  This paper presents data for supercooled squalane's frequency-dependent shear
modulus covering frequencies from 10 mHz to 30 kHz and temperatures from 168 K
to 190 K; measurements are also reported for the glass phase down to 146 K. The
data reveal a strong mechanical beta process. A model is proposed for the shear
response of supercooled liquids. The model is an electrical equivalent-circuit
characterized by additivity of the dynamic shear compliances of the alpha and
beta processes. The nontrivial parts of the alpha and beta processes are
represented by a "Cole-Cole retardation element", resulting in the Cole-Cole
compliance function well-known from dielectrics. The model, which assumes that
the high-frequency decay of the alpha shear compliance loss varies with angular
frequency as $\omega^{-1/2}$, has seven parameters. Assuming time-temperature
superposition for the alpha and the beta processes separately, the number of
parameters varying with temperature is reduced to four. From the temperature
dependence of the best-fit model parameters the following conclusions are
drawn: 1) the alpha relaxation time conforms to the shoving model; 2) the beta
relaxation loss-peak frequency is almost temperature independent; 3) the alpha
compliance magnitude, which in the model equals the inverse of the
instantaneous shear modulus, is only weakly temperature dependent; 4) the beta
compliance magnitude decreases by a factor of three upon cooling in the
temperature range studied. The final part of the paper briefly presents
measurements of the dynamic adiabatic bulk modulus covering frequencies from 10
mHz to 10 kHz in the temperature range 172 K to 200 K. The data are
qualitatively similar to the shear data by having a significant beta process. A
single-order-parameter framework is suggested to rationalize these
similarities.
