Optimizing Formulation Development: Understanding Viscosity’s Role in the Formulation Process and How to Create a Measurement Plan

Zachary Imam

Stacey Elliott

20 January 2021

Formulation –excipient,

temperature

Interactions &Microstructure

Viscosity

2L

h

ሶ𝛾

ho

ሶ𝛾𝑐

Viscosity’s Role in Formulation Development

hrel

𝑇Tm

D

Na+

Cl-

Viscosity Review – Resistance to FlowSteady Shear

𝜂 ≡𝑠ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠

𝑠ℎ𝑒𝑎𝑟 𝑟𝑎𝑡𝑒=𝜎

ሶ𝛾

𝜎 = 𝜂 𝑇, ሶ𝛾, 𝑐, 𝑡 ሶ𝛾

• Velocity gradient perpendicular to flow

• Shearing motion – adjacent fluid elements forced to slide past each other

• Shear viscosity º internal or molecular friction

• Reflects molecular level behavior

• Size, shape, interactions

• Microstructure

x

y

𝑢𝑥 𝑦 = 0 = 0

𝑢𝑥 𝑦 = ℎ = 𝑢𝑝𝑙𝑎𝑡𝑒

h

ሶ𝛾 =𝜕𝑢𝑥𝜕𝑦

=𝑢𝑝𝑙𝑎𝑡𝑒ℎ

𝐹𝑜𝑟𝑐𝑒

𝐴𝑟𝑒𝑎

𝜎

Viscosity – how can it help you?

1. Practical application – injectability, processing, blinking, topical, ageing, aggregation…………

• Predict performance & processability

2. Investigative tool – reflects microscopic behavior• Individual molecules – size, shape

• Pair interaction

• Complex structure formation

• Impact of solution environment on all above

• Intelligent formulation – work smart, not hard!

Formulation –excipient,

temperature

Interactions &Microstructure

Viscosity

VROC - Viscometer/Rheometer-on-a-Chip

Microfluidics and MEMS (Micro-Electro-Mechanical Systems)

MEMS Sensors – Silicon (Si) Pressure Sensor Array

Microfluidics – Precision Glass Micro-Channel

“rectangular-slit method” (USP, chapter 914)

𝜏 ~𝜕𝑃

𝜕𝑥

ሶ𝛾 ~ 𝑄

𝜂 =𝜏

ሶ𝛾

Control

Measure

Dynamic

Viscosity

10

20

30

40

50

60

70

80

90

2 4 6 8 10

Pre

ssu

re (

kP

a)

Sensor Position (mm)

𝜕𝑃

𝜕𝑥

How do I start a measurement plan?

Before you start anything ask: “What do I want to learn about my sample?”“Will this study be narrow and specific?”“Am I performing a broad characterization study?”

• Performance under high shear or low shear?

• Performance at high or low temperature?

• Fluid Structure?

• Molecular Structure?

• Differentiation?

Knowing this information will help with generating a measurement plan and experimental design

vs

2L

1

10

100

10 100 1000 10000 100000

vis

co

sity

(c

P)

shear rate (sec-1)

0.50%

0.25%

0.125%

Performance at high and low shear rate• Not universal, but sample dependent

Xanthan Gum

MW = 1,000,000+

Possibly entangled polymer network

𝜼∞

𝜼𝒐~𝜼 ሶ𝜸 → 𝟏𝟎−𝟒𝒔𝒆𝒄−𝟏

30

32

34

36

38

40

42

44

100 1000 10000 100000

h(c

P)

shear rate (sec-1)

250 mg/mL BgG Phosphate buffer saline (PBS), pH7.4

250 mM Arg-HCl

w/o Arg-HCl

𝜼𝒐

Bovine Gamma Globulin (BgG)

MW = 150,000

Inherently attractive colloid

40

45

50

55

60

65

100 1000 10000 100000 1000000 10000000

h

ሶ𝛾

ho

ሶ𝛾𝑐 h∞

Viscosity vs. Shear Rate – Qualitative InterpretationLow shear plateau

• Restorative mechanism

• Near equilibrium

• Generates thermodynamic stress

High shear plateau

• Far from equilibrium

• Hydrodynamics dominate

• 𝜂𝑜 − 𝜂∞ – degree of structure & thermodynamic forces

Critical shear rate

• Non-Newtonian onset

• Shear flow overcoming

𝜂−𝜂∞

𝜂𝑜−𝜂∞≈

𝜂−𝜇

𝜂𝑜−𝜇

Viscosity scaling

Non-Newtonian Viscosity250 mg/mL BgG (Bovine g-Globulin)

15

25

35

45

55

65

75

85

95

100 1000 10000 100000

h(c

P)

shear rate (sec-1)

30

32

34

36

38

40

42

44

100 1000 10000 100000

h(c

P)

shear rate (sec-1)

25°C

Phosphate buffer, 150 mM NaCl, pH7.2 Phosphate buffer saline (PBS), pH7.4

10°C

18°C

25°C

37°C

250 mM Arg-HCl

w/o Arg-HCl25°C

25C

h0 = 44 cP

h0 = 38 cP

h0 = 35 cP

Shear Rate ScalingPeclet Number

𝑃𝑒 =𝜏𝐵𝜏𝑆

=𝐿2 ሶ𝛾

𝐷𝑠𝑜 =

6𝜋𝜂𝑜𝐿3 ሶ𝛾

𝑘𝑇

𝜏𝐵 =𝐿2

𝐷𝑠𝑜

𝜏𝑠 =1

ሶ𝛾

𝐷𝑠𝑜 =

𝑘𝑇

6𝜋𝜂𝑜𝐿

Peclet number – ratio of characteristic time scales

Brownian motion – restoring equilibrium structure

Shear flow – perturbing equilibrium state

Effective self

diffusion

Increasing time/length scale

Designate thinning onset to

𝑃𝑒 ሶ𝛾𝑐 = 1 to estimate L

0.75

0.8

0.85

0.9

0.95

1

100 1000 10000 100000

(h-

m)/

(ho-m

)

0.85

0.9

0.95

1

100 1000 10000

(h-

m)/

(ho-m

)

shear rate (sec-1)

10°C 18°C

25°C

37°C

250 mM

Arg-HCl

w/o

?

Scaled Viscosity vs. Peclet Number Master Curve

rh~5 nm from [h]

Rg=5.3 nm monomer (*)

Rg=7.6 nm dimer (*)

• Temperature – no significant change in interactions & clustering

• Arginine (excipient)

• Decreases L, consistent with reduced cluster size

• Supports idea of reversible cluster formation increasing viscosity

T (°C) ho (cP) L (nm)

10 91 10

18 54 9.8

25 35 9.8

37 18 9.9

2L

*S. Da Vela et al., Effective Interactions and Colloidal Stability of Bovine g-Globulin in Solution, J. Phys. Chem. B, 2017, 121, 5759-5769.

0.75

0.8

0.85

0.9

0.95

1

0.01 0.1 1 10(h

-m

)/(h

o-m

)𝑷𝒆 =

𝟔𝝅𝜼𝒐𝑳𝟑 ሶ𝜸

𝒌𝑻Arg

(mM)ho (cP) L (nm)

0 44 9.1

250 38 8.1

temperature

excipient

= 25°C

80

90

100

110

120

130

140

150

160

170

10 100 1000

vis

co

sity

(c

P)

shear rate (sec-1)

Sample Differentiation

Real Maple Syrup

Pancake Syrup(Xanthan Gum)

Mix (80/20)

• Initially explore broad range of shear rates• Narrower range possible for QC analysis

1

10

100 1000 10000 100000

vis

co

sity

(c

P)

shear rate (sec-1)

Hydroxypropyl guar

Sodium hyaluronate

Revitalift Prism Maran

Sample Differentiation• Initially explore broad range of shear rates• Narrower range possible for QC analysis

0

5

10

15

20

25

30

35

40

100 1000 10000 100000

Vis

co

sity

(c

P)

Shear Rate (sec-1)

0

2

4

6

8

10

12

14

100 1000 10000

Vis

co

sity

(c

P)

shear rate (sec-1)

Whole Milk Skim Milk Oat Beverage

Unsweet

Almond

Beverage

Almond

BeverageCoconut

Milk

Temperature Sensitive Polymeric Excipients

• Poloxamer (Lutrolâ)• Amphiphilic triblock copolymer

• Poly(propylene oxide) midblock more hydrophobic than poly(ethylene oxide)

• Form complex microstructures dependent on temperature and concentration• Dependent on MW of each block (a,b)

• Reversible

• Applications• Rheology/viscosity modifies

• Solubilizers

• Sedimentation inhibitors

Increasing Concentration, Temperature

Poloxamer Solutions – Type & Concentration

• Not simple Arrhenius behavior –indicates complex reversible microstructure

• Highly sensitive to concentration

• Dependent on Poloxamer type – MW & block ratio

• Detects phase boundaries – fluid-gel (15% P407, 30 – 45°C)

Poloxamer a b MW a/b

188 80 27 7680 – 9510 3

407 101 56 9840 – 14600 1.8

10

30

50

70

90

110

130

150

15 20 25 30 35 40 45 50 55 60 65 70 75

rela

tiv

e v

isc

osi

ty

Temperature (°C)

10

20

30

40

50

60

70

80

90

100

0 20 40 60

rela

tiv

e v

isc

osi

ty

Temperature (°C)

P407 in DI H2O P188 in DI H2O

13%

24%

15%

22%

20%

14%

0

5

10

15

20

0 5 10 15 20

Sh

ea

r Str

ess

(P

a)

Time (s)

400 sec-1

Poloxamer Solutions – Yield Stress

• Can determine whether material is yielding

• We cannot calculate yield stress, but we can determine where we are in the material’s phase diagram

Poloxamer a b MW a/b

407 101 56 9840 – 14600 1.8

0

10

20

30

40

0 5 10 15 20

Sh

ea

r Str

ess

(P

a)

Time (s)

30°C

0

50

100

150

200

0 20 40 60

Sh

ea

r Str

ess

(P

a)

Time (s)

P407 in DI H2O

40°C 50°C

400 sec-1

80 sec-1

300 sec-1

• Can probe different regions of phase diagram with different temperatures.

• At 40°C material is still yielding at 80 and 300 sec-1

Poloxamer SolutionsCombine Temperature/Shear Rate Sweeps

• Rate sweeps at temperatures along profile (20, 25, 30, 45, 70 °C)

• Transitions from Newtonian ® Non-Newtonian ® Newtonian

• Non-Newtonian profiles merge at high shear rates

10

20

30

40

50

60

70

15 20 25 30 35 40 45 50 55 60 65 70 75

rela

tiv

e v

isc

osi

ty

Temperature (°C)

10

20

30

40

50

60

70

100 1000 10000 100000

rela

tiv

e v

isc

osi

ty

shear rate (sec-1)

20 °C

70 °C

45 °C

30 °C

25 °C

14% (wt) P407 in DI H2O

Shear rate sweeps at specified

temperatures

Summary

• Rheological measurements are iterative

• Ask good questions at the beginning leads to good experiments later

• Let the data guide you

• Make educated guesses on what experiment to run and dive in

• Rheology is a broad field

• Applicable to many industries and applications

• Contact us with questions!

• We’re here to help you develop your techniques0

10

20

30

40

100 1000 10000 100000

Vis

cosi

ty (

cP)

Shear Rate (s-1)

10

60

110

15 20 25 30 35 40 45 50 55 60 65 70 75rela

tive

vis

cosi

ty

temperature (°C)

Thank You!Dr. Zachary ImamResearch ScientistRheoSense, Inc.zimam@RheoSense.com+1 (925) 866-3801 ext. 1013

Grace BaekMarketing & Sales RheoSense, Inc.GraceB@RheoSense.com+1 (925)-866-3801 ext. 1013

Dr. Stacey ElliottPrincipal ScientistRheoSense, Inc.Selliott@RheoSense.com+1 (925) 866-3801 ext. 1013

Eden ReidSenior Marketing AssociateRheoSense, Inc.EReid@RheoSense.com+1 (925)-866-3801 ext. 1013