Viscoelasticity Defined Range of Material Behavior Solid Like-Liquid Like Ideal Solid----Most Materials-----/dea/Fluid Purely Elastic-Viscoelastic----Purely Viscous Viscoelasticity:Having both viscous and elastic properties Linear Viscoelasticity .The word viscoelastic means the simultaneous existence of viscous and elastic properties in a material. .It is not unreasonable to assume that all real materials are viscoelastic. .The response of a material to an experiment depends on the time-scale of the experiment in relation to a natural time of the material. .Initially,the restoring force increases linearly with the distance that any deformation takes the material away from its rest state,but eventually non-linearities will be encountered. The meaning and consequences of linearity The development of the mathem 1
1 Range of Material Behavior Solid Like ---------- Liquid Like Ideal Solid ----- Most Materials ----- Ideal Fluid Purely Elastic ----- Viscoelastic ----- Purely Viscous Viscoelasticity Defined Viscoelasticity : Having both viscous and elastic properties Linear Viscoelasticity •The word viscoelastic means the simultaneous existence of viscous and elastic properties in a material. •It is not unreasonable to assume that all real materials are viscoelastic. •The response of a material to an experiment depends on the time-scale of the experiment in relation to a natural time of the material. •Initially, the restoring force increases linearly with the distance that any deformation takes the material away from its rest state, but eventually non-linearities will be encountered
D.where D.is the Deborah number r is the characteristic or relaxation time associate with the material,and T is a characteristic time of the deformation process High Deborah numbers correspond to solids and Low Deborah numbers correspond to liquids Time-Dependent Viscoelastic Behavior: Solid and Liquid Properties of"Silly Putty" Deborah Number [De]=t/T Relaxation time Tis short[k1s】 T is long [24 hours] STORAGE LOSS OF VISCOELASTIC MATERIAL ◆SUPER BALL LOSS TENNIS BALL STORAGE 2
2 Low Deborah numbers correspond to liquids High Deborah numbers correspond to solids and T is a characteristic time of the deformation process is the characteristic or relaxation time associate with the material, and where D is the Deborah number e τ τ T De = Time-Dependent Viscoelastic Behavior: Solid and Liquid Properties of "Silly Putty" T is short [< 1s] T is long [24 hours] Deborah Number [De] = τ / Τ Relaxation time STORAGE & LOSS OF VISCOELASTIC MATERIAL SUPER BALL TENNIS BALL X STORAGE LOSS
Response for Classical Extremes Spring Purely Elastic Dashpot Purely Viscous Response Response Hookean Solid Newtonian Liquid o=Gy o=nt In the case of the classical extremes,all that matters is the values of stress,strain,strain rate.The response is independent of the loading. 为 where where is called b the relaxation time Maxwell Kelvin-Voigt = is called the complaince Mechanical analogs of viscoelastic liquids o=GY 0=71 Maxwell Kelvin-Voigt Burgers The Maxwell,Kelvin-Voigl and Burgers models. 3
3 Response for Classical Extremes Purely Elastic Response Hookean Solid σ = Gγ In the case of the classical extremes, all that matters is the values of stress, strain, strain rate. The response is independent of the loading. Spring Dashpot Purely Viscous Response Newtonian Liquid σ = ηγ. γ = σ 1 G + t η ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ where η G is called the relaxation time γ = σ G 1− e −t τ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ where τ =η G J = γ σ is called the complaince σ ηγ σ γ = & = G Mechanical analogs of viscoelastic liquids
Dynamic Mechanical Testing -An oscillatory (sinusoidal) Deformation deformation (stress or strain) is applied to a sample. -The material response Response (strain or stress)is measured The phase angleδ，or phase shift,between the deformation Phase angle and response is measured. Given y=。sinot For Solids: For Liquids: o=Gy=Gy。sin ot dy=n dt a-mi-nd d (y。sino) 0=7@Y。c0s0M Dynamic Mechanical Testing Response for Classical Extremes Purely Elastic Purely Viscous Response Response (Hookean Solid) (Newtonian Liquid) 8=0° 8=90° Str Strain 4
4 Dynamic Mechanical Testing Deformation Response Phase angle δ –An oscillatory (sinusoidal) deformation (stress or strain) is applied to a sample. –The material response (strain or stress) is measured. –The phase angle δ, or phase shift, between the deformation and response is measured. t t dt d dt d G G t For t Given o o o σ ηω γ ω η γ ω γ σ γ γ ω σ ηγ η γ γ ω cos sin ( sin ) Solids: For Liquids: sin = o = = = = = = & Dynamic Mechanical Testing Response for Classical Extremes Stress Strain δ = 0° δ = 90° Purely Elastic Response (Hookean Solid) Purely Viscous Response (Newtonian Liquid) Stress Strain
Dynamic Mechanical Testing Viscoelastic Material Response Phase angle 0°<8<90 Strain Stress G*1=Yo Complex Parameters their Components G*=G'+iG" Complex Storage Loss Modulus Modulus Modulus G★ Real Root Imaginary Root G tan 8 =G"/G' Dairy Products ·Fluid Milk Cultured Dairy Products cottage cheese cheese yogurt sour cream etc. Ice Cream 5
5 Dynamic Mechanical Testing Viscoelastic Material Response Phase angle 0° < δ < 90° Strain Stress |G*| = σο/γο γο σο Complex Parameters & their Components G* G' G" tan δ = G"/G' G* = G' + iG" Complex Modulus Storage Modulus Loss Modulus Real Root Imaginary Root δ Dairy Products • Fluid Milk • Cultured Dairy Products cottage cheese cheese yogurt sour cream etc. • Ice Cream
Milk pH 6.9 water 87% protein 3.6% fat 4.0% lactose 5.0% ash 0.7% Compositional Standar山 Standard Federal Catiforaia Milkfat GradeA Miaime 325% 35% a ot 825% 黑7% Total Milk No Standard Minimum 12.2% Solids at Milkfat Milk No Minimam Minimum 1.9% SNF.minimam 125% 11.0% Ct Milkfat No Minimum Minimum 0.9% SNF.minimam 《25% 11.0% hm Mitkfat,masimam 原20% 0.20% SNF.minimam 825% 9.% California:Milk Dairy Foods Control http://www.cdfa.ca.gov/ahfss/mdfc/index.htm California Department of Food and Agriculture United States Food and Drug Administration(FDA) United States Department of Agriculture (USDA) 6
6 Milk pH 6.9 water 87% protein 3.6% fat 4.0% lactose 5.0% ash 0.7% Compositional Standards Standard Federal California Milkfat 3.25% 3.5% Grade A Minimum Pasteurized Milk Milk Solids-Not-Fat 8.25% 8.7% (SNF), minimum Total Milk No Standard Minimum 12.2% Solids Grade A Milkfat Maximum Maximum Reduced Fat 2.1% 2.1% Milk No Minimum Minimum 1.9% SNF, minimum 8.25% 11.0% Grade A Maximum Maximum Lowfat Milk Milkfat 1.2% 1.1% No Minimum Minimum 0.9% SNF, minimum 8.25% 11.0% Grade A Milkfat, maximum 0.20% 0.20% Nonfat Milk SNF, minimum 8.25% 9.0% http://www.cdfa.ca.gov/ahfss/mdfc/index.htm California Department of Food and Agriculture United States Food and Drug Administration (FDA) United States Department of Agriculture (USDA) California: Milk & Dairy Foods Control
Dairy Proteins .Casein Proteins 80%of milk proteins a-casein β-casein K-casein isoelectric pH 4.6 Whey Proteins 20%of milk proteins B-lactoglobulin a-lactalbumin isoelectic pH 5.5 Casein Proteins Hydrophilic and hydropobic amino acids largely segregated in primary structure Large amounts of proline Serine phosphate in a and B casein located in hydrophilic section of protein H HO一CH2 -COOH NHz 20P0CH2 -COOH a&B Casein Protein Structure Hydrophilic Hydrophobic amino acids amino acids 7
7 Dairy Proteins • Casein Proteins 80% of milk proteins α-casein β-casein κ-casein isoelectric pH 4.6 • Whey Proteins 20% of milk proteins β-lactoglobulin α-lactalbumin isoelectic pH 5.5 Casein Proteins • Hydrophilic and hydropobic amino acids largely segregated in primary structure • Large amounts of proline • Serine phosphate in α and β casein located in hydrophilic section of protein CH2 COOH NH2 H C -2O3PO CH2 COOH NH2 H HO C α & β Casein Protein Structure Hydrophilic amino acids Hydrophobic amino acids O PO3 = O = 3 PO
Sub-Micelles of a B Caseins o-PO Ca++ *:0P0 Casein Micelle Why do not all Casein sub-micelles aggreate together in a glass of milk and form a gel? ·6 8
8 Sub-Micelles of α & β Caseins -O-PO3 = Ca++ =O3P-OCasein Micelle Why do not all Casein sub-micelles aggreate together in a glass of milk and form a gel?
K-Casein Oligosaccharide Hydrophilic Hydrophobic and almost no PO4 k-Casein Hairs (non calicum binding) Casein Micell 9
9 κ - Casein Hydrophilic and almost no PO4 -- Hydrophobic Oligosaccharide k - Casein Hairs (non calicum binding) ++ Casein Micell
Hairless Micelles rennet pH5.5 Other Mechanism Caseins proteins have an isoelectri point at pH =4.6 Adjusting pH to 4.6 will neutralize net charge of the caseins proteins and allow aggregate of charge neutral proteins. Rennet curd formation Add casein to skim milk Stir for I hour at 4C Add 0.1%rennet Incubate in ice-bath for 24 hours In situ curd formation 10
10 Hairless Micelles + rennet pH 5.5 Other Mechanism Caseins proteins have an isoelectri point at pH = 4.6 Adjusting pH to 4.6 will neutralize net charge of the caseins proteins and allow aggregate of charge neutral proteins. Rennet curd formation Add casein to skim milk Stir for 1 hour at 4°C Add 0.1% rennet Incubate in ice-bath for 24 hours In situ curd formation •Heat at 32°C for 15 minutes •Cool to 20°C for 30 minutes •Measurements at 20°C