1Pavan Muttil, Ph.D.PHRM 701 Pharmaceutics IFall 2014

From rheo(toflow)andlogos(science) StudyofdeformationandflowpropertiesofmatterCanbeappliedtoallformsofmatter Primarilyfocusedonliquidsandsemisolidsinpharmaceuticalsciences

Usedtodescribetheconsistencyofdifferentproducts Viscosity measureofresistancetofloworthickness Elasticity stickinessorstructure

2Rheologyofsemisolids

Newtonian

NonNewtonian

Plastic

Pseudoplastic

DilitantThixotropy

ShearStress Velocity(v)ofamaterialspreadoverasmalldistance(x)thatittravels(rateofshear)isproportionaltosheerstress applicationofhorizontalforce(F)overaunitarea(A)

Coefficientofviscosity() Parameterthatdefinestheresistancetoflow

3Shearstress Unitsofforce/unitarea=dynes/cm2

Rateofshear Unitsofvelocity/unitsofdistance=(cm/s)/cmor1/secorsec1

Viscosity() (dynes/cm2)s dynes=g(cm/s2)

[g(cm/s2)]s/cm2 =g/cms poise cps(usedforlowviscosityliquids)1cps=(1/100)poise

Reciprocalofviscosity =1/Rheogram

Graphicrepresentationofrateofshearversussheerstress

Rat

e of

She

ar (s

-1)

Shear Stress (dynes/cm2)

Slope = fluidity

units for fluidity- cm s/g (reciprocal of poise)

4Rate of Shear (s-1) 200 400 600 800 1000

Shear Stress (dynes/cm2)

50 100 150 200 250

ThefollowingdatashowtherateofshearasafunctionofshearstressforaNewtonianfluidat25C.Determinethefluidityandviscosityofthefluid.

Rate of Shear (s-1) 200 400 600 800 1000

Shear Stress (dynes/cm2)

50 100 150 200 250

Viscosity= 50/200 = 0.25

Fluidity = 1/0.25 = 4

5 Viscosityisindependentofshearstress AlsoknowasAbsoluteViscosity Slopeisconstant

Commonlyhavelowmolecularweightsandmolecularhomogeneity Acetone,water,ethanol,oliveoil,glycerin

Viscositydecreasessharplywithincreasingtemperature

Viscositydecreasessharplywithincreasingtemperature

A = Constant (same units as viscosity)

Ev = Activation energy (cal/mol or kcal/mol)

R = Universal Gas Constant (1.987 cal/mol K)

T = Absolute temperature (C + 273)

ln

1/T (K-1)

Y-int = ln A

Slope = Ev/R

Y= b + mx

6Theviscosityofhumanplasmaat37Cis1.2cps.AssumingtheplasmabehaveslikeaNewtonianfluid,determinetheviscosityofplasmarequiredforaninfusionthatiskeptatroomtemperature(25C). Theactivationenergyofplasmais4.25x103 cal/mole

73types

Plasticrheology Pseudoplasticrheology Dilatant rheology

Observedincomplexheterogeneoussystems(Relationshipbetweenshearstressandrateofshearisnonlinear)

Describesasituationinwhichnoflowoccursinresponsetoshearstressuntilatransitionpointisreached Yieldvalue() Minimumshearstressrequiredbythesystembeforeitdeformsandbeginstoflow

Onceyieldvalueisreached,therelationshipbetweenshearstressandrateofshearbecomeslinear

8Rat

e of

She

ar (s

-1)

Shear Stress (dynes/cm2)

Slope = fluidity

= yield value

BinghambodiesSeeningels,ointments,andcreamsImportanttodetermine offinalproduct Magnitudeofstressiscriticalforpatientuseofproduct Measurementofforcerequiredtospreadtheproductontheskin Toohighavaluewillnotalloweasyrubbing Toolowavaluewillresultinaproductthatruns

9Rate of Shear (s-1) 250 500 750 1000 1500

Shear Stress (dynes/cm2)

162.5 275 387.5 500 725

The following data show the rate of shear as a function of shear stress for a topical formulation that exhibits plastic rheology. Determine the yield value and viscosity of the fluid.

10

Observedinsystemsthatdeformandflowinstantaneouslywithappliedstress Relationshipisnotlinear

Rat

e of

She

ar (s

-1)

Shear Stress (dynes/cm2)

A

B

Shearthinningsystem viscosityatpointAishigherthanatpointB

Tears

Ketchup

11

Increase shear stress

Decrease shear stress

Globular Form(higher viscosity)

Uncoiled Form(lower viscosity)

Rat

e of

She

ar

(s-1

)

Shear Stress (dynes/cm2)

A

B

Observedinsystemsthatdeformandflowinstantaneouslywithappliedstress Relationshipisnotlinear

Rat

e of

She

ar (s

-1)

Shear Stress (dynes/cm2)

A

B Shearthickeningsystem viscosityatpointAislowerthanatpointB

Whippingcream

12

Thecomparativelyslowrecoveryofthematerialstructureonstandingthatwaslostbyshearthinning

TimerequiredfortherecoveryofpolymerconfigurationoncestresshasbeenREMOVED

Rat

e of

She

ar (s

-1)

Shear Stress (dynes/cm2)

A

B

D

C

DegreeofHysteresis maytakeashorterorlongertimetoreacquirestructureandbecomeviscousuponstanding

Suspensionandemulsions

SpreadingandAdherencetotheSkinRemovalfromjarsorextrusionfromtubesCapacityofsolidstomixwithmiscibleliquidsReleaseofdrug frombase