Method of predicting optical properties and physical characteristics to formulate optimum coating system
First Claim
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1. A method of providing at least one optical property of a coating system having a coating adjacent a base sheet comprising:
- a) providing a radiative transfer equation that relates a number of physical characteristics of the coating system selected from the group consisting of coating thickness, coating pore size distribution, coating pigment particle size, a coating pigment particle size distribution, a coating roughness, scattering coefficient, absorption coefficient, anisotropy factor, and optical properties of a base sheet to one or more optical properties for a coating system selected from the group consisting of gloss, brightness, and opacity, wherein providing the radiative transfer equation comprises application of diffusion approximation to transport of light, said diffusion approximation defining average radiance U(r,t) as follows;
D∇
2U(r,t)−
μ
aU(r,t)−
∂
U(r,t)/∂
t=S(r,t),wherein isotropic source density is denoted by S(r,t), r and t are the variables of position and time, and D is the diffusion coefficient which is defined in units of length asD=1/3[μ
a+μ
s(1−
g)] in terms of the absorption and scattering coefficients μ
a and μ
s, respectively, and g is the anisotropy factor;
b) solving the equation by inputting a number of the physical characteristics of the coating system to obtain at least one optical property output of the coating system; and
c) formulating a pigment coating including the obtained at least one optical property output.
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Abstract
Method of predicting optical properties and physical characteristics of coated paper or other sheet products for the purpose of formulating enhanced coating or sheet forming systems, and in particular to a method, which uses a diffusion approximation model derived from a radiative transfer theory employing various inputs of the properties and/or characteristics to predict coating or sheet system performance.
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Citations
21 Claims
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1. A method of providing at least one optical property of a coating system having a coating adjacent a base sheet comprising:
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a) providing a radiative transfer equation that relates a number of physical characteristics of the coating system selected from the group consisting of coating thickness, coating pore size distribution, coating pigment particle size, a coating pigment particle size distribution, a coating roughness, scattering coefficient, absorption coefficient, anisotropy factor, and optical properties of a base sheet to one or more optical properties for a coating system selected from the group consisting of gloss, brightness, and opacity, wherein providing the radiative transfer equation comprises application of diffusion approximation to transport of light, said diffusion approximation defining average radiance U(r,t) as follows;
D∇
2U(r,t)−
μ
aU(r,t)−
∂
U(r,t)/∂
t=S(r,t),wherein isotropic source density is denoted by S(r,t), r and t are the variables of position and time, and D is the diffusion coefficient which is defined in units of length as D=1/3[μ
a+μ
s(1−
g)] in terms of the absorption and scattering coefficients μ
a and μ
s, respectively, and g is the anisotropy factor;b) solving the equation by inputting a number of the physical characteristics of the coating system to obtain at least one optical property output of the coating system; and c) formulating a pigment coating including the obtained at least one optical property output. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11)
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12. A method of predicting at least one physical characteristic of a coating system having a pigment coating adjacent a base sheet comprising:
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a) providing a radiative transfer equation that relates a number of physical characteristics of the coating system selected from the group consisting of coating thickness, coating pore size distribution, a coating pigment particle size distribution, a coating roughness, and optical properties of a base sheet to one or more optical properties for a coating system selected from the group consisting of gloss, brightness, and opacity, wherein providing the radiative transfer equation comprises application of diffusion approximation to transport of light, said diffusion approximation defining average radiance U(r,t) as follows;
D∇
2U(r,t)−
μ
aU(r,t)−
∂
U(r,t)/∂
t=S(r,t),wherein isotropic source density is denoted by S(r,t), r and t are the variables of position and time, and D is the diffusion coefficient which is defined in units of length as D=1/3[μ
a+μ
s(1−
g)] in terms of the absorption and scattering coefficients μ
a and μ
s, respectively, and g is the anisotropy factor; andb) solving the equation by inputting a number of the physical characteristics and at least one optical property to obtain the at least one physical characteristic output based on a coated system employing the inputted physical characteristics and the at least one optical property; and c) formulating a pigment coating including the at least one physical characteristic output. - View Dependent Claims (13, 14, 15, 16, 17, 18, 19)
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20. A method of predicting at least one physical characteristic of a coating system having a coating adjacently contacting a substrate comprising:
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a) providing a radiative transfer equation that relates a number of physical characteristics of the coating system selected from the group consisting of coating thickness, coating pore size, a coating pigment particle size distribution, a coating roughness, and optical properties of a substrate comprising metal or plastic to one or more optical properties for a coating system selected from the group consisting of gloss, brightness, and opacity, wherein providing the radiative transfer equation comprises application of diffusion approximation to transport of light, said diffusion approximation defining average radiance U(r,t) as follows;
D∇
2U(r,t)−
μ
aU(r,t)−
∂
U(r,t)/∂
t=S(r,t),wherein isotropic source density is denoted by S(r/t), r and t are the variables of position and time, and D is the diffusion coefficient which is defined in units of length as D=1/3[μ
a+μ
s(1−
g)] in terms of the absorption and scattering coefficients μ
a and μ
s, respectively, and g is the anisotropy factor; andb) solving the equation by inputting a number of the physical characteristics and at least one optical property to obtain the at least one physical characteristic output based on a coated system employing the inputted physical characteristics and the at least one optical property; and c) formulating a pigment coating including the at least one physical characteristic output. - View Dependent Claims (21)
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Specification