We present the results of Brownian dynamics simulations of a series of diff
erent polymer models which have been used to examine the recent experimenta
l findings of Smith et ad. (1999) who studied the dynamics of a single DNA
molecule in steady shear flow. The steady average extension at various Weis
senberg numbers (Wi) is shown to be well predicted by multimode nonlinear m
odels. Quite surprisingly, the normalized average extension x/L asymptotes
to less than 1/2 even for extremely large Wi and we discuss this result on
a physical basis. The probability density function of molecular extension a
t various values of Wi using the Kramer's chain and the finitely extensible
nonlinear elastic dumbbell suggests that the number of internal modes is i
mportant in a model designed to capture the dynamics of a real DNA molecule
. Three different frequency regimes in the power spectral density observed
at finite Wi in the experiments are shown to arise from the coupling of the
Brownian fluctuations in the gradient direction and the convection in the
streamwise direction. Our simulation results, especially in light of the ex
cellent agreement with experiment, demonstrate the basic physical elements
necessary for any rheological model to capture the dynamics of single polym
er chains in flow. (C) 2000 The Society of Rheology. [S0148-6055(00)00604-0
].