Material Polimer Final

Material Polimer

Solving the equation of motion

1. Example of simple flow2. Lubrication approximation3. Single screw extruder4. Macroscopic energy balances5. Temperature increasing during flow

Example of simple flowThere is some simple flow:1. Parallel plates (couette) flow: the fluid

confined between parallel plates and dragged by one of the plate that moves along x with a velocity Ux. No external pressure.

Example of simple flow

2. Pressure driven flow in a slit: the fluid is confined between two motionless parallel plates and it is driven to flow by a constant pressure gradient along x.


3. Pressure driven flow in a cylindrical pipe: the fluid flow in along cylindrical pipe pushed by constant pressure.

The Equation of Energy in Terms of Energy and Momentum Fluxes in Cylindrical Coordinate Systems

The Equation of Motion in Terms of t in Cylindrical Coordinate Systems


4. Combined drag and pressure flow: the flow between parallel plates, where the upper plates move along x with velocity Ux and there is externally pressure along x.

P

Lubrication Approximation

• Lubrication Approximation ini sangat berguna pada laminar flow. Ini adalah metode untuk menyelesaikan perhitungan flow.

Lubrication Approximation• Assumptions of the method– Laminar flow– Steady state flow– Isothermal condition– Incompressible fluid– Generalized Newtonian fluid– No slip at the wall– Negligible inertia– Slowly varying geometry– Negligible normal velocities– No transverse flow

Reynolds equation

Reynolds equation

Single screw extruder

The most used and widely spread polymer processing machine is extruder. It machine have screw rotating inside a cylindrical heated barrel.

There are two types of extruder: (1) single-screw extruders(2) twin-screw extruders.

The single-screw extruder is one of the most important pieces of equipment in the processing of thermoplastic polymers.


There are two types of single-screw extruders: 1. Plasticating : The plasticating single-screw extruder

conveys a solid polymer from the feed section to the melting section, where most of the melting (or softening) occurs, and then transports the melted or softened polymer to a shaping device (e.g., dies and molds).

2. Melt-conveying : The meltconveying extruder does not include a melting section; it simply transports an already softened polymer to a shaping device (e.g., rubber extruder).


In the design of plasticating single-screw extruders, one needs information on

(1)the physical and thermal properties of polymers (e.g., friction coefficient between the solid polymer and barrel wall, thermal conductivity of polymer, specific heat as a function of temperature, melting point of polymer, and heat of fusion of polymer)

(2)rheological properties of polymers as functions of shear rate and temperature


Of the three sections, the melting section has received the most attention by researchers. This is understandable because in the melting section one must deal not only with the phase transition of a polymer from the solid state to fluid state, but also with the flow of rheologically complex molten polymers in a complicated flow geometry.

Single screw extruderThe heart of a plasticating extruder is the screw, the design of which varies

with the type of polymer to be extruded; that is, whether the polymer can be regarded as soft or rigid, or whether the polymer is semicrystalline or amorphous, whether the polymer has a high or low melting temperature, or whether the polymer is sensitive to thermal degradation or not.

Typical single screws: (a) standard metering screw, (b) metering screw with the Maddock mixing head, and (c) barrier screw with the Maddock mixing head.

Single screw extruderAnalysis of the Solid-Conveying SectionIn the solid-conveying section, the pressure builds up as

polymer pellets or powders are transported by the rotating motions of the screw. At the same time, the temperature of the polymer, especially near the barrel wall, increases due to the heat conducted from the barrel wall and the heat generated by the friction between the polymer and the barrel wall. The heat generated due to the frictional force will help form thin melt films at and near the barrel wall.

We present the Darnell–Mol analysis (Darnell and Mol 1956) to determine the temperature profiles along the screw axis and the position at which melting begins. Subsequently, this information will be used as initial conditions for the analysis of the melting section.

Single screw extruderAnalysis of the Melting SectionMaddock (1959) was the first to have performed a very

significant experiment in order to understand the melting process in a plasticating single-screw extruder, which formed the basis of a proposed melting mechanism, which is today referred to as the “Maddock melting mechanism.”

The Maddock melting mechanism states that the solid particles in contact with the hot barrel surface partially melt and form a thin melt film over the barrel surface. This melt film is dragged by the barrel surface, meeting the leading edge of the advancing flight, and is then mixed with previously melted material, forming a melt pool, while the width of the solid bed gradually decreases. The melting process comes to an end when the solid bed disappears completely.

Maddock melting mechanism

Divided into five zones (A) solid bed, (B) melt pool, (C) a thin melt film between the barrel surface and the solid bed, (D) a thin melt film between the screw surface and the solid bed, and (E) a thin melt film between the screw flight and the solid bed. The barrel surface is at the top, moving at constant velocity Vb with velocity components Vbx and Vbz in the cross-channel and down-channel directions, respectively. The screw surface is at the bottom, and the screw flights are at the two sides.

Performance of Fluted Mixing Heads in a PlasticatingSingle-Screw Extruder

In an attempt to improve the mixing capabilities of single-screw extruders, some investigators (LeRoy 1969; Gregory and Street 1968) suggested that a barrier-type mixing section, today generally referred to as a “fluted mixing device,” be placed near the end of a metering screw. Maddock (1967) offered an explanation as to how such a fluted mixing device might help to improve the mixing capability of metering screws.


Schematic of the Maddock mixing head: (a) side view and (b) cross-sectional view.


The Maddock mixing head consists of four pairs of deeply grooved inlet and outlet channels, a barrier flight (referred to as the “mixing land”), and a wiping flight (referred to as the “wiping land”)

The rationale behind its design lies in that when a stream of molten polymer from the metering section of a single screw enters the inlet channel of the mixing head, it flows over the barrier flight into the outlet channel by the rotation of the screw.

Since the space between the barrier flight and the inner wall of the barrel is very small compared with the depth of the inlet channel, any pellets that are still unmelted when they reach the mixing head can be prevented from crossing over into the outlet channel and will therefore have the chance to be melted completely while flowing through the inlet channel of the mixing head.

Macroscopic energy balancePolymer processing operations, by and large, are nonisothermal.

Plastics pellets are compacted and heated to the melting point by interparticle friction, solid deformation beyond the yield point, and conduction.

The starting point is the first law of thermodynamics, which states mathematically the great principle of conservation of energy:

where E is the total energy of a system, dQ is the heat added to the system, and dW is the work done on the system.

Macroscopic energy balanceThe simplest way to calculate total energy balance in a

processing machine is examine the energy input and output. In the following the symbol D implies the difference between exit and entry in a machine where no chemical reaction takes place:

Work due to the flow: D(PVs)=VsDPfor incompressible fluid (Vs=1/r)

Shaft work: As, (per berat)this ini positif since work is done on the system

Added heat: Q(positive if added, negative if the system is cooled

Macroscopic energy balanceThe total energy given to the machine in the form of shaft

work and heat result in increase in the internal energy of the material and in work due to flow

DU+D(PVs)=Q + As or DH=Q + As.

The following cases can be seen:

Isothermal without phase change: DU=0 Q+As=VsDPIsothermal with melting: DU=l Q+As-VsDP=lAdiabatik: Q=As=0, U=CpDT,

CpDT+VsDP=0, DT=DP/(rCp)

The Equation of Energy in Terms of Energy and Momentum Fluxes in Several Coordinate Systems

The Equation of Thermal Energy in Terms of Transport Properties (for Newtonian fluids at constant r,p and k. Note that constant q r implies that Cv = Cp)

Temperature increasing during flow

Macro balances give average temperature and energy needs for the process. Because of the low heat conduction coefficients and the high viscous dissipation, high temperature spot may also exist in processing equipment. Hot spot are dangerous because there is a possibility of degradation.

An example of how one deals with such a problem is given below for non-isothermal of generalized newtonian fluid in a slit die. Assuming that the viscosity does not change with the temperature. With this information, the equation of energy is:

Temperature increasing during flow

This equation has been solved for boundary condition of a constant temperature at the wall, Tw, and a constant initial (at z=0) temperature Tin.

In general the viscosity depens on temperature and follows Arrhenius function far away from the melting point or the glass transition temperature: h=A exp [E/RT]. A more convenient way to present this dependence is to compare the viscosity at T with its value at a references temperature, Tr:

h/hr= A exp [E/RT]/A exp [E/RTr]=exp {E/R[(Tr-T)/Tr^2]}

Eelementary Step I

• Penanganan particulate solid– Yang termasuk pada langkah ini adalah

penyimpanan dan perpindahan dari raw polymeric material:• Raw Material:

- Pellets - Powders1-5 mm < 1 mm•Properties of particulate solids:• Flow• Withstand static stresses• Stresses are proportional to normal load rather than shear• Aglomeration

Distribusi Tekanan pada Bins and Hoppers

• Tekanan statis dibawah liquid column isotropik dan ditentukan oleh ketinggian column(h) dan juga massa jenis dari liquid tersebut(ρ)

P = ρgH• Di column yang mengandung particulate solid,

tekanan di dasar, tidak akan mengikuti rumus diatas.

• Pada gambar 4.5 shear stress pada dinding

• Dimana βw adalah kemiringan dari hopper tersebut, dan cw adalah koeffisien kohesi dari dinding.

• Untuk spesial Bin, yang memiliki h=H, dimana P1=0 dan cw=0( tak ada adhesi antara dinding dan solids.

Flow and Flow Instabilities in Hoppers

• Di saat pemmrosesan polimer kita harus memastikan bahwa semua polymer melewati flow rate hopper (gravitational flow) yang seharusnya.

• Ada 2 tipe gravitational flow, yaitu “mass” flow dan “funnel” flow

• Dari velocity and porosity fields, akhirnya dibagi atas 4 region:– Region A: Rupture zone, dimana deformasi banyak

terjadi– Region B: Rigid-body behavior– Region C: Free flow zone– Region D: Plug-flow zone

Particulate in the Extruder

• Sebuah tempat yang merupakan “solids” yang bergerak searah positif x, yang memiliki kecepatan u, yang dilapisi oleh sebuah lapisan yang bergerak secara konstan dengan V0, di kemiringan y, terhadap z.

Particulate in the Extruder

•V0 adala kecepatan pada bagian atas, f adalah kecepatan dari solids•Selanjutnya, keseimbangan gaya dari elemen diferensial pada Fig.4.16

Langkah Dasar II : Melting• Persamaan Kesetimbangan Energi.

Dimana adalah mungkinnya sumber energi homogen (i.e dielectric heating), adalah total jumlah bersih dari kenaikan internal energi per unit volum akibat sumber luar yaitu konduksi termal, adalah (dapat balik) laju kenaikan energi internal akibat kompresi, dan adalah (tak dapat balik) laju kenaikan energi internal akibat aliran dan deformasi.

Langkah Dasar II : Melting• Dua metode yang digunakan untuk memanaskan dan

melelehkan Polimer :a. Conduction Melting :

- tanpa pemindahan lelehan (jarang)- dengan pemindahan lelehan (i.e dengan

penambahan forced convection)b. Dissipative melt mixing

penggunaan paling efektif Viscous dissipation dan friction.

Langkah Dasar II : Melting

• Rendahnya nilai k (konduktifitas termal), menyebabkan konduksi tidak bisa bekerja sendiri dengan efektif untuk melelehkan polimer, harus menggunakan viscous dissipation dan konveksi untuk memindahkan bagian polimer yang telah dipanaskan dari permukaan pemanas dan membawa material baru ke permukaan pemanas.


• Untuk melelehkan beberapa polimer, dibutuhkan energi termal, berdasarkan nilai Entalpi dari masing-masing polimer.

Langkah Dasar II : Melting• Skematik representasi dari compacted polymeric solids yang meleleh

akibat panas permukaan dari luar. (gambar 1)

Conduction melting without melt removal


• Coduction MeltingPada gambar 1 terlihat bahwa, pada permukaan surface solids, terbentuk molten polymer akibat kontak antara polimer dengan permukaan solid dengan temperatur relatif tinggi terhadap polimer.mekanisme inilah yang dikenal dengan Conduction Melting without melt removal.

Langkah Dasar II : Melting• Conduction Melting

Faktor pengontrol laju :a. Termal konduktivitasb. Gradien temperatur yang dapat diterimac. Luas area kontak antara permukaan dan padatan yang meleleh.

Maka dari itu, sifat termal konduktifitas yang rendah dan temperatur sensivitas (degradasi termal) adalah pembatas/limit utama dari fluks panas yang dapat diterima oleh polimer.


• Conduction Melting without melt removal

Langkah Dasar II : Melting• Drag-induced and pressure induced melt removal

Mekanisme ini meningkatkan efisiensi pelelehan polimer, dengan memberikan tekanan terhadap polimer yang akan dilelehkan dengan tujuan memindahkan layer polimer yang telah terlelehkan, karena penurunan suhu antara hot surface dan solid polymer mengalami penurunan secara eksponensial.


• Conduction melting with forced melt removala. Drag Induced removal


• Conduction Melting with forced melt removal


• Pressure Induced Melt Removal


• The elegant drag-removal in SSEs.Punya beberapa kelebihan :a. signifikan gradien temperatur dapat dipertahankan.b. secara cepat memindahkan material yang baru terlelehkan dari vicinity (zona temperatur tinggi)c. Mereduksi resiko degradasi termald. Menghasilkan panas melalui viscous dissipation.


• Compressive Melting-) Polymer dan lelehannya incompressible-) Tekanan tinggi dibutuhkan untuk istilah

dalam menjelaskan secara rasional-) Menges dan Albe menunjukan bahwa proses compressive melting dapat berlangsung dalam proses injection molding.

Langkah Dasar II : Melting• Deformation Melting

Viscous liquid :a. sama dengan dan menunjukan nilai Viscous Energy Dissipation (VED) yang dikarenakan Friksib. Menunjukan proses konversi irreversible deformasi mekanis menjadi panas.c. Mekanisme heat generation :

1. Plastic energy dissipation (PED)2. Frictional energy dissipation (FED) stricly

speaking


• Deformation Melting


• Homogenous Internal Meltinga. menggunakan Dielectric charge sebagai sumber panas, dan membuat Volumwide homogenous heat source.b. Persamaan kesetimbangan energi

c. Limited dalam Polymer processing.


• Summary :


• Summary :



Material Polimer Final

Documents

langkah dasar

fluted mixing

thin melt

cylindrical

fluted mixing

maddock melting

maddock mixing

forced melt