Recent advances in Rheometry for process relevant material characterisation Dr Dan Curtis Complex Fluids Research Group Swansea University IChemE Technical Event: Mixing Port Talbot, South Wales 25th April 2017 The next 40 minutes (ish)….. The Very Basics: Mixing Low Viscosity Newtonian Fluids Complex Fluids Mixing Complex Fluids Traditional approaches for characterising Complex Fluids Small Amplitude Oscillatory Shear Fourier Transform Mechanical Spectroscopy Novel approaches for characterising Complex Fluids Optimal Fourier Rheometry / Optimally Windowed Chirps Superposition Rheometry Future projects ……. Recent advances in Rheometry for process relevant material characterisation The Very Basics: Mixing Low Viscosity Newtonian Fluids The very basics – Po = f(Re). Chhabra & Richardson (2008), Non-Newtonian Flow and Applied Rheology: Engineering Applications. Elsevier 2008. The very basics – Po = f(Re). Dimensional Analysis: P = f(μ, ρ, D, DT ,N, g, geometric dimensions) 푃 푁퐷2 푁2퐷 = 푓 , , 푔푒표푚푒푡푟푐 푟푎푡표푠 푁3퐷5 휇 푔 Power Reynolds Froude Number Number Number Chhabra & Richardson (2008), Non-Newtonian Flow and Applied Rheology: Engineering Applications. Elsevier 2008. The very basics – Po = f(Re). Chhabra & Richardson (2008), Non-Newtonian Flow and Applied Rheology: Engineering Applications. Elsevier 2008. The very basics – Po = f(Re). Dimensional Analysis: P = f(μ, ρ, D, DT ,N, g, geometric dimensions) 푃 푁퐷2 푁2퐷 = 푓 , , 푔푒표푚푒푡푟푐 푟푎푡표푠 푁3퐷5 흁 푔 Viscosity The Very Basics – Measuring Viscosity. 푠ℎ푒푎푟 푠푡푟푒푠푠 푣푠푐표푠푡푦 = 푠ℎ푒푎푟 푠푡푟푎푛 푟푎푡푒 푠ℎ푒푎푟 푓표푟푐푒 푠ℎ푒푎푟 푠푡푟푒푠푠 = 푎푟푒푎 훿휃 훿푢 푠ℎ푒푎푟 푠푡푟푎푛 푟푎푡푒 = ≈ 훿푡 훿푦 퐹 = 퐴 i.e. the velocity gradient The Very Basics – Measuring Viscosity. U-tube Flow Basic Rheometer3 Viscometer1 Cup1 Viscometer2 £100 - 150 £200 £2k £30k – 80k 1 Barnes (2000) Handbook of Elementary Rheology, INNFM 2 Brookfield DV1 3 TA Instruments, AR-G2 NOTE: Other viscometers/rheometers are available The Very Basics – Measuring Viscosity. U-tube Flow Basic Rheometer3 Viscometer1 Cup1 Viscometer2 £100 - 150 £200 £2k £30k – 80k 1 Barnes (2000) Handbook of Elementary Rheology, INNFM 2 Brookfield DV1 3 TA Instruments, AR-G2 NOTE: Other viscometers/rheometers are available Recent advances in Rheometry for process relevant material characterisation Complex Fluids What is a complex fluid anyway? What is a complex fluid anyway? Non-Newtonian Fluid: Apparent viscosity depends on shear rate Newtonian Fluid What is a complex fluid anyway? Non-Newtonian Fluid: Apparent viscosity depends on shear rate Newtonian Fluid Shear Thinning What is a complex fluid anyway? Non-Newtonian Fluid: Apparent viscosity depends on shear rate Newtonian Fluid Shear Thinning Shear Thickening What is a complex fluid anyway? Non-Newtonian Fluid: Apparent viscosity depends on shear rate Newtonian Fluid Shear Thinning Shear Thickening Yield Stress Characterising an inelastic non-Newtonian Fluid The Power Law 푛−1 휂 훾 = 푘2훾 n is the power law index n < 1 : Shear Thinning n = 1 : Newtonian n > 1 : Shear Thickening Recent advances in Rheometry for process relevant material characterisation Mixing (inelastic) non-Newtonian Fluids Metzner & Otto (1957) Is there a relationship between Po and Re for inelastic non-Newtonian fluids? Question 1: What viscosity should be used in determining the Reynolds Number? Question 2: What is the characteristic shear rate of the mixer? 1) Using the fluid & mixer of interest, determine Po. 2) Determine Re from a Newtonian Po(Re) curve (for the same geometry) 3) Obtain an estimate of an equivalent viscosity from the value of Re. 4) Determine the characteristic shear rate from the flow curve 5) Determine ks from the equation 푘푠 = 훾푐 푁 6) Use Po(Re) curves (Re < 10) to determine Po given that 휇푒푓푓 = 푓 푘푠푁 Metzner & Otto (1957) Generally gives adequate predictions of Power consumption PROVIDED that the value of ks is determined for a fluid and geometry that closely relate to the application. 1) Using the fluid & mixer of interest, determine Po. 2) Determine Re from a Newtonian Po(Re) curve (for the same geometry) 3) Obtain an estimate of an equivalent viscosity from the value of Re. 4) Determine the characteristic shear rate from the flow curve 5) Determine ks from the equation 푘푠 = 훾푐 푁 6) Use Po(Re) curves (Re < 10) to determine Po given that 휇푒푓푓 = 푓 푘푠푁 Recent advances in Rheometry for process relevant material characterisation Complex Fluids II: Elasticity What is a complex fluid anyway? What is a complex fluid anyway? Video courtesy of the Institute of Non-Newtonian Fluid Mechanics What is a complex fluid anyway? Material has a characteristic relaxation time, 휆 What is a complex fluid anyway? Material has a characteristic relaxation time, 휆 What is a complex fluid anyway? The Deborah & Weissenberg Numbers can be used to determine the extent to which elasticity will affect a process Characteristic time of material Characteristic time of the process 휆 퐷푒 = 푇 λ푈 푊 = 퐿 Weissenberg number is used where the material undergoes a time and space invariant strain rate. What is a complex fluid anyway? The Deborah & Weissenberg Numbers can be used to determine the extent to which elasticity will affect a process Characteristic time of material Characteristic time of the process 휆 퐷푒 = 푇 De < 1 : Process time is longer than relaxation time and coils can completely relax giving rise to viscous flow behaviour What is a complex fluid anyway? The Deborah & Weissenberg Numbers can be used to determine the extent to which elasticity will affect a process Characteristic time of material Characteristic time of the process 휆 퐷푒 = 푇 De > 1: The process time is not sufficient to allow relaxation of the coils and hence the flow process will be effected by the fluid elasticity. What is a complex fluid anyway? The Deborah & Weissenberg Numbers can be used to determine the extent to which elasticity will affect a process Characteristic time of material Characteristic time of the process 휆 퐷푒 = 푇 De > 1: The process time is not sufficient to allow relaxation of the coils and hence the flow process will be effected by the fluid elasticity. How can we determine the relaxation time? Recent advances in Rheometry for process relevant material characterisation Characterising Complex Fluids I: SAOS: A Traditional Approach Traditional Approaches: SAOS For a Newtonian liquid: ∝ 훾 훿 = 90° For a Hookean Solid: ∝ 훾 훿 = 0° Traditional Approaches: SAOS Phase Phase Angle For a Newtonian liquid: ∝ 훾 훿 = 90° For a Hookean Solid: ∝ 훾 훿 = 90° 훿 = 0° 훿 = 0° Traditional Approaches: FTMS How can I get information regarding as wide a range of frequency (time scales) as possible in as short as possible a time Use Fourier Analysis…… Fourier Transform to extract Rheological Information at frequencies corresponding to the component waveforms. Traditional Approaches: Summary “No satisfactory correlations are available enabling the estimation of power consumption in viscoelastic fluids” Chhabra & Richardson (2008), Non-Newtonian Flow and Applied Rheology: Engineering Applications. Elsevier 2008. Material with FLOW PROCESS complex rheology Controlled Stress Parallel Superposition Rheometry Recent advances in Rheometry for process relevant material characterisation Characterising Complex Fluids II: Novel Approaches Recent Advances: Superposition Rheometry SAOS CSPS (Quiescent) (Flow Conditions) G’ Storage Modulus G’|| Storage Modulus under CSPS G’ Loss Modulus G’’|| Loss Modulus under CSPS d Balance of Loss and Storage moduli d|| Balance of Loss and Storage moduli under CSPS Recent Advances: Superposition Rheometry Optimum balance between elastic and viscous properties appears to exist but this is ONLY apparent under CSPS conditions EPSRC Centre for Innovative Manufacturing in Large Area Electronics Recent Advances: Superposition Rheometry Optimum balance between elastic and viscous properties appears to exist but this is ONLY apparent under CSPS conditions EPSRC Centre for Innovative Manufacturing in Large Area Electronics Recent Advances: Superposition Rheometry Optimum balance between elastic and viscous properties appears to exist but this is ONLY apparent under CSPS conditions EPSRC Centre for Innovative Manufacturing in Large Area Electronics Recent Advances: Superposition Rheometry Ratio of energy loss to energy storage phenomena – Higher values – more “lossy” (viscous character). Lower values – dominated by energy storage (elastic character). Advanced Rheology for Printing Large Area 25/04/2017 40 Electronics (ARPLAE) Recent Advances: Superposition Rheometry Ratio of energy loss to energy storage phenomena – Higher values – more “lossy” (viscous character). Lower values – dominated by energy storage (elastic character). Advanced Rheology for Printing Large Area 25/04/2017 41 Electronics (ARPLAE) Recent Advances: Superposition Rheometry Silver-based Functional Ink Time to acquire spectrum using FT-CSPS < 30 s Time to acquire equivalent spectrum using standard CSPS > 6 min Advanced Rheology for Printing Large Area 25/04/2017 42 Electronics (ARPLAE) Recent Advances: Superposition Rheometry Silver-based Functional Ink Advanced Rheology for Printing Large Area 25/04/2017 43 Electronics (ARPLAE) Recent Advances: Superposition Rheometry Silver-based Functional Ink Advanced Rheology for Printing Large Area 25/04/2017 44 Electronics (ARPLAE) Recent Advances: Superposition Rheometry Silver-based Functional Ink Can we get MORE data, MORE quickly? Advanced Rheology for Printing Large Area 25/04/2017 45 Electronics (ARPLAE) More Recent Advances: OFR Optimal Fourier Rheometry More Recent Advances: