The integrated multiple mixing chamber

Physica IOY & 110B (1082) 2122-2115 North-Holland Publishing Company

2122

THE

INTEGRATED

Ralph

MULTIPLE

MIXING

CHAMBER*

ROSENBAUM

Depat?ment of Physics and Astronomy,

Tel Aviv University, Ramat Aviv 69978, Israel

The integrated multiple mixing chamber is a novel component which incorporates many mixing chambers, interconnected in tandem, into a single block of low thermal conductivity material. The integrated chamber is simple to build and easy to install, is leak-free, and is efficient and convenient to use in the “He circulating dilution refrigerator. It has vielded a factor of 2.5 or more in the reduction of the temperature over the minimum temperature of a single mixing chamber (12 mK).

1. Introduction The

trated in fig. 1, a small fraction of the initial “He charge per second (typically 10%) is allowed to

multiple

simple

mixing

and powerful

to temperatures dilution heat

step

transfer

colder

below

is a 3He

10 mK prior

3He-4He

solution

this method

avoids

boundary

resistance

problem

supported

direct

3He and the

in each the nasty

heat exchangers mixing chamber

* This work was partially

to the final

employs

the warmer

chamber;

conventional the multiple

scheme

of precooling

[l, 21. This method between

dilute

chamber

method

which

mixing

dilute or evaporate in each mixing chamber. This dilution process cools the remaining 3He in each chamber, significantly;

process absorbs any heat leaks The “He liquid is typically

Kapitza

proximately

plagues

chamber,

below 30 mK. In scheme as illus-

by the Israel Commission

for Basic Research.

thus reducing the and, in addition,

cooling reduction

5 mK in each is entirely

in temperature

@ 1982 North-Holland

In the last

from the previous

evaporated, of a factor

yielding

a

of 1.5-2.5

over the incoming temperature depending upon the magnitude of the heat leak to this chamber and upon the amount of 3He circulated per

Fig. 1. Schematic view of N mixing chambers incorporated into a single block of material. All of the chambers connected in tandem by holes or channels. The arrows designate the flow direction of the ‘He liquid.

037%4363/82/0000-0000/$02.75

enthalpy dilution

to the chamber. cooled by ap-

chamber.

any “He that remains steps

3He the

are internally

2123

R. Rosenbaum / Integrated multiple mixing chamber

second. initial

It is desirable

that

about

50%

of the

per second be evaporated

“He charge

in

the last chamber.

chamber

is relatively

0.3erg/s, minimum

as in our case, then number of chambers

lowest

temperature

above

The

Eindhoven

infinite

number

group

has

considered

of mixing

chambers

absence

of heat

tandem

in the

practical number

considerations, of mixing

connected leaks

of

there is a unique which yields the

of additional

mixing

yields

poor

this number

illustrated

say on the order

in the last mixing

The employment 2. Theoretical predictions

large,

only

chamber. chambers results,

as

in fig. 2. For our case of C& = 0.3 erg/s

an

and ri = 90 /Lmoles/s,

in

recommended.

three

to four chambers

are

[3]. For

we now consider a finite chambers connected in

3. Fabrication details

tandem. If the heat leak to each chamber, say on the order (based that

upon

eight

tandem

&

of 0.01 erg/s or less, then theory

conservation

or more

of enthalpy)

chambers

[4]. However,

should

if the heat

predicts be used

leak

It is highly

is small,

in

to each

desirable

tiple mixing block

of

rather

than

discrete

chamber low

thermal There

for integrating

numerous

the chambers:

in fabrication;

material,

the configuration are

(b) mechanical

the mulinto a single

conductivity

to construct

units.

leaks;

to “integrate” configuration

from

advantages

(a) minimization

ruggedness;

of

(c) simplicity

and (d) convenience

in use [2,4].

the success of the integrated Surprisingly, chamber is based upon excellent thermal isolation between adjacent chambers via the high

Tin =3OmK

Kapitza boundary resistance between the helium liquids and the walls of each mixing chamber and

k$ d x =Experimental Points.

via

the

low

thermal

conductivity

of the

body

material. Heat leak 6, =Wergs/sec 6

The integrated

X

‘iI \

from

\

greater l--______--

using

has been

100 A epoxy

casts well and machines

X x

Epibond

chamber

mechanical

since

easily

strength,

constructed this

material

[5]. However, one might

for

consider

Al for the body material since this metal low thermal conductivity in its

has an extremely ,f

tIeat!\

superconducting

state

below

1.1 K [6]. Fig.

shows a cross-sectional chamber. All of the

view outer

of the mixing

(excluding I

I

I

012345678

I

I

I

I

I

I

9

N(Totol

Number oft&‘s)

Fig. 2. Theoretical dependence of the temperature of the last mixing chamber as a function of the total number of mixing chambers employed. The calculations assume that each mixing chamber absorbs a heat leak of 0.3erg/s, that ri = ‘X)~~moles/s, and that the last mixing chamber dilutes 50% of ri.

holes

drilled

the

last

one)

45” apart

were

from

one

8 mm

3

integrated chambers diameter

another

on a

hole circle having a 48mm diameter. The last chamber was simply a 20 mm diameter hole cleared through the center of the body. Each chamber was interconnected to its adjacent neighbor through a 1.2 mm diameter hole drilled diagonally from the top of each chamber to the

2124

R. Rosenbaum

/ Integrated

multiple mixing chamber channel

to the top of the body

diameter

hole cleared

through

through

small diameter

return mixing

channel into the bottom of each chamber. The flow impedance

(128/7r)(L/d4)

into

outer (Z =

chamber

the top

of 20 mm each [3,7].

caps from epoxy holes

and

the

is diluted in that range in diameter

for the first few mixing

and have a length

Top and bottom mixing

from the

of each small hole determines

of the 3He which The holes typically

from 0.5, 0.6 and 0.8mm chambers

are drilled

In ad-

dition,

fraction chamber.

holes

a 4 mm

the body.

and

bottom

seal off the

the channels surfaces.

cap also has an epoxy-to-copper

milled

The

bottom

flange

adaptor

so that simple and rapid access to the last mixing chamber is possible (fig. 3). The completed chamber has a height of about 65 mm. The outer Fig. 3. Cross-sectional view of the integrated chamber fabricated from an epoxy rod. Details of the epoxy to flange adaptor are also shown. The arrows indicate the flow direction of the ‘He in the dilute 3He-4He return channel; not shown is the cleared vertical hole through the body through which the dilute 3He-4He exits to the top surface.

mixing chambers have depths of 25 mm, the small connecting holes have lengths of 20 mm, and the caps have thicknesses of 10 mm.

4. Experimental bottom

of its next adjacent

interconnection

directs

3He-4He solution upward the

(fig. 1). This

the 3He into

the colder

it is precooled

as it rises

where

to the phase

rather

neighbor

high

boundary

thermal

(fig. 1). Owing

conductivity

of

to 3He

Preliminary tegrated

connected

channel into

the

isolation. into

the

samples,

by

a long

of 1.5 mm width top

surface,

Another top

(10cm)

and 2 mm depth

mixing

ber

is shown

which

reason

provides

for directing

of the last chamber

which

are inserted

into

I

winding milled

results

using

chamber

the temperature

below 10 mK, the last two chambers must not be connected by a short diagonal drilled hole, but rather

results the quintuple

appear

(5) in-

in fig. 4, where

of the last (fifth) mixing as a function

I

of the

I

I

“INTEGRATED”

I

QUP\ITET(5)

cham-

total

I

I

3He

--l

MIXING

CHAMBER * ..

thermal the 3He

n‘

--.-1%

the last cham-

ber, from blocking the 3He flow. Each mixing chamber must also be connected to the dilute “He-4He return channel. This return channel is machined ‘into the bottom surface of the body; it is a 3 mm wide and 3mm deep channel which winds underneath all of the outer mixing chambers before making a long winding annular path (lo-15 cm long) to the last mixing chamber. The dilute stream exits from this return

i

_

is to prevent

‘\ Al--L_ 80

1 90

DO i

110

I

I

I20

130

/

140

4

(~moles/sec)

Fig. 4. Temperature dependence of the last (fifth) mixing chamber as a function of the total ‘He circulation rate. The integrated quintuple (5) mixing chamber was tested in this case.

R. Rosenbaum

circulation

rate.

A

minimum

/ Integrated

temperature

of

4.8 mK was reached in view of several problems: (a) a large external heat leak; (b) non-optimized flow impedances fabrication

for MC-3

mistake

diagonal

hole

diagonally

of

between

and MC-4;

in which a short 1.2 mm the

diameter last

bers: this short path resulted to the last mixing In

conclusion.

replace

two

was

drilled

mixing

cham-

in a large heat leak

the

integrated single

chamber mixing

yielding

a reduction

in temperature

2.5 or

more

the

temperature the dilution

1.5 mm long

chamber.

the conventional over

and (c) a

single

without any other refrigerator.

of a factor mixing

can

chamber, of

chamber

modifications

to

multiple mixing chamber

11175

References [l] A.Th.A.M. De Waele, A.B. Reekers and H.M. Gijsman. Physica 81B (1976) 323. [2] G.M. Coops, A.Th.A.M. De Waele and H.M. Gijsman. Cryogenics 19 (1979) 659. [3] Ralph Rosenbaum, preprint TAUP YSl-Xl of Ihe Department of Physics and Astronomy. Tel-Aviv IJniversity, Ramat-Aviv, 69978, Israel. [4] E. Polturak, R. Rosenbaum and R.J. Soulen, Jr., Cry ogenics 19 (1979) 715. [5] Epibond 100 Type A Epoxy has been discontinued; Emerson and Cumings’s Stycast 1266 epoxy can be substituted. [6] R.M. Mueller, C. Buchal, T. Oversluizen and F. Pobell. Rev. Sci. Instrum. 40 (1978) 515. [7] E. Polturak and R. Rosenbaum, Proc. Hakone Int. Symp., Japan (1977), T. Sugawara. ed. (Phys. Sot. of Japan, IY7X) p. 274.