No abstract

A general expression is derived for the fluid force on a body of simple shape moving with a velocity v through inviscid fluid in which there is an unsteady non-uniform rotational velocity field u0(x,t) in two or three dimensions. It is assumed that the radius is small compared with the scale over which the strain rate changes, though for the sphere it is also assumed that the changes in the ambient velocity field over the scale of the sphere are small compared with the velocity of the body relative to the flow. Given these approximations it is shown that the effects of the rate of change of the vorticity of the ambient flow is of second order and can be neglected. However the rate of change of the irrotational straining motion is included in the analysis. It is shown that the inertial forces derived by many authors for irrotational flow can be simply added to a generalization of the lift force derived by Auton (1987) in a companion paper. It is shown how this lift force is made up of a rotational and an inertial or added-mass component. For three-dimensional bluff bodies the latter is generally larger (by a factor of three for a sphere), and can be simply calculated from the added-mass coefficient. For illustration, the general expression is used to derive formulae for (i) the motion of a spherical bubble in a steady non-uniform flow to contrast with the motion in an unsteady flow, and (ii) the motion of rigid volumes of neutral density across an inviscid shear flow. These results show how added-mass (and lift) forces lead to different motions for a sphere and a cylinder. The general expression is useful in two-phase flow calculations, and for indicating the forces and motions of ‘lumps of fluid’ in turbulent flows.

Purpose A pathologic complete response (pCR; ypT0N0) of a rectal tumor after neoadjuvant radiochemotherapy (RCT) is associated with an excellent prognosis. Several retrospective studies have investigated the effect of increasing the delay after RCT. The aim of this study was to evaluate the effect of increasing the interval between the end of RCT and surgery on the pCR rate. Methods GRECCAR6 was a phase III, multicenter, randomized, open-label, parallel-group controlled trial. Patients with cT3/T4 or Tx N+ tumors of the mid or lower rectum who had received RCT (45 to 50 Gy with fluorouracil or capecitabine) were included. Patients were randomly included in the 7-week or the 11-week (11w) group. Primary end point was the pCR rate defined as a ypT0N0 specimen (NCT01648894). Results A total of 265 patients from 24 centers were enrolled between October 2012 and February 2015. The majority of the tumors were cT3 (82%). After RCT, surgery was not performed in nine patients (3.4%) because of the occurrence of distant metastasis (n = 5) or other reasons. Two patients underwent local resection of the tumor scar. A total of 47 (18.6%) specimens were classified as ypT0 (four had invaded lymph nodes [8.5%]). The primary end point (ypT0N0) was not different (7 weeks: 20 of 133, 15.0% v 11w: 23 of 132, 17.4%; P = .5983). Morbidity was significantly increased in the 11w group (44.5% v 32%; P = .0404) as a result of increased medical complications (32.8% v 19.2%; P = .0137). The 11w group had a worse quality of mesorectal resection (complete mesorectum [I] 78.7% v 90%; P = .0156). Conclusion Waiting 11 weeks after RCT did not increase the rate of pCR after surgical resection. A longer waiting period may be associated with higher morbidity and more difficult surgical resection.