
Nozzle slit spacing: B [m]
Thermal conductivity of air: λ [J / m · s · K]
Solvent-air gas phase diffusion coefficient: Dg [m 2 / s]
Air density: ρ [kg / m 3 ]
Nozzle wind speed: u 0 [m / s]
Air viscosity: μ [Pa · s]
Specific heat of air: Cp [J / K · kg]
From these equations, the following equation is derived.
また、２次元平板衝突噴流の局所ヌッセルト数の式は次のようになる。
この式を、計算領域Ｌにおいてｘ方向に積分したものと、淀み点におけるヌッセルト数Ｎｕの式と、座標方向ｘにおける空気のヌッセルト数平均値の式により、上述した平均伝熱係数ｈａｍの式が得られる。
The formula of the local Nusselt number of the two-dimensional flat plate impinging jet is as follows.
The above equation for the average heat transfer coefficient ham is obtained by integrating this equation in the x direction in the calculation region L, the equation for the Nusselt number Nu at the stagnation point, and the equation for the average Nusselt number of air in the coordinate direction x. can get.
〔平均物質移動係数〕
平均伝熱係数の場合と同様、図４に示すように、本実施形態では、２次元平板垂直衝突噴流を考える。ｘ軸を基材の移動方向（又はその逆方向）にとり、隣接したノズルの中間点を原点とする。
拡散方程式を計算するのに必要な平均物質移動係数ｋｍを、次のように表す。
Ｈ≦４Ｂの場合
As in the case of the average heat transfer coefficient, as shown in FIG. 4, in this embodiment, a two-dimensional flat plate vertical collision jet is considered. The x-axis is taken in the direction of movement of the substrate (or the opposite direction), and the midpoint between adjacent nozzles is the origin.
The average mass transfer coefficient km required to calculate the diffusion equation is expressed as follows:
When H ≦ 4B
各記号が表す量は次の通りである。
平均物質移動係数：ｋｍ［ｍ／ｓ］（各ステップで計算）
空気の密度：ρ［ｋｇ／ｍ3］（各ステップで計算）
ノズル風速：ｕ0［ｍ／ｓ］（後掲の表参照）
ノズルのスリット間隔：Ｂ［ｍ］（後掲の表及び図４参照）
空気の粘度：μ［Ｐａ・ｓ］（後掲の表参照）
計算領域：Ｌ［ｍ］（４参照）
ノズル−フィルム間距離：Ｈ［ｍ］（後掲の表及び図４参照）
溶剤−空気の気相拡散係数：Ｄｇ［ｍ2／ｓ］（後掲の表参照）
The quantity represented by each symbol is as follows.
Average mass transfer coefficient: km [m / s] (calculated at each step)
Air density: ρ [kg / m 3 ] (calculated at each step)
Nozzle wind speed: u 0 [m / s] (see table below)
Nozzle slit spacing: B [m] (see table below and FIG. 4)
Air viscosity: μ [Pa · s] (See table below)
Calculation area: L [m] (see 4)
Nozzle-film distance: H [m] (see the table below and FIG. 4)
Solvent-air gas phase diffusion coefficient: Dg [m 2 / s] (see table below)
Ｈ≦４Ｂの場合、平均物質移動係数ｋｍは、概略的には、次のように求められる。
淀み点における２次元平板垂直衝突噴流の式を用いる。
ノズルのスリット間隔：Ｂ［ｍ］
溶剤−空気の気相拡散係数：Ｄｇ［ｍ2／ｓ］
空気の密度：ρ［ｋｇ／ｍ3］
ノズル風速：ｕ0［ｍ／ｓ］
空気の粘度：μ［Ｐａ・ｓ］
これらの式から次の式が導かれる。
The formula of the two-dimensional vertical impinging jet at the stagnation point is used.
Nozzle slit spacing: B [m]
Solvent-air gas phase diffusion coefficient: Dg [m 2 / s]
Air density: ρ [kg / m 3 ]
Nozzle wind speed: u 0 [m / s]
Air viscosity: μ [Pa · s]
From these equations, the following equation is derived.
また、２次元平板衝突噴流の局所シャーウッド数は次のようになる。
この式を、計算領域Ｌにおいてｘ方向に積分してから、したものと、淀み点におけるシャーウッド数Ｓｈの式と、座標方向ｘにおける空気のシャーウッド数平均値の式により、上述した平均物質移動係数ｋｍの式が得られる。
The local Sherwood number of the two-dimensional flat plate impinging jet is as follows.
The above-mentioned average mass transfer coefficient is obtained by integrating this formula in the calculation region L in the x direction, the formula of the Sherwood number Sh at the stagnation point, and the formula of the average value of the Sherwood number of air in the coordinate direction x. km formula is obtained.
〔溶剤蒸気圧〕
ポリマ濃度が小さい場合、温度Ｔにおける溶剤蒸気圧Ｐ（Ｔ）を、次のＡｎｔｏｉｎｅ式から算出することが好ましい。
When the polymer concentration is small, the solvent vapor pressure P (T) at the temperature T is preferably calculated from the following Antoine equation.
各記号が表す量は次の通りである。
溶剤のＡｎｔｏｉｎｅ数：ＡＡ、ＡＢ、ＡＣ［無次元］（後掲の表参照）
塗膜内における溶剤の体積分率：φi［無次元］（各ステップで計算）
塗膜内におけるポリマの体積分率：φp［無次元］（各ステップで計算）
Ｆｌｏｒｙ−Ｈｕｇｇｉｎｓ理論の相互反応パラメータ：ｘip［無次元］（後掲の表参照）
The quantity represented by each symbol is as follows.
Antoine number of solvent: AA, AB, AC [dimensionless] (see table below)
Volume fraction of solvent in the coating: φ i [Dimensionless] (calculated at each step)
Volume fraction of polymer in the coating: φ p [Dimensionless] (calculated at each step)
Interaction parameters of Flory-Huggins theory: x ip [dimensionless] (see table below)
〔溶剤拡散係数〕
２つの溶剤のうちの一方の溶剤の溶剤拡散係数Ｄａは、次の式を用いて求める。
The solvent diffusion coefficient Da of one of the two solvents is obtained using the following equation.
各記号が表す量は次の通りである（添字「ａ」は、一方の溶剤を意味する。）。
溶剤拡散係数：Ｄａ［ｍ2／ｓ］
基準溶剤拡散係数：Ｄａ＊［ｍ2／ｓ］（任意の数）
拡散係数パラメータ：ａａ、ｂａ［無次元］（後掲の表参照）
溶剤濃度：Ｃａ［ｋｇ／ｍ3］
ポリマ濃度：Ｃｓ［ｋｇ／ｍ3］
基準ポリマ濃度：Ｃｓ＊［ｋｇ／ｍ3］（任意の数）
活性化エネルギー：Ｅｏａ［Ｊ／ｍｏｌ］（後掲の表参照）
理想気体定数：Ｒ［Ｊ／ｍｏｌ・Ｋ］（後掲の表参照）
The amount represented by each symbol is as follows (subscript “a” means one solvent).
Solvent diffusion coefficient: Da [m 2 / s]
Standard solvent diffusion coefficient: Da * [m 2 / s] (arbitrary number)
Diffusion coefficient parameters: aa, ba [dimensionless] (see table below)
Solvent concentration: Ca [kg / m 3 ]
Polymer concentration: Cs [kg / m 3 ]
Reference polymer concentration: Cs * [kg / m 3 ] (arbitrary number)
Activation energy: Eoa [J / mol] (See the table below)
Ideal gas constant: R [J / mol · K] (see table below)
他方の溶剤の溶剤拡散係数Ｄｂも、Ｄａと同様の式を用いて求める。 The solvent diffusion coefficient Db of the other solvent is also determined using the same formula as Da.
この溶剤拡散係数は、予め実験室内で行った実験データを基にして、Ｒｅｇｕｌａｒ Ｒｅｇｉｍｅ理論を用いて求められる（非特許文献３）。
例えば、溶剤拡散係数を求めるべき塗液（ポリマ及び溶剤）について、ポリマを溶剤に溶かして容器に入れ、熱風を当てて乾燥させる。それにより、時間に対する重量の変化を測定し、それを含溶媒率（溶剤重量［ｋｇ］／ポリマ重量［ｋｇ］＝Ｃａ／ｃｓ）に対する乾燥速度ｒ（塗液の減少重量［ｋｇ］／塗液の表面積［ｍ2］・時間［ｓ］）に変換する。変換によって得られた曲線を乾燥速度曲線という。条件を変えて、乾燥速度曲線を2つ以上求める。
次に、乾燥速度曲線（ｒ）に、温度補正（次式）を施し、補正乾燥速度曲線（ｒ＊）を求める。
また、Ｄａが先の式で表される場合，Ｒｅｇｕｌａｒ Ｒｅｇｉｍｅの特性関数（ＣＦＲＲ）の近似式（近似乾燥速度式）は流束比較法により次のように表わされる。
For example, with respect to the coating liquid (polymer and solvent) for which the solvent diffusion coefficient is to be obtained, the polymer is dissolved in a solvent, placed in a container, and dried by applying hot air. Thus, the change in weight with respect to time was measured, and the change was measured with respect to the solvent content (solvent weight [kg] / polymer weight [kg] = Ca / cs). Surface area [m 2 ] · time [s]). The curve obtained by the conversion is called a drying rate curve. Find two or more drying rate curves under different conditions.
Next, temperature correction (following equation) is performed on the drying speed curve (r) to obtain a corrected drying speed curve (r *).
When Da is expressed by the above equation, an approximate expression (approximate drying rate expression) of the characteristic function (CFRR) of Regular Regime is expressed as follows by the flux comparison method.
なお、例えば、ポリマー重量は、ポリマー密度×塗工面積×製品膜圧で計算する。 For example, the polymer weight is calculated by polymer density × coating area × product film pressure.
次に、図５を参照して、塗工乾燥シミュレーションのアルゴリズムを説明する。 Next, the algorithm of the coating / drying simulation will be described with reference to FIG.
図５に示すように、本発明の塗工乾燥シミュレーションシステムは、ＳＴＡＲＴから始まりＥＮＤで終了する。 As shown in FIG. 5, the coating and drying simulation system of the present invention starts from START and ends at END.
入力において、本発明の塗工乾燥シミュレーションシステムで必要とされる値を入力する部分である。例えば、表１、表２に示す値の入力を行う。初期値計算・設定において、塗工開始時の溶剤とポリマを含む塗液の初期値を設定する。データ保存において、当該塗工乾燥シミュレーションシステムから出力された値を保存する。 In the input, it is a part for inputting values required in the coating / drying simulation system of the present invention. For example, the values shown in Table 1 and Table 2 are input. In the initial value calculation / setting, the initial value of the coating liquid containing the solvent and polymer at the start of coating is set. In data storage, the value output from the coating / drying simulation system is stored.
計算終了判定において、経過時間と基材の搬送速度との関係から、溶剤とポリマを含む塗液が乾燥炉内のどの位置に在るのかを判断し、乾燥炉出口を越えた時点で計算を終了する判定を行う。ここで、溶剤とポリマを含む塗液が乾燥炉出口に未到達と判断すると、次ステップの条件設定部分に計算が移る。 When determining the end of calculation, determine the position in the drying furnace where the coating liquid containing the solvent and polymer is located based on the relationship between the elapsed time and the conveyance speed of the substrate, and calculate when the temperature exceeds the outlet of the drying furnace. Make a decision to finish. Here, when it is determined that the coating liquid containing the solvent and the polymer has not reached the outlet of the drying furnace, the calculation shifts to the condition setting portion of the next step.
次ステップの条件設定において、時間刻み幅を１つ進めたシミュレーションをする上で必要なデータの書換・設定を行う。 In the next step condition setting, data rewriting / setting necessary for the simulation with the time step incremented by one is performed.
計算（ａ）において、シミュレーションすべき塗工機の乾燥能力を算出する。具体的には、拡散方程式に用いる平均物質移動係数ｋｍと、伝熱方程式に用いる平均伝熱係数ｈａｍを算出する。 In calculation (a), the drying capacity of the coating machine to be simulated is calculated. Specifically, the average mass transfer coefficient km used for the diffusion equation and the average heat transfer coefficient ham used for the heat transfer equation are calculated.
計算（ｂ）において、シミュレーションすべき基材に塗布された溶剤とポリマを含む塗液（以下、「塗膜」という）内の温度分布、塗液が塗布された基材内の温度分布を、上述した伝熱モデルに基づいて計算する。ここでの離散化手法は、例えば、両辺を１次精度差分法により離散化を行う。また、計算手法として、例えば、ニュートン・ラプソン法を用いる。この計算（ｂ）により、ステップごとに、塗膜及び基材内の温度分布が更新される。 In the calculation (b), the temperature distribution in the coating liquid containing the solvent and the polymer applied to the substrate to be simulated (hereinafter referred to as “coating film”), the temperature distribution in the substrate coated with the coating liquid, Calculation is based on the heat transfer model described above. In this discretization method, for example, both sides are discretized by the first-order accuracy difference method. As a calculation method, for example, the Newton-Raphson method is used. By this calculation (b), the temperature distribution in the coating film and the substrate is updated for each step.
計算（ｃ）において、予め各溶剤とポリマを含む塗液の乾燥速度の実測値からＲｅｇｕｌａｒ Ｒｅｇｉｍｅ理論、流束比較法を用いて導出した溶剤拡散係数、及び、各溶剤について計算した溶剤蒸気圧を用いて、シミュレートすべき塗膜内の濃度分布を、溶剤ごとに、上述した拡散モデルに基づいて算出する。ここでの離散化手法は、例えば、両辺を２次精度差分法により離散化を行う。また、計算手法として、例えば、ニュートン・ラプソン法を用いる。この計算（ｃ）により、ステップごとに、溶剤の濃度分布が溶剤ごとに更新される。 In calculation (c), the solvent diffusion coefficient derived from the measured values of the drying speed of the coating liquid containing each solvent and polymer in advance using the Regular Regime theory and the flux comparison method, and the solvent vapor pressure calculated for each solvent are The concentration distribution in the coating film to be simulated is calculated for each solvent based on the diffusion model described above. In this discretization method, for example, both sides are discretized by the secondary accuracy difference method. As a calculation method, for example, the Newton-Raphson method is used. By this calculation (c), the solvent concentration distribution is updated for each solvent at each step.
計算（ｄ）において、各乾燥炉ゾーン入口からその乾燥炉ゾーン出口までの溶剤蒸発量を算出し、それと乾燥炉ゾーン体積との関係を用いて、各乾燥炉ゾーン内のガス濃度Ｖｐを次式で算出することが好ましい。
各記号が表す量は次の通りである。
ガス濃度：Ｖｐ［ｐｐｍ］
塗工幅：Ｗｃｏｔ［ｍ］
各乾燥炉長：Ｌｚｏｎｅ［ｍ］
各乾燥炉内排気量：Ｖｏｕｔ［ｍ3／ｓ］
The quantity represented by each symbol is as follows.
Gas concentration: Vp [ppm]
Coating width: Wcot [m]
Each drying oven length: Lzone [m]
Displacement in each drying furnace: Vout [m 3 / s]
計算（ｅ）において、溶剤とポリマを含む塗液内の発泡有無を算出することが好ましい。具体的には、塗膜内の溶剤蒸気圧分布を算出し、各分布部位に対して大気圧より値が大きくなった時点で発泡有と判断する。また、塗膜内の溶剤蒸気圧分布は、上述したものと同じ次式を利用する。
更に、溶剤とポリマを含む塗液の表面濃度から、溶剤とポリマを含む塗液の表面皮バリの有無をシミュレーションしてもよい。例えば、塗液表面での固形分率が９５％以上である場合、塗液表面での固形分率が表面の下層の固形分率の１．２５倍以上である場合、又は両者を満たす場合に、皮バリが有るとする。 Furthermore, the presence / absence of surface burr of the coating liquid containing the solvent and the polymer may be simulated from the surface concentration of the coating liquid containing the solvent and the polymer. For example, when the solid content ratio on the coating liquid surface is 95% or more, when the solid content ratio on the coating liquid surface is 1.25 times or more of the solid content ratio of the lower layer on the surface, or when both are satisfied Suppose that there is a skin burr.
上記アルゴリズムは、プログラム言語ｆｏｒｔｒａｎを用いてプログラムにされるのがよい。 The algorithm is preferably programmed using the program language fortran.
図６は、実機及び実際の乾燥作業に合わせた値を示す表１及び表２の値を用いて、各乾燥炉ゾーン内における各溶剤の残溶剤率をシミュレーションした結果と、シミュレーションされた値（計算値）の妥当性を検証すべく、実機実測値とを比較した図である。塗液は、１つのポリマ成分であるエポキシ樹脂と、２つ有機溶剤成分であるトルエンと酢酸エチルを含有する。基材は、例えば、ＰＥＴフィルムである。図６において、本発明の塗工乾燥シミュレーションシステムにてシミュレーションされた値（計算値）と実機実測値を比較すると、シミュレーションされた値（計算値）と実機実測値は比較的近似しており、塗工乾燥シミュレーションシステムの妥当性があることと判断できる。 FIG. 6 shows the result of simulating the residual solvent ratio of each solvent in each drying furnace zone using the values in Table 1 and Table 2 showing values according to the actual machine and the actual drying operation, and the simulated values ( It is the figure which compared with the actual machine actual value in order to verify the validity of (calculated value). The coating solution contains one polymer component, an epoxy resin, and two organic solvent components, toluene and ethyl acetate. The substrate is, for example, a PET film. In FIG. 6, when the value (calculated value) simulated by the coating drying simulation system of the present invention and the actual machine actual value are compared, the simulated value (calculated value) and the actual machine actual value are relatively approximate, It can be judged that the coating drying simulation system is appropriate.
上述した計算（ｃ）において、単一の時間ステップでは、溶剤ごとの濃度分布が計算されるが、次の時間ステップにおける計算のときに、溶剤相互に関係した量が変化し、一方の溶剤の計算に他方の溶剤の計算の影響がおよび、これにより２つの溶剤成分の拡散方程式を連立させて解く事と同様の効果が得られるため、最終的な計算結果の精度が向上する。 In the calculation (c) described above, the concentration distribution for each solvent is calculated in a single time step. However, in the calculation in the next time step, the amount related to the solvent changes, and Since the calculation is influenced by the calculation of the other solvent, and the same effect as that obtained by solving the diffusion equations of the two solvent components simultaneously is obtained, the accuracy of the final calculation result is improved.
以上説明したように、本発明によれば、コータ部で基材上に溶剤とポリマを含んだ塗液を塗り、ｎ個の連続したゾーンに分けられている乾燥炉で、基材に塗布された塗液中の溶剤を除去するフィルム塗工において、各乾燥炉ゾーン内の塗液中残溶剤率を予測することができ、かつ、各乾燥炉ゾーン内の基材に塗布された塗液の品質を安定させることができる塗工乾燥シミュレーションシステムを提供することが可能となった。 As described above, according to the present invention, a coating liquid containing a solvent and a polymer is applied onto the base material at the coater, and is applied to the base material in a drying furnace divided into n continuous zones. In the film coating to remove the solvent in the coating liquid, the residual solvent ratio in the coating liquid in each drying furnace zone can be predicted, and the coating liquid applied to the substrate in each drying furnace zone It became possible to provide a coating drying simulation system that can stabilize the quality.
Claims (4)
有機溶剤とポリマを含む塗液の溶剤乾燥速度を実測値で求め、当該溶剤乾燥速度からレギュラーレジーム理論（Ｒｅｇｕｌａｒ Ｒｅｇｉｍｅ理論）及び流束比較法を用いて溶剤拡散係数を導出し、
有機溶剤とポリマを含む塗液中に含まれる有機溶剤の溶剤蒸気圧をＦｌｏｒｙ−Ｈｕｇｇｉｎｓ理論から算出し、
各乾燥炉ゾーン能力より物質移動係数を算出し、
乾燥炉能力から有機溶剤とポリマを含む塗液及び該塗液が塗布されたＰＥＴフィルムの伝熱係数を算出し、
前記溶剤拡散係数、前記溶剤蒸気圧、前記物質移動係数を用いて、各有機溶剤とポリマを含む塗液内に含まれる溶剤濃度分布を１次元非定常拡散方程式により算出し、
有機溶剤とポリマを含む塗液及び該塗液が塗布されたＰＥＴフィルムの物性値より定まる熱伝導度及び温度伝導率、及び前記伝達係数を用いて、ＰＥＴフィルムに塗布された有機溶剤とポリマを含む塗液（塗膜）内、及び該塗液が塗布されたＰＥＴフィルム内の温度分布を１次元非定常熱伝導方程式により算出し、
前記溶剤濃度計算値より単位換算をすることにより塗液中残溶剤率をシミュレーションすることを特徴とする塗工乾燥シミュレーション方法。 Coating when drying a PET film coated with a coating solution containing a two-component organic solvent and a one-component polymer using a coating drying furnace divided into n consecutive zones (n is a positive integer) A method for simulating industrial drying,
Obtain the solvent drying rate of the coating solution containing the organic solvent and the polymer by actual measurement, and derive the solvent diffusion coefficient from the solvent drying rate using the regular regime theory (Regular Regime theory) and the flux comparison method,
The solvent vapor pressure of the organic solvent contained in the coating liquid containing the organic solvent and the polymer is calculated from the Flory-Huggins theory,
Calculate the mass transfer coefficient from the capacity of each oven,
Calculate the heat transfer coefficient of the coating liquid containing the organic solvent and the polymer from the drying furnace capacity and the PET film coated with the coating liquid,
Using the solvent diffusion coefficient, the solvent vapor pressure, and the mass transfer coefficient, the solvent concentration distribution contained in the coating liquid containing each organic solvent and polymer is calculated by a one-dimensional unsteady diffusion equation,
Using the thermal conductivity and temperature conductivity determined from the physical properties of the coating liquid containing the organic solvent and the polymer and the PET film coated with the coating liquid, and the transfer coefficient, the organic solvent and the polymer applied to the PET film are The temperature distribution in the coating liquid (coating film) containing and in the PET film coated with the coating liquid is calculated by a one-dimensional unsteady heat conduction equation,
A coating / drying simulation method characterized by simulating the residual solvent ratio in the coating liquid by converting the unit from the calculated value of the solvent concentration.
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