C2_Rheology - An Introduction to Rheology Basic concepts...

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An Introduction to Rheology Basic concepts and definitions Rheology : defined as the science of deformation and flow. Rheometry : concerned with measurements of stress and strain of materials in simple or complex deformation/flow geometry. o Simple deformation/flow geometries commonly studied in rheometry: - Shear of a solid body x y 11 =x / y Initial state =/ A τ f Stress Shear deformation γ Δ Strain f f 1 y 1 x Δ 1 x 1 y
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An Introduction to Rheology Basic concepts and definitions - Shear of a fluid 1 11 1 x u dx d dt y dt y γ Δ == ± Strain rate Shear flow u x 1 y f x y
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An Introduction to Rheology Basic concepts and definitions - Small-amplitude oscillatory shear Oscillatory flow
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An Introduction to Rheology Basics concepts and definitions (con.) Stress tensor in a fluid o Fluid at rest: static pressure 23 100 0 0 010 0 0 001 0 0 s pp p p p =++ ⎛⎞ ⎜⎟ ≡= ⎝⎠ 1 τδ δ δ n f p= A Pressure z x y p p p 1 δ 2 δ 3 δ p p p
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is understood as the shear stress in the x direction acting on a plane perpen- dicular to the y direction, at a position y (called y-plane). or as the flux of molecular x- momentum transferred across a plane perpendicular to the y direction at a position y, in the direction of decrease in velocity An Introduction to Rheology Basics concepts and definitions (con.) Stress tensor in a fluid o Fluid in motion: Newton’s law of viscosity x yx y du dy τμ ⎛⎞ =− ⎜⎟ ⎝⎠ yx τ t = 0 Small t Large t x u x u Stationary Set in motion y x
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An Introduction to Rheology Quiz Interpret the physical meanings of: xz yz τ x z P (x,y,z) y
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1. u j is parallel with the unit vector δ j , and decreasing in the positive i- direction: 2. u j is parallel with the unit vector δ j , and increasing in the positive i- direction: 3. u j is anti-parallel with the with the unit vector δ j
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This note was uploaded on 09/01/2011 for the course PGE 312 taught by Professor Peters during the Fall '08 term at University of Texas at Austin.

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C2_Rheology - An Introduction to Rheology Basic concepts...

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