MTT 651: Polymer Rheology (Introduction to elongational flow)

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Prof. Dr. Narongrit Sombatsompop

Polymer PROcessing and Flow (P-PROF) Group

MTT 651: Polymer Rheology

(Introduction to elongational flow)

King Mongkut’s University of Technology Thonburi

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Extrusion Blow Moulding

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Elongation Flow

• Applications in melt spinning, injection and extrusion blow mouldings, blown film, fiber spinning, vacuum forming and extrusion coatings.

• The tensile viscosity () of polymer melts was first determined by Trouton.

• It is found that the tensile viscosity of a fluid is three time its shear viscosity (). Look at the below:

– A polymer melt cannot be moulding by pouring it into the mould.

– The bobble does not easily burst in blown film extrusion

• Tensile viscosity () is the ratio of tensile stress () to tensile strain rate ().

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Elongation Flow

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Elongation and shear viscosities

• The tensile viscosity of a fluid is usually

three time its shear viscosity (at low strain rate < 10-3 s-1)

3ηλ

osityshear viscviscosityalelongation

ηλ

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Elongation flow component (De)

Three components of deformation may be

considered in tension. These include;

– Bond stretching - Hookean - Ds - Modulus

– Chain uncoiling - Rubbery - Du - Elastic

– Chain slippage - Flowable - Dc Viscous

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sDcDuDeD

)cos( ityvisincreasedcDuDsD

)cos( ityvisdecreasedsDcDuD

)stretching(bond เลกลุืืดตวัของโมกระบวนการยsD

slippage)(chain กลุอ่ืนๆ ืานสายโมเลคล่ือนท่ีผกระบวนการเcD

)(uncoilingเลกลุายตวัของโมกระบวนการคuD

ืึงสียรูปแบบดลกัษณะการเeD

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Type of Elongation Flow

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Type of Elongation Flow

• Troutonian is usually the term used to refer to the elongational deformation of fluids.

• Troutonian is equivalent to the Newtonain in shear flow and, non-Troutonian behaviour is analogous to non-Newtonian one.

• Non-Troutonian can be subdivided into tension stiffening and tension thinning. In tension stiffening non-Troutonian fluids, the tensile viscosity increases with strain rate whereas in tension thinning fluids, the viscosity decreases with the rate of strain.

• Most polymer melts respond to the Troutonain. Branched LDPE and cis 1,4-polyisoprene at the low temperature (~80 oC) exhibits tension stiffening. Linear polyolefins such as HDPE, poly(4-methyl pentene-1) and PP are tension thinning.

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Tensile test

• This method is known as a constant stress test. A polymer rod is clamped at each end and immersed in an oil bath, one clamp being fixed while the other is allowed to move in the opposite direction to the first.

• The stress is kept at a constant using the cam, while the cross-sectional area of the extending specimen decreases. The results are in the form of a plot between extension and time. By extrapolating the curve back to zero time the elastic component can be determined.

• This method has been found to face many difficulties such as clamping the test specimen and limitation of material viscosity and testing time.

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Tensile test

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AF

Eζ

0L1Lln

LdL

E1L

0L

ε

dtdL

1L1

dtEd

e ε

εF = แรงท่ีกระท าบนระนาบพ้ืนท่ีหนา้ตดั A ในเวลา t L0, L1 = ความยาวเร่ิมตน้และภายหลงัการไหลของล าดบั

Tensile test

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EEε

δλ

รียดยืดดึงค าอตัราเคE

นยืดดึงค าความเค้E

viscosity)nal(elongatio ปแบบยืดดึงกการเสียรูดท่ีเกิดจาค าความหนื

λ

Tensile test

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Drawing a monofilament

• Extension process of a single faliment is a

constant rate test. This must be

appreciated that the cross section of the

test specimen is changing rapidly during

testing.

• The principle is that the stress varies with time along the extension line

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Drawing a monofilament

• With the technique of drawing a monofilament, melt strength information needs to be known and recorded.

• This method has been questioned on the variation of elongation rate along the filament line.

• This technique is a very close approximation to determine the apparent elongational viscosity of polymer melts.

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Drawing a monofilament

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QFv

AF

Eζ

Q1Fv

E(max)ζ

0v1vlnE ε

Drawing a monofilament

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EQε

Feh

Eε

t.E(max)ζλ

ืิเมอร์)บดึงสายพอลนรูปถึงระบ(จากหัวข้ึ

ใยรีดของเส้นระยะการอดัeh ืืดดึงแรงท่ีใชย้F

ตามล าดบั เมอร์ดึงสายพอลิและท่ีระบบ

ดๆรูปท่ีจุดใท่ีหวัข้ึนงพอลิเมอร์ความเร็วขอ1vและv,0vลอตัราการไหQทดสอบเวลาของการt

Drawing a monofilament

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Sheet inflation method

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dtdR

L1

Eε

ε2e(t)ΔP

02HR

Eζ

ยืดดึงืื ืองจากแรงความเคน้เนE

รงกลมื์รูปคร่ึงท ืนพอลิเมอรรัศมีของแผRงกลมรูปคร่ึงทรนพอลิเมอร์ารทดสอบแผ งจุดท่ีท ากระยะระหว าL

นพอลิเมอร์กระท าบนแผ ความดนัท่ีP

ื์ ืนพอลิเมอรืิมตน้ของแผความหนาเร 0H

ζ

Δ

Sheet inflation method

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Convergent flow

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Convergent flow

• This method is based on elastic deformation of the polymer melt as it flows at the die entry of a capillary rheometer under isothermal condition.

• The flow profile in the barrel is assumed to be simple convergent cone flow.

• The elastic strain is considered to be equal to log B2 where B is the maximum die swell for dies of zero length. Total strain is equal to log A2 where A is the ratio of diameter of convergent cone (ro) in the barrel to that (r) in the die entry.

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)2Blog2AQ(log

aAr2ΔPπRλ

ืใช้วข้ึนรูปทีรัศมีของหัคือRและ

ตามล าดบั) 0.25 และ 3.5 มาณจะมีค าประaและ(A0rhaและ

1r0rA

Convergent flow

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Orifice flow

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ε

Δλ

entP

)(π

ε diecircular)cos(130R

)3Q(sinE

)(ε dieslit22WH

)Q(sinE

หวัข้ึนรูปความสูงของHััวข้ึนรูปความกวา้งหW

ของการไหลมุมทางเขา้วข้ึนรูปรัศมีของหัRลอตัราการไหQ

Orific flow

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Shear-extensional flow

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entP1)(n83

E Δζ

entP1)3(n4

E Δ

γηε

รียดเฉือนค าอตัราเคγ

นเฉือนค าความเค้η

ดดึงามเครียดยืค าอตัราควEε

ืัวข้ึนรูป ือมบริเวณหวามดนัตกครของการไหลคมุมทางเขา้entΔP

รไหลค าดชันีกาn

นยืดดึงค าความเค้Eζ

Shear-extensional flow