Lecture 10 and Flow (Ch. 6) This chapter is a study of the shear stress as a function of the shear rate for Newtonian and non-newtonian biological materials. 1
Lecture 10 and Flow (Ch. 6) When a fluid or semisolid is subjected to a constant shearing force it flows, ie., it deforms continuously at a velocity that increases as the applied shearing force increases. : quantifies the resistance of the fluid to flow 2
Lecture 10 and Flow (Ch. 6) Liquids and semisolids are usually pumped during processing plays a huge part in pump and conveyance system design may be dependent on moisture content, concentration, composition and prior treatments. 3
Lecture 10 and Flow (Ch. 6) Newtonian Fluids (Newton 1687) Simplest model Covers most, but not all, ag products Velocity behaves linearly w/ distance Shear stress is linear function of the shear rate Dynamic viscosity: proportionality constant for this relationship 4
Lecture 10 and Flow (Ch. 6) The viscosity can be measured where the fluid of interest is sheared between two flat plates which are parallel to one another Known as planar Couette flow. The shear stress is the ratio of the tangential force F needed to maintain the moving plate at a constant velocity V to the plate area A. Couette flow:low-speed, steady motion of a viscous fluid between two infinite plates moving parallel to each other. http://www.answers.com/topic/viscosity?cat=biz-fin 5
Lecture 10 and Flow (Ch. 6) Dynamic viscosity (Figure 6.1) dvz 2 τ yz = µ ; where τ =shear stress (N/m = Pa), dy dv dy z µ = 1 =shear rate (s ), proportionality constant aka dynamic viscosity (Pa-s) 6
Lecture 10 and Flow (Ch. 6) Kinematic viscosity: dynamic viscosity/density (no force involved) υ µ 2 =,m s = stokes ρ 7
Lecture 10 and Flow (Ch. 6) Non-Newtonian Fluids Relationship between shear stress and shear rate is NOT linear Some also have a yield stress which must be obtained before flow begins. 8
Lecture 10 and Flow (Ch. 6) Most common: pseudoplastic convex curve towards the shear stress axis (Fig. 6.1b) Apparent viscosity will decrease as shear rate increases Dilatant fluids: concave toward shear stress axis (corn flour, wet beach sand: stiffens when walked on..select pumps carefully!) Apparent viscosity increases as shear rate increases Plastic: linear but intercept is at the yield stress (toothpaste: must stay on brush but must be exudable) Casson-type plastic: has a yield stress but is not linear (chocolate) 9
Lecture 10 and Flow (Ch. 6) Apparent viscosity = shear rate ratio at any given shear rate Pseudoplastic and Dilatant materials, eqtn. 6.2, Table 6.2) dv τ = k dy n ; where: τ =shear stress k=consistency coefficient n=flow behavior index Newtonian: n=1, k=dynamic viscosity 10
Lecture 10 and Flow (Ch. 6) Plastic and Casson-type plastic behavior (more general case Herschel-Bulkley model, eqtn. 6.3 Table 6.3) n dv τ = k + τ 0; where: τ =shear stress, τ 0 = yield stress dy k=consistency coefficient n=flow behavior index Chocolate and other Casson materials follows this where N = ½ and the yield stress is taken to the ½ power 11
Lecture 10 and Flow (Ch. 6) Temperature Dependency: decreases with an increase in Temp. Typically 2% per degree C For some materials (fruit juices) the T effect follows an Arrhenius relationship (Eqtn. 6.5 page 193) Ea = exp, = viscosity, Pa-s RT µ µ µ 12
Lecture 10 and Flow (Ch. 6) Time dependent (figure 6.2 page 196) 13
Lecture 10 and Flow (Ch. 6) Time dependent Thixotropic examples (viscosity decreases with time)»gelatin, shortening, cream, paints Rheopectic examples (viscosity increases with time)»highly concentrated starch solutions gravy 14
Lecture 10 and Flow (Ch. 6) Flow in a pipe: Darcy-Weisbach Newtonian 2 L v H = f d 2 g -Non-newtonian K4L 8V P = d d n 15
Lecture 10 and Flow (Ch. 6) Examples of viscometers 16
and Flow of Liquids and Semisolids Chapter 6 17
HW Due 2/19 Problem 1: Name three applications where knowing the viscosity of a food product would be important. Are the food products Newtonian or non- Newtonian? How do you know which it is? (because the book says so is not the right answer!) Problem 2: Pick one of the different kinds of viscometers, explain briefly how it works and where or how it would be used. Problem 3: 6.1 in the Stroshine Book 18