Pharmaceutics Exam 1 PDF

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Pharmaceutics outline/study guide for exam 1...

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Chapter 6 Rheology Viscosity, Rheology and the Flow of Fluids Viscosity: a fluids resistance to flow 

Reciprocal of viscosity is fluidity

Rheology: the study of flow and deformation properties of matter Newtonian Fluids 

Dynamic Viscosity o Rate of flow (γ) is directly related to the applied stress (σ)  The constant of proportionality is the coefficient of dynamic viscosity (η) – viscosity  Simple fluids which obey this relationship are Newtonian fluids o Velocity gradient  Exists when a tangential force is applied to uppermost layer, it is assumed that each subsequent layer will move at progressively decreasing velocity and that the bottom layer will be stationary  Calculated by dividing velocity of upper layer in m s^-1 by height of cube in meters. Result is the rate of shear or shear rate, γ, with units of s^-1  Shear stress, σ, is derived by dividing applied force by area of upper layer, units in N m^-2  Newton’s law

σ =η γ  η=



σ γ





η takes the units of N s m^-2 o Viscosity should be referred to in Pa s or, mPa s (dynamic viscosity of water)  Viscosity is inversely related to temperature  As temperature increases, viscosity decreases Kinematic Viscosity o Kinematic viscosity (v) is also used and defined as the dynamic viscosity divided by the density of the fluid (ρ) o



v=

η ρ

 With units of mm^2 s^-1 Relative and Specific Viscosities o Viscosity ratio or relative viscosity ( ηr ) of a solution is the ratio of viscosity of solution to viscosity of solvent ( ηo )  

ηr =

η ηo

Specific viscosity ηsp

C=ηr −1

 

o

For these calculations the solvent can be of any nature, although most pharmaceutical products use water For colloidal dispersions  ηo ( 1+2.5 ϕ) η=¿  Where ϕ is the volume fraction of colloidal phase (volume of dispersed phase divided by total volume of dispersion)   

η =1+2.5 ϕ  ηo η−η0 η −1= =2.5 ϕ  η0 η0 ηsp  =2.5 ϕ 



 

Volume fraction (φ) will be directly related to concentration (C)

ηsp =k C k is a constant

Intrinsic viscosity

ηsp , the viscosity number or reduced viscosity, is determined at a range of polymer C concentration (g dL−1 ) plotted as a function of concentration, a linear relationship is

o

If

o

obtained.  When intercept is extrapolated from line, you get the limiting viscosity number or intrinsic viscosity, [ η] The limiting viscosity number may be used to determine approximate Mark- Houwink equation  [ η]=K M α 

o

Where K and α are constants at a given temperature for specific polymer-solvent system that must be obtained through light-scattering or osmometry o Once constants are determined, viscosity measurements provide a quick and precise method for the viscosity-average molecular mass determination of pharmaceutical polymers o Values of the two constants provide indication of molecular shape in solution:  Spherical molecules α = 0  Extended rods α = >1  Randomly coiled molecules α = ~0.5 Specific viscosity may be used to determine the volume of molecules within solution 

ηSP =2.5 C 

NV M

C is concentration, N is Avogadro’s number, V is hydrodynamic volume of each molecule, and M is molecular mass

 

This can only be used when assuming all polymeric molecules for spheres in solution

Huggins constant

ηsp C

o

Equal to the slope of the plot determined using the information received from

o

Gives an indication of the interactions between the polymer molecule and the solvent  Positive slope is produced from a polymer that interacts weakly with solvent  Becomes less positive as interactions increase

Boundary Layers  



Rate of flow of a fluid over an even surface will be dependent on the distance from that surface Velocity, which will be almost zero at the surface, increases with increasing distance from the surface until the bulk of the fluid is reached and the velocity becomes constant o The region over which such differences in velocity are observed is the boundary layer  Arises due to the intermolecular forces between the liquid molecules and those of the surface result in a reduction of movement of the layer adjacent to the wall to zero  Dependent on the viscosity of the fluid and the rate of flow in bulk fluid  High viscosity and low flow rate will result in thick boundary layer  Becomes thinner as either viscosity decreases or flow rate or temperature increase In case of capillary tube o The two boundary layers meet at center of tube, such that velocity distribution is parabolic  With an increase in either diameter of tube or fluid velocity, proximity of two boundary layers is reduced and velocity profile becomes flattened

Laminar, Transitional, and Turbulent Flow 



For conditions under which a fluid flows through a pipe o Streamline or laminar flow  When liquid undergoes none to little change throughout the tube (remains as a thread), liquid is considered to flow as a series of concentric cylinders o Transitional flow  When speed of fluid is increased, a critical velocity is reached where liquid begins to waver and break up, although no mixing occurs o Turbulent flow  With even greater increase in speed, movement of molecules is totally haphazard, although average movement is in direction of flow Flow conditions affected by four factors: o Diameter of pipe and viscosity, density and velocity of fluid o These factors combine to give to following equation:



ℜ=

ρud η



o

ρ is density, u is velocity, η is dynamic viscosity of fluid, and d is diameter of circular cross section of pipe  Re is Reynolds number  Re = 4000, turbulent flow occurs  Re = 2100, signifies change from laminar to turbulent flow  An important parameter to predict the type of flow that will occur in a specific situation Type of flow is important to know because:  With laminar flow there is no component at right angles to the direction of flow and fluid cannot move across the tube  Fluid will act as a barrier to transfer, therefore mass transfer will occur only by molecular diffusion, which is a much slower process  For turbulent flow, this component is strong and interchange across the tube is rapid  Mass, in a latter case, will be rapidly transported

Determination of the Flow Properties of Simple Fluids 



Capillary viscometers o Used to determine viscosity provided that the fluid Newtonian and the flow is laminar  Rate of flow through capillary is measured under influence of gravity or externally applied pressure Calculation of viscosity from capillary viscometers o Poiseuille’s law 

η= 



π r 4 tP 8 LV r is the radius of the capillary, t is the time of flow, P is the pressure difference across the ends of the tube, L is the length of the capillary, and V is the volume of liquid As radium and length of capillary, as well as the volume flowing, are constants o η=KtP 





Where K =

π r4 8 LV

Pressure difference, P, depends on the density, ρ, of the liquid, the acceleration due to gravity, g, and the difference in the heights of the two menisci in the two arms of the viscometer Falling sphere viscometer o Based on Stokes law  When a body falls through a viscous medium is experiences a resistance or viscous drag which opposes downward motion



If a body falls through a liquid under the influence of gravity, an initial acceleration period is followed by motion at a uniform terminal velocity when gravitational force is balanced by the viscous drag

Non-Newtonian Fluids 

Types of non-Newtonian behavior o Plastic Flow  Plastic material does not flow until such a value of shear stress has been exceeded, and at lower stresses the substance behaves as a solid (elastic) material

o

 Pseudoplastic flow

 



Material will flow as soon as a shear stress in applied  Slope of curve gradually decreases with increasing shear rate, and since the viscosity is directly related to slope, it therefore decreases as shear rate increases Power law  σ =η' γ n

o

o

Where η' is a viscosity coefficient, and exponent, n, is an index of pseudoplasticity, and γ is shear rate  When n = 1, η' becomes dynamic viscosity (η)

Dilatant flow

   

Opposite type of flow to psuedoplastic Viscosity increases with increase in shear rate (Shear-thickening) Similar equation to psuedoplastic, but value of exponent n will be...