Andrey Varlamov SPIN-CNR, Italy in collaboration with

Attilio Rigamonti, Giuseppe Balestrino

Physicist in the kitchen: exploring the gastronomic universe

School  &  Conference  on  Nanoscience  and  Quantum  Transport    Kiev,  October,  9,  2016  

Outline  

General formula for the cooking time

Heat flow

D  

∂T ρ,τ( )∂τ

=κΔT ρ,τ( ) =κ 1ρ2

∂∂ρ

ρ2∂T ρ,τ( )∂ρ

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1τ

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τ cook = aD2 + b

1.  So--­‐boiled  egg  

τ cook = 0.451M2/3 ln 0.76

Tegg −TwaterTyolk −Twater

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Dr.  Charles  D.  H.  Williams,  a  lecturer  in  physics  at  University  of  Exeter  :  

Mass (pounds)

Cooking time (hours)

6 3 8 3.5

12 4.5 16 5.5 20 6.5 24 7.35

2. The Thanksgiving day turkey secret

τ cook = aM2/3 + b

τ cook3

M 2

3. Physics of Pasta

Het flow and water diffusion

Cooking time: τ = aD2 +b

Heat transfer:

Water diffusion:

∂T∂τ

=κΔT

∂n∂τ

= DΔn

Tipo di pasta Diametro est. D

Diametro int. d

Tempo di cottura sper.

Tempo di cottura teor.

Capellini n.1 1.15 mm -- 3 min 2 min

Spaghettini n. 3

1.45 mm -- 5 min 5.0 min

Spaghetti n. 5

1.75 mm -- 8 min 8.2 min

Vermicelli n. 7 1.90 mm -- 11 min 10.7 min

Vermicelli n. 8 2.05 mm -- 13 min 13.0 min

Bucatini 2.70 mm 1mm 8 min 25 min ?!

a = 3.8 min / mm2 b = - 3 min

Table of cooking times for the different types of cylindrical shape pasta

τ=aD2 +b

The case of bucatini requires the particular treatment. The

correct formula is: τ=a(D-d)2 +b

For bucatini: τ = 8.2 min !

P=ρgh=2σ/rmin

dmin=2 rmin ~ 4σ/ ρgh h=2cm, σ=0.05 N/m

g=9.8 m/s 2

dmin ~ 1mm

Fall down of our simple theory for too thin pasta

Capellini: D = 1.15 mm

τcap = 3.8 [1.15]2 - 3 ≈ 2 min

aDcr2 + b = 0

Dcr = | b | /a ≈ 0.85mm

Why spaghetti do not break into two pieces?

The breaking dynamics: (B.Audoli, S.Neukirch, PRL, August 2005)

When the rod is broken, one could expect that the generated elastic waves help to both pieces of rod to relax to equilibrium.

Invece, si verifica che queste onde aumentano lo stress locale, rendendo probabile la rottura della bacchetta anche in altri punti. Ne consegue una frammentazione.

Fast removing of the constrain from the extremity of the half-rod results in generation of the elastic wave:

Simul.mov

Chinese  vapor  cooked  dumplings  

5. Physics of a Good Coffee

Italian Moca

Filtration: the Darcy Law

P(T)=Patm+ΔP

}

 ΔP  =  Q  η  L/(Sρ  κ)    

 η( °C) = 10 -3 Pa s

ΔP∼4·∙104 Pa → T* ~ 110 °C

 Q  =  m/t~200  g/min  

L~ 1 cm

P=Patm

→

S~ 10 cm2

κ ~ 10-12

Q =κ ⋅S ⋅ρ ⋅ ΔP

L ⋅η

The limitation of the Darcy Law at small pressures: opening of the cappillars

Espresso machine

Q =κ ⋅S ⋅ρ ⋅ ΔP

L ⋅η

Ancestors  of  pizza  in    ancient  Lmes  Pharaonic    birthdays  in  Ancient  Egypt  

Flat  cakes  with  vegetables  used  to  eat  in  the  Near  East  and  pharaonic  Egypt  

Ancestors  of  pizza  in    ancient  Rome  In  Pseudo  Virgilio,  poem  “Il  Moretum”,  cooking  of  some  kind  of  a  flat  cake  dressed  by  olive  oil,  salt,  garlic  and  spice  herbs  was  described  

Mozzarella  as  the  result  of    Longobardi  invasion  

Arrival  of  tomato’s  from  America  to  Naples  due  Spanish  and  Bourbon  rule  

Birth  of  the  modern  pizza  in  Naples  at  the  end  of    XVIII  

Royal  visit  of  Naples  in  1889  

Beginning  of  XX:  pizza  emigraLon  

CelebraLon  of  100  years  of  Margherita  in  1989  Naples  

The  facts  to  think  

Pizza  Romana  325-­‐  330  0С  à  2  min  

Pizza  Napoletana:  460-­‐490  0С  .    

40  -­‐50  à80-­‐100  customers        In  rush  Lme  330  0С  à  390  0С  .    

97  F  =36.10С  

t0  

x  

Homogeneous  temperature  distribuLon  

Temperature  profile  in  homogeneous  media  

The  same  but  with  a  cooler  steel  “head”  

Normal  head  

Temperature  profile  in  non-­‐homogeneous  media  

c= 1MΔQΔT

Specific  heat  capacity:  

Heat  flow:  

Heat  flow:  a  ligle  bit  of  school  physics  

M  is  the  body  mass,  ΔQ  is  the    Heat  transferred  to  it,  ΔT  is  the    change  of  its  temperature.    

q= - ΔQSΔt

 -­‐  “speed”  of  temperature  change    in  the  space  

Heat  flow  in  a  cylinder  from  hot  (T0+DT)  to  cold  (T0).  NoIce,  the  temperature  decreases  from  leL  to  right!  

ΔTΔx"

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 coefficient  of  thermal  conducLvity    

L t( )

ΔQS ⋅ t

= c ⋅ρ ⋅L t( ) ⋅ ΔT

t= κ ΔT

L t( )

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$%%

&

'((

χ= κc ⋅ρ

PropagaLon  of  the  heat  front  

Heat  length  

-­‐-­‐  is  the  coefficient  of  the  temperature  conducLvity    

Exact  answer  is  

Temperature  at  interface  between  two  semispaces  

T1  T0  T2  

L1 t( ) = χ1 ⋅ t

L2 t( ) = χ2 ⋅ t q  

Interface  temperature  

T0 =T1 +νT21+ν

ν =κ2κ1

χ1χ2

Wood  oven:  Dough/firebrick:    νDf=0.65  

T1=330  0C,  T2=20  0C  

T1=330  0C,  T2=20  0C,  T0=280  0C    

T1=230  0C,  T2=20  0C,  T0=208  0C    

Electric    oven  with  steel  bogom:    Dough/steel:  νDS=0.1  

What  temperature  in  oven  would  be  good  for  pizza?  

Three  ways  of  heat  transfer  

Thermal  radiaIon  

σ = 5.67 ⋅10−8W / K 4 ⋅m2( )

Its  intensity,  i.е.,  the  amount  of  radiaLon  energy  arriving  each  second  to  1сm2  of  surface  in  the  oven,  is  determined  by  the  Stefan-­‐Boltzmann  law:    

is  the  so-­‐called  Stefan-­‐Boltzmann  constant    

ELECTRIC  OWEN  

For  the  much  less  heated  electric  oven  (t=230  0C=503  K)    the    corresponding  amount  of  energy,  incident  to  1сm2  of  pizza  surface,    is  more  than  twice  less:  

WOOD  OVEN  

RadiaLon  contribuLon  for  baking  pizza  

Here    one    should    noLce,    that,    in    its    turn,    the    pizza    also    irradiates    out    a    “flow”    of    the    intensity        Since  the  major  part  of  the  baking  Lme  is  required  for  the  evaporaLon  of  water  contained  in  the  dough  and  toppings,  we  can  assume    

           𝑇pizza=  100℃  =  373  𝐾  ,      which    results    in    a    radiaLon    intensity    of      

                       104𝑊/𝑚2,      i.e.,  15%  of  the  obtained  radiaLon,  the  pizza  “returns”  to  the  oven.      

The  amount  of  heat  1  cm2  of  pizza  receives  per  second    through  its  bogom    

Total  amount  of  heat  1  cm2  of  pizza  receives  per  second  

This  value  is  used  to  heat  1  cm2    of  pizza  from  20  0C  to  the  boiling  temperature  of  water  100  0C        

During  the  process  of  baking  the  perfect  pizza  we  apparently    evaporate  water  from  the  dough,  tomatoes,  cheese,  and  other  ingredients.  We  need  to  take  the  required  energy  for  this  into  account  as  well.    If  one  assumes  that  the  mass  fracLon  α  (which  is  water,  for  Roman  pizza  α=20%)  evaporates  from  the    dough  and  all  topping  one  gets:    

Смачного!