JP5673570B2 - Method for estimating dry state of coating film - Google Patents
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Description
本発明は、塗膜の乾燥状態推定方法、特に、粒子と溶媒とを混合したペーストを基材の表面に塗布して、基材の表面にペーストからなる塗膜を形成した後に、塗膜を乾燥させることによって粒子を有する多孔体を形成する期間中の塗膜の乾燥状態を推定する方法に関する。 The present invention relates to a method for estimating a dry state of a coating film, and in particular, after a paste in which particles and a solvent are mixed is applied to the surface of a base material to form a coating film made of the paste on the surface of the base material, The present invention relates to a method for estimating a dry state of a coating film during a period of forming a porous body having particles by drying.
特許文献１には、基材上の塗布層の乾燥速度推定方法が開示されている。具体的には、塗布層表面の境膜伝熱係数と、塗布層内の水分質量を算出する式と、塗布層内の水分質量変化を算出する式とを利用して、基材上の塗布層の乾燥速度を推定する方法が開示されている。 Patent Document 1 discloses a method for estimating the drying rate of a coating layer on a substrate. Specifically, coating on the substrate using the film heat transfer coefficient of the coating layer surface, the formula for calculating the moisture mass in the coating layer, and the formula for calculating the moisture mass change in the coating layer A method for estimating the drying rate of a layer is disclosed.
ところで、リチウムイオン二次電池や燃料電池などの電池の電極は、次のようにして作製する。まず、電極材料である粒子（活物質粒子）と溶媒とバインダを混合したペーストを用意する。次いで、このペーストを基材の表面に塗布して、基材の表面にペーストからなる塗膜を形成する、その後、この塗膜を乾燥（溶媒を蒸発）させることで、粒子を有する多孔体（バインダによって多数の粒子が結合してなる膜であって、粒子間に形成された空隙によって多孔質となる膜）を形成する。 By the way, an electrode of a battery such as a lithium ion secondary battery or a fuel cell is manufactured as follows. First, a paste in which particles (active material particles) that are electrode materials, a solvent, and a binder are mixed is prepared. Next, the paste is applied to the surface of the base material to form a coating film made of the paste on the surface of the base material, and then the coating film is dried (solvent is evaporated) to thereby have a porous body having particles ( A film in which a large number of particles are bonded by a binder, and a porous film is formed by voids formed between the particles.
近年、上述のような粒子と溶媒とを混合したペーストからなる塗膜を乾燥させる期間中に、塗膜の乾燥状態を適切に推定できる方法が求められている。しかしながら、特許文献１では、このような塗膜の乾燥状態を適切に推定することはできなかった。その理由は、以下の通りである。粒子と溶媒とを混合したペーストからなる塗膜を乾燥させた場合、乾燥開始からしばらくの期間は、溶媒の蒸発速度を一定とした定率乾燥期間となる。 In recent years, there has been a demand for a method that can appropriately estimate the dry state of a coating film during a period of drying the coating film made of a paste in which particles and a solvent are mixed as described above. However, in patent document 1, the dry state of such a coating film was not able to be estimated appropriately. The reason is as follows. When a coating film made of a paste in which particles and a solvent are mixed is dried, a fixed period drying period with a constant evaporation rate of the solvent is performed for a while after the start of drying.
しかしながら、溶媒（その一部）の蒸発により塗膜の厚みが多孔体（乾燥完了後の塗膜）と同一の厚みに達した後、すなわち、溶媒量が多孔体内の空隙体積と一致して溶媒が多孔体内の空隙をちょうど満たす状態になった後は、溶媒の蒸発速度が減少してゆく減率乾燥期間となる。具体的には、この減率乾燥期間では、多孔体（塗膜）内に溶媒の液相と気相とが混在した状態となり、溶媒が、多孔体（塗膜のうち溶媒が蒸発により消失している部分）内の孔（空隙）を通じて、多孔体の外部へ移動（蒸発）してゆくことになる。このため、この減率乾燥期間においては、多孔体（塗膜のうち溶媒が蒸発により消失している部分）内の毛管圧駆動による溶媒移動、溶媒の液相から気相への相変化、気相における拡散による溶媒移動を考慮して、塗膜の乾燥状態を推定する必要があった。 However, after the solvent (a part thereof) evaporates, the thickness of the coating reaches the same thickness as the porous body (the coating after drying), that is, the amount of solvent matches the void volume in the porous body. After the state just fills the voids in the porous body, it becomes a decreasing rate drying period in which the evaporation rate of the solvent decreases. Specifically, in this decreasing rate drying period, the liquid phase and gas phase of the solvent are mixed in the porous body (coating film), and the solvent disappears due to evaporation of the porous body (coating film within the coating film). It moves (evaporates) to the outside of the porous body through the pores (voids) in the portion. For this reason, during this reduced rate drying period, the solvent is moved by capillary pressure driving in the porous body (the part of the coating film where the solvent has disappeared due to evaporation), the phase change from the liquid phase to the gas phase of the solvent, It was necessary to estimate the dry state of the coating film in consideration of solvent movement due to diffusion in the phase.
本発明は、かかる現状に鑑みてなされたものであって、溶媒（その一部）の蒸発により塗膜の厚みが多孔体（乾燥完了後の塗膜）と同一の厚みに達した後において、塗膜の乾燥状態を適切に推定することができる方法を提供することを目的とする。 The present invention has been made in view of the current situation, and after the thickness of the coating film reaches the same thickness as the porous body (coating after completion of drying) by evaporation of the solvent (part thereof), It aims at providing the method which can estimate the dry state of a coating film appropriately.
本発明の一態様は、粒子と溶媒とを混合したペーストを基材の表面に塗布して、上記基材の表面に上記ペーストからなる塗膜を形成した後に、上記塗膜を乾燥させることによって上記粒子を有する多孔体を形成する期間中の上記塗膜の乾燥状態を推定する方法において、上記溶媒の一部の蒸発により上記塗膜の厚みが上記多孔体と同一の厚みに達した後、多孔体内の気液２相流の方程式である下記式（１）のうち、溶媒濃度Ｃを下記式（２）で表される数式に変換すると共に、溶媒の気相の実効拡散係数Ｄeffを下記式（３）で表される数式に変換し、この変換した式から飽和度ｓを算出する塗膜の乾燥状態推定方法である。
上述の塗膜の乾燥状態推定方法では、溶媒の一部の蒸発により上記塗膜の厚みが上記多孔体と同一の厚みに達した後において、多孔体内の気液２相流に関する方程式である式（１）のうち、溶媒濃度Ｃを式（２）で表される数式（右辺）に変換すると共に、溶媒の気相の実効拡散係数Ｄeffを式（３）で表される数式（右辺）に変換し、この変換した式から飽和度ｓを算出する。ここで、飽和度ｓとは、上記多孔体の空隙中に溶媒の液相が占める割合を表す値であり、０〜１の範囲の数値（多孔体の空隙の１００％を溶媒の液相が占めるとき、ｓ＝１となる）で表される。 In the dry film state estimation method described above, an equation relating to a gas-liquid two-phase flow in the porous body after the thickness of the coated film reaches the same thickness as the porous body due to evaporation of a part of the solvent. Among (1), the solvent concentration C is converted into a mathematical formula (right side) represented by the formula (2), and the effective diffusion coefficient D eff of the gas phase of the solvent is represented by the formula (3) (right side). And the degree of saturation s is calculated from the converted expression. Here, the degree of saturation s is a value that represents the ratio of the liquid phase of the solvent in the voids of the porous body, and is a numerical value in the range of 0 to 1 (100% of the voids of the porous body represents the liquid phase of the solvent. S = 1 when occupied).
ここで、式（１）の左辺の第２項は、対流による溶媒の輸送（移動）を表す式である。また、式（１）の右辺の第１項は、蒸気による溶媒の輸送を表す式であり、第２項は、毛管圧による溶媒の輸送（移動）を表す式である。 Here, the second term on the left side of the equation (1) is an equation representing the transport (movement) of the solvent by convection. Further, the first term on the right side of the formula (1) is an equation representing the transport of the solvent by the vapor, and the second term is an equation representing the transport (movement) of the solvent by the capillary pressure.
また、式（２）の右辺の第１項は、溶媒の液相の割合を表す式であり、第２項は、溶媒の気相（蒸気）の割合を表す式である。また、式（３）は、溶媒の気相における拡散による移動を考慮した実効拡散係数を表す式である。 Further, the first term on the right side of the formula (2) is a formula representing the ratio of the liquid phase of the solvent, and the second term is a formula representing the ratio of the gas phase (vapor) of the solvent. Equation (3) is an equation representing an effective diffusion coefficient in consideration of movement of the solvent due to diffusion in the gas phase.
従って、上述のように飽和度ｓを算出することで、溶媒（その一部）の蒸発により塗膜の厚みが多孔体（乾燥完了後の塗膜）と同一の厚みに達した後において、多孔体（塗膜のうち溶媒が蒸発により消失している部分）内の毛管圧駆動による溶媒移動、溶媒の液相から気相への相変化、気相における拡散による移動を考慮して、塗膜の乾燥状態（飽和度ｓ）を適切に推定することができる。 Therefore, by calculating the saturation s as described above, the porous film (the coated film after drying) reaches the same thickness as that of the porous body (the coated film after drying) by evaporation of the solvent (part thereof). In consideration of the solvent movement by capillary pressure driving in the body (the part of the coating film where the solvent has disappeared due to evaporation), the phase change of the solvent from the liquid phase to the gas phase, and the movement by diffusion in the gas phase It is possible to appropriately estimate the dry state (saturation degree s).
なお、「溶媒（その一部）の蒸発により塗膜の厚みが多孔体（乾燥完了後の塗膜）と同一の厚みに達した後」とは、「塗膜中の溶媒量が多孔体の空隙体積と一致して、溶媒が多孔体内の空隙をちょうど満たす状態になった後」をいう。 “After the thickness of the coating film reaches the same thickness as the porous body (coating after completion of drying) due to evaporation of the solvent (part thereof)” means that “the amount of solvent in the coating film is "After the solvent has just filled the voids in the porous body, consistent with the void volume".
また、「溶媒の一部の蒸発により塗膜の厚みが多孔体と同一の厚みに達した」か否かは、例えば、次のようにして判断することができる。基材の表面に塗膜を形成した時（乾燥前）の塗膜の状態及び乾燥条件に基づいて、溶媒の定率（恒率）蒸発速度を求め、この定率蒸発速度に基づいて現在の塗膜の厚みを推定することにより判断することができる。 Further, whether or not “the thickness of the coating film has reached the same thickness as the porous body by evaporation of a part of the solvent” can be determined as follows, for example. The constant rate (constant rate) evaporation rate of the solvent is determined based on the state of the coating and the drying conditions when the coating is formed on the surface of the substrate (before drying), and the current coating based on this constant rate evaporation rate This can be determined by estimating the thickness of the film.
具体的には、まず、基材の表面に塗膜を形成した時（乾燥前）の塗膜の厚み、この塗膜に含まれる溶媒量（体積）、及び、多孔体の厚みを、予め把握しておく。そして、基材の表面に形成した塗膜の乾燥を開始したら、公知の方法により、溶媒の蒸発速度（定率、一定）を算出する。例えば、膜表面熱伝達係数（境膜伝達係数）、物質伝達係数（物質移動係数）を算出し、これらの値に基づいて、溶媒の定率（恒率）蒸発速度を求めることができる。 Specifically, first, the thickness of the coating film when the coating film is formed on the surface of the substrate (before drying), the amount of solvent (volume) contained in this coating film, and the thickness of the porous body are grasped in advance. Keep it. Then, when drying of the coating film formed on the surface of the substrate is started, the evaporation rate (constant rate, constant) of the solvent is calculated by a known method. For example, a film surface heat transfer coefficient (boundary film transfer coefficient) and a mass transfer coefficient (mass transfer coefficient) can be calculated, and a constant rate (constant rate) evaporation rate of the solvent can be obtained based on these values.
その後、溶媒の蒸発速度（定率）と乾燥時間との積を算出することで、蒸発した溶媒量を求める。さらに、蒸発した溶媒量から、減少した塗膜の厚み（塗膜の体積減少分は、蒸発した溶媒の体積に一致する）を求める。そして、乾燥前の塗膜の厚みから、溶媒の蒸発により減少した塗膜の厚みを差し引くことで、現在の塗膜の厚みを推定することができる。その後、推定した塗膜の厚みが、多孔体と同一の厚みに達したか否かを判定することで、「溶媒の一部の蒸発により塗膜の厚みが多孔体と同一の厚みに達した」か否かを判定することができる。 Thereafter, the amount of evaporated solvent is obtained by calculating the product of the evaporation rate (constant rate) of the solvent and the drying time. Further, the reduced thickness of the coating film (the volume decrease of the coating film matches the volume of the evaporated solvent) is determined from the amount of solvent evaporated. And the thickness of the present coating film can be estimated by subtracting the thickness of the coating film reduced by evaporation of the solvent from the thickness of the coating film before drying. Then, by judging whether or not the estimated thickness of the coating film reached the same thickness as the porous body, “the thickness of the coating film reached the same thickness as the porous body due to evaporation of a part of the solvent. It can be determined whether or not.
また、２次元レーザー変位計により、塗膜の厚みを測定して、測定された塗膜の厚みが多孔体と同一の厚みに達したか否かを判定することで、「溶媒の一部の蒸発により塗膜の厚みが多孔体と同一の厚みに達した」か否かを判定するようにしても良い。 Further, by measuring the thickness of the coating film with a two-dimensional laser displacement meter and determining whether or not the measured thickness of the coating film has reached the same thickness as the porous body, You may make it determine whether the thickness of the coating film reached the same thickness as the porous body by evaporation.
さらに、蒸気の塗膜の乾燥状態推定方法であって、算出された前記飽和度ｓの値が０になったか否かを判定し、飽和度ｓの値が０になったと判定した場合は、前記塗膜の乾燥が完了したと判断する塗膜の乾燥状態推定方法とすると良い。 Furthermore, in the method for estimating the dry state of the coating film of steam, it is determined whether or not the calculated value of the saturation s is 0, and when it is determined that the value of the saturation s is 0, A method for estimating the dry state of the coating film that determines that the drying of the coating film has been completed may be used.
多孔体の空隙中に溶媒の液相が占める割合が「０」になったとき、すなわち、飽和度ｓの値が０になったとき、塗膜の乾燥が完了したといえる。そこで、上述の塗膜の乾燥状態推定方法では、前述のようにして算出された飽和度ｓの値が０になった場合は、塗膜の乾燥が完了したと判断するようにした。これにより、塗膜の乾燥完了（終了）を適切に判断することができる。 When the ratio of the liquid phase of the solvent in the voids of the porous body becomes “0”, that is, when the value of the saturation s becomes 0, it can be said that the drying of the coating film is completed. Therefore, in the above-described method for estimating the dry state of the coating film, when the value of the saturation s calculated as described above becomes 0, it is determined that the drying of the coating film is completed. Thereby, the completion (end) of drying of a coating film can be judged appropriately.
なお、塗膜の乾燥を開始した時から飽和度ｓの値が０になったと判定されるまでの時間を計測することで、塗膜の乾燥時間（塗膜の乾燥を完了させるのに要する時間）を把握することができる。すなわち、塗膜の乾燥を開始した時から飽和度ｓの値が０になったと判定されるまでの時間を、塗膜の乾燥を完了させるのに要する時間として把握することができる。 In addition, by measuring the time from when the drying of the coating film is started until it is determined that the value of the saturation s becomes 0, the drying time of the coating film (the time required to complete the drying of the coating film) ). That is, the time from when the drying of the coating film is started until it is determined that the value of the saturation s becomes 0 can be grasped as the time required to complete the drying of the coating film.
次に、本発明の実施形態について、図面を参照しつつ説明する。
図１〜図４は、基材の表面に形成した塗膜を乾燥させたときの様子を示す図である。具体的には、図１は、粒子２１と溶媒２３とを混合したペースト２５を、基材１０の表面に塗布して、基材１０の表面にペースト２５からなる塗膜２０を形成したとき（乾燥前）の様子を示す図である。図１に示すように、基材１０の表面にペースト２５からなる塗膜２０を形成したとき（乾燥前）は、塗膜２０は、溶媒２３中に粒子２１が分散した状態となっている。図中のＢＦは、気液界面を表している。
Next, embodiments of the present invention will be described with reference to the drawings.
1-4 is a figure which shows a mode when the coating film formed on the surface of the base material is dried. Specifically, FIG. 1 shows a case where a paste 25 in which particles 21 and a solvent 23 are mixed is applied to the surface of the base material 10 to form a coating film 20 made of the paste 25 on the surface of the base material 10 ( It is a figure which shows the mode of (before drying). As shown in FIG. 1, when the coating film 20 made of the paste 25 is formed on the surface of the substrate 10 (before drying), the coating film 20 is in a state where the particles 21 are dispersed in the solvent 23. BF in the figure represents a gas-liquid interface.
なお、粒子２１としては、例えば、黒鉛粒子やリチウム遷移金属複合酸化物粒子などが挙げられる。また、溶媒２３としては、例えば、有機溶剤（ＮＭＰなど）や水などがあげられる。ペースト２５は、溶媒２３中に、粒子２１を分散させたものであり、粒子２１の他にバインダ等を含有させても良い。また、基材１０としては、例えば、金属箔（銅箔やアルミニウム箔など）を挙げることができる。 Examples of the particles 21 include graphite particles and lithium transition metal composite oxide particles. Examples of the solvent 23 include organic solvents (such as NMP) and water. The paste 25 is obtained by dispersing the particles 21 in the solvent 23 and may contain a binder or the like in addition to the particles 21. Moreover, as the base material 10, metal foil (copper foil, aluminum foil, etc.) can be mentioned, for example.
図２は、塗膜２０の乾燥（溶媒２３の蒸発）が進み、塗膜２０の厚みＴ１が多孔体３０（図４参照）の厚みＴ２に達したとき（Ｔ１＝Ｔ２になったとき）の様子を示している。換言すれば、溶媒２３（その一部）の蒸発により、塗膜２０中の溶媒２３の量が多孔体３０の空隙Ｖの体積と一致して、溶媒２３が多孔体３０内の空隙Ｖをちょうど満たす状態になったときの様子を示している。 FIG. 2 shows a state in which drying of the coating film 20 (evaporation of the solvent 23) proceeds and the thickness T1 of the coating film 20 reaches the thickness T2 of the porous body 30 (see FIG. 4) (when T1 = T2). It shows a state. In other words, due to the evaporation of the solvent 23 (part thereof), the amount of the solvent 23 in the coating film 20 coincides with the volume of the void V of the porous body 30, so that the solvent 23 just passes the void V in the porous body 30. It shows the situation when the condition is met.
なお、図１に示す状態から図２に示す状態に至るまでの期間は、溶媒２３の蒸発速度を一定とした定率乾燥期間となる。一方、図２に示す状態に達した後、すなわち、溶媒２３（その一部）の蒸発により塗膜２０の厚みが多孔体３０と同一の厚みに達した後は、溶媒２３の蒸発速度が減少してゆく減率乾燥期間となる。 The period from the state shown in FIG. 1 to the state shown in FIG. 2 is a constant rate drying period in which the evaporation rate of the solvent 23 is constant. On the other hand, after reaching the state shown in FIG. 2, that is, after the thickness of the coating film 20 reaches the same thickness as the porous body 30 due to evaporation of the solvent 23 (part thereof), the evaporation rate of the solvent 23 decreases. It becomes a decreasing rate drying period.
図３は、塗膜２０の乾燥（溶媒２３の蒸発）がさらに進み、塗膜２０（多孔体３０）内に、溶媒２３の液相と気相とが混在した状態を示している。すなわち、気液界面ＢＦが、塗膜２０の内部に入り込んだ（塗膜２０の表面よりも下方となった）状態である。なお、塗膜２０のうち、気液界面ＢＦよりも上方に位置する部分（溶媒２３が蒸発により消失した部分）は、多孔体（多孔体３０の一部）となっている。 FIG. 3 shows a state where the drying of the coating film 20 (evaporation of the solvent 23) further proceeds and the liquid phase and the gas phase of the solvent 23 are mixed in the coating film 20 (porous body 30). That is, the gas-liquid interface BF is in a state where it enters the inside of the coating film 20 (below the surface of the coating film 20). In addition, the part (part where the solvent 23 disappeared by evaporation) located above the gas-liquid interface BF in the coating film 20 is a porous body (a part of the porous body 30).
図４は、塗膜２０の乾燥（溶媒２３の蒸発）が完了して、基材１０の表面に粒子２１を有する多孔体３０が形成された（塗膜２０が多孔体３０となった）様子を示している。多孔体３０は、例えば、図示しないバインダによって多数の粒子２１が結合してなる多孔質膜（層）であって、粒子２１間に形成された空隙Ｖによって多孔質となった膜（層）である。 FIG. 4 shows a state in which the drying of the coating film 20 (evaporation of the solvent 23) is completed, and the porous body 30 having the particles 21 is formed on the surface of the substrate 10 (the coating film 20 becomes the porous body 30). Is shown. The porous body 30 is, for example, a porous film (layer) in which a large number of particles 21 are bonded by a binder (not shown), and is a film (layer) that is made porous by voids V formed between the particles 21. is there.
図２に示す状態から図４に示す状態に至るまでの期間は、溶媒２３の蒸発速度が減少してゆく減率乾燥期間となる。具体的には、この減率乾燥期間では、塗膜２０（多孔体３０）内に溶媒２３の液相と気相とが混在した状態となり、溶媒２３が、多孔体（多孔体３０の一部）内の孔（空隙Ｖ）を通じて、多孔体の外部（図２及び図３において上方）へ移動（蒸発）してゆくことになる。このため、この減率乾燥期間においては、多孔体内の毛管圧駆動による溶媒２３の移動、溶媒２３の液相から気相への相変化、気相における拡散による溶媒１０の移動を考慮して、塗膜の乾燥状態を推定する必要がある。 The period from the state shown in FIG. 2 to the state shown in FIG. 4 is a decreasing rate drying period in which the evaporation rate of the solvent 23 decreases. Specifically, in this decreasing rate drying period, the liquid phase and the gas phase of the solvent 23 are mixed in the coating film 20 (porous body 30), and the solvent 23 is a part of the porous body (part of the porous body 30). ) Will move (evaporate) to the outside of the porous body (upward in FIGS. 2 and 3) through the holes (voids V) inside. For this reason, in this decreasing rate drying period, considering the movement of the solvent 23 by capillary pressure driving in the porous body, the phase change of the solvent 23 from the liquid phase to the gas phase, the movement of the solvent 10 by diffusion in the gas phase, It is necessary to estimate the dry state of the coating film.
そこで、本実施形態では、後述するように、溶媒２３（その一部）の蒸発により塗膜２０の厚みＴ１が多孔体３０の厚みＴ２と同一になった後は、多孔体内の気液２相流方程式である下記式（１）に基づいて、塗膜の乾燥状態を推定するようにしている。具体的には、式（１）のうち、溶媒濃度Ｃを下記式（２）で表される数式（右辺）に変換すると共に、溶媒の気相の実効拡散係数Ｄeffを下記式（３）で表される数式（右辺）に変換し、この変換した式から飽和度ｓを算出する。 Therefore, in this embodiment, as described later, after the thickness T1 of the coating film 20 becomes equal to the thickness T2 of the porous body 30 due to evaporation of the solvent 23 (part thereof), the gas-liquid two-phase in the porous body is obtained. Based on the following equation (1), which is a flow equation, the dry state of the coating film is estimated. Specifically, in the formula (1), the solvent concentration C is converted into a formula (right side) represented by the following formula (2), and the effective diffusion coefficient D eff of the gas phase of the solvent is represented by the following formula (3). And the saturation s is calculated from the converted expression.
ここで、飽和度ｓとは、多孔体の空隙中に溶媒の液相が占める割合を表す値であり、０〜１の範囲の数値（多孔体の空隙の１００％を溶媒の液相が占めるとき、ｓ＝１となる）で表される。 Here, the degree of saturation s is a value representing the proportion of the liquid phase of the solvent in the voids of the porous body, and a numerical value in the range of 0 to 1 (100% of the voids of the porous body is occupied by the liquid phase of the solvent). S = 1).
上述のように飽和度ｓを算出することで、溶媒２３（その一部）の蒸発により塗膜２０の厚みが多孔体３０（乾燥完了後の塗膜）と同一の厚みに達した後において、多孔体（塗膜２０のうち溶媒２３が蒸発により消失している部分、図３において塗膜２０のうち気液界面ＢＦより上方に位置する部分）内の毛管圧駆動による溶媒移動、溶媒の液相から気相への相変化、気相における拡散による移動を考慮して、塗膜の乾燥状態（飽和度ｓ）を適切に推定することができる。 By calculating the saturation s as described above, after the thickness of the coating film 20 reaches the same thickness as the porous body 30 (coating after completion of drying) due to evaporation of the solvent 23 (part thereof), Solvent movement and liquid of solvent by capillary pressure driving in the porous body (portion of coating film 20 where solvent 23 has disappeared due to evaporation, portion of coating film 20 positioned above gas-liquid interface BF in FIG. 3) The dry state (saturation degree s) of the coating film can be appropriately estimated in consideration of the phase change from the phase to the gas phase and the movement due to diffusion in the gas phase.
次に、本実施形態にかかる塗膜の乾燥状態推定方法について説明する。図５は、本実施形態にかかる塗膜の乾燥状態推定方法の流れを示すフローチャートである。
図示しない乾燥装置により、基材１０の表面に形成した塗膜２０（図１参照）の乾燥を開始すると、ステップＳ１において、公知の手法により、溶媒１０の蒸発速度（定率）を算出する。例えば、桐栄良三著の「乾燥装置（日刊工業新聞社発行）」に記載されている「恒率乾燥速度」の算出方法により、溶媒１０の蒸発速度（定率）を算出することができる。恒率乾燥速度が、溶媒１０の蒸発速度（定率）に相当する。
Next, the dry state estimation method of the coating film concerning this embodiment is demonstrated. FIG. 5 is a flowchart showing a flow of a coating film dry state estimation method according to the present embodiment.
When drying of the coating film 20 (see FIG. 1) formed on the surface of the substrate 10 is started by a drying device (not shown), the evaporation rate (constant rate) of the solvent 10 is calculated by a known method in step S1. For example, the evaporation rate (constant rate) of the solvent 10 can be calculated by the calculation method of “constant rate drying rate” described in “Drying device (published by Nikkan Kogyo Shimbun)” written by Ryozo Kiri. The constant rate drying rate corresponds to the evaporation rate (constant rate) of the solvent 10.
次に、ステップＳ２に進み、溶媒蒸発速度と乾燥時間との積を算出することで、蒸発した溶媒１０の量を求める。
なお、本実施形態では、基材１０の表面に塗膜２０を形成した時（乾燥前）の塗膜２０の厚み、この塗膜２０に含まれる溶媒量（体積）、及び、多孔体３０の厚みは、予め把握しておき、ステップＳ１〜Ｓ７の処理を行うコンピュータ（図示なし）に記憶させておく。
Next, it progresses to step S2 and calculates | requires the quantity of the solvent 10 which evaporated by calculating the product of a solvent evaporation rate and drying time.
In this embodiment, the thickness of the coating film 20 when the coating film 20 is formed on the surface of the substrate 10 (before drying), the amount of solvent (volume) contained in the coating film 20, and the porous body 30 The thickness is grasped in advance and stored in a computer (not shown) that performs the processes of steps S1 to S7.
その後、ステップＳ３に進み、現在の塗膜２０の厚みを求める。具体的には、ステップＳ２で求めた溶媒蒸発量から、減少した塗膜２０の厚み（塗膜２０の体積減少分は、蒸発した溶媒１０の体積に一致する）を求める。そして、乾燥前の塗膜２０の厚みから、溶媒の蒸発により減少した塗膜２０の厚みを差し引くことで、現在の塗膜２０の厚みＴ１を算出することができる。 Then, it progresses to step S3 and calculates | requires the present thickness of the coating film 20. FIG. Specifically, the reduced thickness of the coating film 20 (the volume reduction amount of the coating film 20 coincides with the volume of the evaporated solvent 10) is obtained from the solvent evaporation amount obtained in step S2. And the thickness T1 of the present coating film 20 is computable by subtracting the thickness of the coating film 20 which decreased by evaporation of the solvent from the thickness of the coating film 20 before drying.
次いで、ステップＳ４に進み、ステップＳ３で算出された塗膜２０の厚みＴ１が、多孔体３０と同一の厚みＴ２に達したか否かを判定する。ステップＳ４において、未だ、塗膜２０の厚みＴ１が多孔体３０の厚みＴ２に達していない（ＮＯ）と判定された場合は、前述のステップＳ２〜Ｓ４の処理を繰り返す。 Next, the process proceeds to step S4, and it is determined whether or not the thickness T1 of the coating film 20 calculated in step S3 has reached the same thickness T2 as that of the porous body 30. In step S4, when it is determined that the thickness T1 of the coating film 20 has not yet reached the thickness T2 of the porous body 30 (NO), the processes of steps S2 to S4 described above are repeated.
一方、塗膜２０の厚みＴ１が多孔体３０の厚みＴ２に達していない（ＮＯ）と判定された場合は、ステップＳ５に進み、多孔体内の気液２相流の方程式である下記式（１）のうち、溶媒濃度Ｃを下記式（２）で表される飽和度ｓに関する数式に変換すると共に、溶媒１０の気相の実効拡散係数Ｄeffを下記式（３）で表される数式に変換する。 On the other hand, when it is determined that the thickness T1 of the coating film 20 does not reach the thickness T2 of the porous body 30 (NO), the process proceeds to step S5, and the following equation (1) which is an equation of gas-liquid two-phase flow in the porous body: ), The solvent concentration C is converted into an equation relating to the degree of saturation s represented by the following equation (2), and the effective diffusion coefficient D eff of the gas phase of the solvent 10 is converted into an equation represented by the following equation (3). Convert.
但し、前記式（１）において、
また、式中、Ｃは、溶媒の気相と液相の混合濃度である。ρｌは、溶媒の液相の密度である。Ｍは、溶媒の分子量である。ｓは、上記多孔体の空隙中に溶媒の液相が占める割合を表す飽和度である。Ｃｇは、溶媒の飽和蒸気濃度である。εは、上記多孔体の空隙率である。Ｄ0は、溶媒の気相の拡散係数である。Ｋは、上記多孔体の浸透率である。ν＝１／（ｋrl ／νl＋ｋrg ／νg ）である。νlは、溶媒の液相の動粘度である。νgは、溶媒の気相の動粘度である。ｋrl ＝ｓ3である。ｋrg ＝（１−ｓ）3である。Ｐcは、毛管圧である。σは、溶媒の表面張力である。θは、溶媒の接触角である。Ｊ（ｓ）は、レベレッタ関数である。ｄは、上記粒子の平均粒径である。
これらの値を上記式に代入して、次のステップＳ６において演算を行う。
In the formula, C is a mixed concentration of the gas phase and the liquid phase of the solvent. ρl is the density of the liquid phase of the solvent. M is the molecular weight of the solvent. s is the degree of saturation representing the proportion of the liquid phase of the solvent in the voids of the porous body. Cg is the saturated vapor concentration of the solvent. ε is the porosity of the porous body. D 0 is the gas phase diffusion coefficient of the solvent. K is the permeability of the porous body. ν = 1 / (k rl / ν 1 + k rg / ν g ). ν l is the kinematic viscosity of the liquid phase of the solvent. ν g is the kinematic viscosity of the solvent in the gas phase. k rl = s 3 . k rg = (1−s) 3 . P c is the capillary pressure. σ is the surface tension of the solvent. θ is the contact angle of the solvent. J (s) is a leveler function. d is the average particle diameter of the particles.
By substituting these values into the above equation, calculation is performed in the next step S6.
次に、ステップＳ６に進み、上述のように変換した後の式（１）を計算し、飽和度ｓを算出する。このように飽和度ｓを算出することで、溶媒２３（その一部）の蒸発により塗膜１０の厚みＴ１が多孔体３０（乾燥完了後の塗膜２０）と同一の厚みＴ２に達した後において、多孔体（塗膜２０のうち溶媒２３が蒸発により消失している部分）内の毛管圧駆動による溶媒２３の移動、溶媒２３の液相から気相への相変化、気相における拡散による移動を考慮して、塗膜の乾燥状態（飽和度ｓ）を適切に推定することができる。 Next, it progresses to step S6, Formula (1) after converting as mentioned above is calculated, and saturation s is calculated. By calculating the saturation degree s in this way, after the thickness T1 of the coating film 10 reaches the same thickness T2 as the porous body 30 (coating film 20 after drying) by evaporation of the solvent 23 (part thereof). In the porous body (the portion of the coating film 20 where the solvent 23 has disappeared due to evaporation), the movement of the solvent 23 by capillary pressure driving, the phase change of the solvent 23 from the liquid phase to the gas phase, and the diffusion in the gas phase Considering the movement, the dry state (saturation degree s) of the coating film can be appropriately estimated.
その後、ステップＳ７に進み、算出された飽和度ｓの値が０であるか否かを判定する。飽和度ｓの値が０でない（ＮＯ）と判定した場合は、前述のステップＳ５〜Ｓ７の処理を繰り返す。 Then, it progresses to step S7 and it is determined whether the value of the calculated saturation s is 0. If it is determined that the value of the saturation s is not 0 (NO), the processes of steps S5 to S7 described above are repeated.
一方、ステップＳ７において、飽和度ｓの値が０になったと判定した場合は、ステップＳ８に進み、塗膜２０の乾燥が完了したと判断し、一連の処理を終了する。多孔体３０の空隙Ｖ中に溶媒２３の液相が占める割合が「０」になったとき、すなわち、飽和度ｓの値が０になったとき、塗膜２０の乾燥が完了したといえるからである。これにより、塗膜２０の乾燥完了（終了）を適切に判断することができる。 On the other hand, if it is determined in step S7 that the value of the saturation s has become 0, the process proceeds to step S8, where it is determined that the drying of the coating film 20 has been completed, and the series of processes is terminated. When the ratio of the liquid phase of the solvent 23 in the voids V of the porous body 30 becomes “0”, that is, when the value of the saturation s becomes 0, it can be said that the drying of the coating film 20 is completed. It is. Thereby, the completion (end) of drying of the coating film 20 can be determined appropriately.
なお、本実施形態では、塗膜２０の乾燥を開始した時から、ステップＳ７において飽和度ｓの値が０になったと判定されるまでの時間ｔｆを計測する。計測された時間ｔｆを、塗膜２０の乾燥を完了させるのに要する時間として把握する。 In the present embodiment, the time tf from when the drying of the coating film 20 is started until it is determined that the value of the saturation s becomes 0 in step S7 is measured. The measured time tf is grasped as the time required to complete the drying of the coating film 20.
以上において、本発明を実施形態に即して説明したが、本発明は上記実施形態に限定されるものではなく、その要旨を逸脱しない範囲で、適宜変更して適用できることはいうまでもない。 In the above, the present invention has been described with reference to the embodiments. However, the present invention is not limited to the above embodiments, and it is needless to say that the present invention can be appropriately modified and applied without departing from the gist thereof.
例えば、実施形態では、定率乾燥期間中は、ステップＳ１〜Ｓ３の処理を行って、塗膜２０の厚みを算出した。具体的には、溶媒２３の蒸発速度を算出し、この蒸発速度に基づいて、塗膜の厚みを算出した。 For example, in the embodiment, the processing of steps S1 to S3 is performed during the constant rate drying period, and the thickness of the coating film 20 is calculated. Specifically, the evaporation rate of the solvent 23 was calculated, and the thickness of the coating film was calculated based on this evaporation rate.
しかしながら、定率乾燥期間中、２次元レーザー変位計により、塗膜２０の厚みを測定するようにしても良い。具体的には、２次元レーザー変位計について、厚み方向変位Ｙの０基準（Ｙ＝０μｍの位置）を、基材１０の表面に設定して、塗膜２０の厚み方向変位Ｙを測定し、測定された厚み方向変位Ｙの値を塗膜２０の厚みＴ１として取得する。その後、ステップＳ４において、測定された塗膜２０の厚みＴ１が多孔体３０と同一の厚みＴ２に達したか否かを判定するようにしても良い。 However, the thickness of the coating film 20 may be measured with a two-dimensional laser displacement meter during the constant rate drying period. Specifically, with respect to the two-dimensional laser displacement meter, the thickness direction displacement Y reference 0 (position of Y = 0 μm) is set on the surface of the substrate 10, and the thickness direction displacement Y of the coating film 20 is measured. The value of the measured thickness direction displacement Y is acquired as the thickness T1 of the coating film 20. Thereafter, in step S <b> 4, it may be determined whether the measured thickness T <b> 1 of the coating film 20 has reached the same thickness T <b> 2 as the porous body 30.
１０ 基材
２０ 塗膜
２１ 粒子
２３ 溶媒
２５ ペースト
３０ 多孔体
ＢＦ 気液界面
Ｔ１ 塗膜の厚み
Ｔ２ 多孔体の厚み
Ｖ 多孔体の空隙
DESCRIPTION OF SYMBOLS 10 Base material 20 Coating film 21 Particle 23 Solvent 25 Paste 30 Porous body BF Gas-liquid interface T1 Coating film thickness T2 Porous body thickness V
Claims (2)
上記溶媒の一部の蒸発により上記塗膜の厚みが上記多孔体と同一の厚みに達した後、多孔体内の気液２相流の方程式である下記式（１）のうち、溶媒濃度Ｃを下記式（２）で表される数式に変換すると共に、溶媒の気相の実効拡散係数Ｄeffを下記式（３）で表される数式に変換し、この変換した式から飽和度ｓを算出する
塗膜の乾燥状態推定方法。
After the thickness of the coating film reaches the same thickness as the porous body due to evaporation of a part of the solvent, the solvent concentration C in the following formula (1), which is an equation of gas-liquid two-phase flow in the porous body, is While converting into the numerical formula represented by the following formula (2), the effective diffusion coefficient D eff of the gas phase of the solvent is converted into the mathematical formula represented by the following formula (3), and the saturation s is calculated from the converted formula. A method for estimating the dry state of a coating film.
算出された前記飽和度ｓの値が０になったか否かを判定し、飽和度ｓの値が０になったと判定した場合は、前記塗膜の乾燥が完了したと判断する
塗膜の乾燥状態推定方法。 A method for estimating a dry state of a coating film according to claim 1,
It is determined whether or not the calculated value of saturation s has become 0, and when it is determined that the value of saturation s has become 0, drying of the coating film is determined to be complete. State estimation method.
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