ALBERT

Description: We study the flow of a thin liquid film along a flexible substrate. The flow is modelled using lubrication theory, assuming that gravity is the dominant driving force. The substrate is modelled as an elastic beam that deforms in two dimensions. Steady solutions are found using numerical and perturbation methods, and several different asymptotic regimes are identified. We obtain a complete characterization of how the length and stiffness of the beam and the imposed liquid flux determine the profile of the liquid film and the resulting beam deformation. © 2013 Cambridge University Press.

Description: A boundary-layer model, based on computational results, describes a number of features of two-dimensional convection in a porous medium: the heat flux, velocity, length and temperature scales and the pattern of flow. The cell structure is different from that for convection in a viscous fluid. The model is valid for a limited range of the Rayleigh number. © 1976, Cambridge University Press. All rights reserved.

Description: SUMMARYSeventy-nine Finnish Landrace x Dorset Horn ewes in lamb to Suffolk rams were used in a comparative slaughter experiment to assess the effects of numbers of foetuses on the growth of the products of conception. The mean number of foetuses was 2·7, with a range from 1 to 5. The ewes were individually penned and given a standard diet with metabolizable energy concentration 7·7 MJ/kg and N concentration 21 g/kg, rationed at 2 kg/day during the first month and 1·25 kg/day during the second and third. Allowances beyond that time were on two scales and depended on the number of foetuses being carried as diagnosed by radiography. The ewes were slaughtered between 50 and 145 days of gestation. The gravid uterus was dissected into foetal, placental, foetal fluid and empty uterus components. Equations were fitted to the weights of each component to describe the effects of stage of gestation, litter size and ewe weight. For the mean weight per foetus (Y, kg) the preferred equation isIn (Y)= 2·419–17·574e-0.01976t–00079ft+0–0046w,where tis the time in days from conception, / is the number of foetuses and wis the weight (kg) of the ewe at mating. This is a version of the Gompertz equation, with additional terms to express the effects of / and w.The weights of the placenta and of the empty uterus were similarly fitted by versions of the Gompertz equation but the mean weight of fluids per foetus (Z, kg) or, rather, its natural logarithm was best described by a third degree polynomial, which isIn(Z) = –11·518 + 0–326t;–0·00316t2+0·0000102t3.None of the weights was significantly affected by the level of feeding in late pregnancy.Estimates of mean weights from the equations and of daily rates of gain in weight from the first differentials of the equations are tabulated against stage of gestation and litter size, and the forms of the weight, growth rate and specific growth-rate curves are illustrated graphically.The equation for foetal weight estimates that at the end of pregnancy the mean weight per foetus is reduced by a factor of 0–89 for each additional foetus being carried. The mathematical model implies that the differences originate in early pregnancy, when the factor is very close to unity, and that the mean weights gradually diverge. In the absence of direct evidence this would appear to be the simplest hypothesis, rather than the assumption in most of the earlier literature that the effect is entirely confined to the last 4 or 5 weeks of gestation.Just before parturition the total daily weight gain of quadruplet foetuses was about 250 g and was associated with a similar gain in weight of foetal fluids, the ratio of fluid weight to foetal weight appearing to increase with litter size. The ewes were clearly under considerable physical stress. It is suggested that this aspect must be closely considered when greater prolificacy is sought.

Description: SUMMARYFrom 62 days of gestation to parturition, 20 Finnish Landrace x Dorset Horn ewes were each offered one of four diets with roughage to concentrate ratios of 20:80; 40:60; 60:40 and 80:20, at daily metabolizable energy and digestible crude protein intakes of 490 kJ and 3·55 g/kg W0·75 respectively. Plasma concentration of free fatty acids, glucose and urea were determined weekly, and nitrogen balance and digestibility trials were carried out at 70–80 and 130–140 days of gestation.On all treatments the concentration of plasma free fatty acids increased during pregnancy from approximately 200–600 μ-equiv./l and the concentration of glucose and urea decreased by approximately 25%.Digestibility coefficients for dry matter and organic matter increased from 58 to 68% and from 60 to 70% respectively as the proportion of concentrates in the diet increased and were not affected by stage of gestation. The apparent digestibility of nitrogen was not affected by the energy concentration of the diet.Between mid and late gestation there was a mean increase in daily nitrogen retention of 2·5 g and an improvement in the efficiency of nitrogen utilization of 19 percentage units.Nitrogen retention and the efficiency with which the apparently digested nitrogen intake was retained increased as the dietary energy concentration was increased. The mean daily increases in nitrogen retention were 0·0135 and 0·0039 g for each percentage unit increase in the concentrate portion of the diet at mid and late gestation respectively. The corresponding values for the improvement in the efficiency of nitrogen utilization were 0·13 and 0·10%.

Description: SummaryMeasurements of 21 bone lengths and breadths were made on radiographs of 215 foetuses of known gestational ages ranging from 50 to 145 days obtained from 80 Finnish Landrace x Dorset Horn ewes. Number of foetuses per ewe varied from 1 to 5, but the main statistical analyses were based on the 22 sets of twins, 34 of triplets and 11 of quadruplets. Equations were fitted to relate each of the linear measurements to foetal weight alone, to foetal age alone, to foetal age together with number of foetuses, and to foetal age together with foetal weight. It was found that there were significant differences between the twins, triplets, and quadruplets in the lengths their bones attained at any specified weight or at any specified age but not when both weight and age were fixed. The relationships to weight and age jointly were significantly closer than to either of them alone even after allowing for number of foetuses. The mathematical model that fitted best was a modified Gompertz equation of the formwhere ywas the measured length, w was the number of days prior to expected parturition, w was foetal weight, wu was an estimate of the expected foetal weight at time u, and P, Q, R and Dwere fitted constants.

Description: SUMMARYSeventy-eight Finnish Landrace × Dorset Horn ewes in lamb to Suffolk rams were slaughtered serially between 50 and 145 days of gestation. The mean litter size was 2·7. The daily feeding regime aimed to provide each ewe with 15 MJ of metabolizable energy (ME) in the first month of gestation and 9·4 MJ in the second and third. Thereafter the ewes were provided with a basal intake of either 9·6 MJ (low plane, LP) or 13·4 MJ (high plane, HP) plus 1·3 MJ for each foetus.For ewes with 2, 3 and 4 foetuses the mean percentage changes in maternal body weight over pregnancy were respectively — 5, — 10 and — 14 (LP) or + 3, — 2 and — 6 (HP). Changes in weights of blood, liver and the empty gastro-intestinal tract through gestation varied with the plane of nutrition but not with number of foetuses. In contrast, udder weight at parturition was dependent on number of foetuses but not on plane of nutrition.Increased hydration of the maternal tissues in late pregnancy tended to mask concurrent losses of body fat. For example, over the last 2 months, HP ewes carrying quadruplets lost on average 1·0 kg in body weight but 5·5 kg of (chemically determined) fat. The latter was lost at a rate which increased up to an average of 170 g/day over the last 2 weeks of pregnancy. Net changes in body protein were estimated to be relatively small, but there was some redistribution, including loss from muscle and gain by the udder. There was no evidence of any demineralization of the maternal skeleton.The practical significance of the changes in body composition is discussed, in particular that of the increasing rates of loss of body fat with increasing litter size. It is suggested that the dangers implicit in these rates of fat loss must be taken into consideration when deciding on dietary regimes and the timing of breeding cycles for highly prolific ewes, or indeed when embarking on a programme of increased prolificacy.

Description: SUMMARYNine individually penned Finnish Landrace x Dorset Horn ewes with a mean litter size of 2·33 were offered a diet containing 63% digestible organic matter (DOM) and 13% crude protein in the dry matter at a daily intake of 0·82 kg DOM (1·3 x maternal maintenance) from 95 to 110 days of gestation. On day 111 DOMI was abruptly reduced to either 0·67 kg (T1, 0·54 kg (T2) or 0·36 kg (T3)/day and kept at these levels until a few days pre-partum.Daily N balance before food restriction was 4·9 ± 0·51 g/day. During the periods 3·9 (S1), 11·17 (S2) and 19·25 (S3) days after food restriction daily N balance was 2·8, 2·8 and 3·6 g for θwes on T1, 1·0,1·0 and 0·8 g for those on T2 and –4·1, -4·0and -4·0 g for those on T3. Total lamb birth weight was 8·0, 7·2 and 6·5 kg for treatments T1, T2 and T3 respectively. Using regression analysis it was calculated that plasma glucose concentration in late pregnancy for ewes with a total lamb birth weight of 8 kg fell below the pre-restriction value of 52 mg/100 ml when daily DOMI was reduced to 747 g. At this intake the plasma FFA concentration was 585/i-equiv./I compared with 288 before food restriction. Corresponding values for daily N balance were 5·1 and 4·9 g. A reduction in daily energy intake below 0·75 kg DOM resulted in a rapid decrease in plasma glucose and N balance, the latter being proportional to the increase in the concentration of plasma FFA. The mean daily loss of N from the maternal body was estimated to be 0·4, 1·6 and 6·1 g for treatments T1 to T3 respectively during the period of food restriction.

Description: SUMMARYTwelve Finnish Landrace × Dorset Horn ewes with a mean litter size of 1·92 and a mean body weight of 75±3 kg were individually penned from 80 days of gestation to parturition and offered a diet with a metabolizable energy (ME) and crude protein content in the dry matter of 9·7 MJ/kg and 11·4% respectively. At 120 days of gestation daily ME intake was abruptly reduced from a mean of 0·48 to 0·25 MJ/kg W0·75 for a period of 10 days.The observed increase in the plasma concentration of urea due to the reduction in food intake was better correlated with lamb birth weight (r = 0·87) than was the increase in plasma free fatty acid concentration (r = 0·53) or the decrease in plasma glucose concentration (r = 0·76). Mean daily nitrogen balance decreased from a mean of 5·6 g before food restriction to – 1·8 g after food restriction. Although the effect was not significant, single bearing ewes excreted more total and urea nitrogen in the urine than multiple bearing ewes before food restriction. During food restriction the trend was reversed. The change in urea nitrogen excretion (Y, g/day) that resulted from the reduction in food intake was correlated (r = 0·73, P 〈 0·01) with lamb birth weight (X, kg); the relationship was Y = 0·54(±0·16)X – 3·48. It was estimated that the daily loss of nitrogen from the maternal body during the period of food restriction was approximately 80% of published values for the urinary nitrogen excretion of fasting non-pregnant sheep.

Description: SUMMARYThe concentrations of dry matter, crude protein, fat and ash and of Ca, P, Mg, Na and K were determined for 22 sets of twin foetuses, 33 of triplets and 11 of quadruplets of known gestational ages within the range 55–145 days. In addition, determinations were made of the concentrations of dry matter, crude protein, fat and ash in their associated placentae and empty uteri, and of dry matter, nitrogen, energy and ash in the foetal fluids. The dry matter, crude protein and fat concentrations in the placentae increased with foetal age and decreased with increasing litter size. Ash concentrations were unaltered. There was no effect of litter size or foetal age on the concentration of nutrients in the empty uteri. Dry matter and nitrogen concentrations in the fluids increased with foetal age but were independent of litter size, whereas ash concentrations increased with litter size but not with age.The form of the mathematical model for foetal growth is considered in relation to the estimation of rates of accretion and the estimation of the differences in composition to be expected between foetuses that are heavy and others that are light relative to their age. When the weights of the foetal constituents were fitted by Gompertz equations extended to include foetal weight as an allometric term, the effects of litter size on foetal composition could be estimated from the foetal weights for each size of litter. Concentrations of dry matter and of most constituents in the foetuses became less as numbers of foetuses increased, irrespective of stage of gestation.A description of the changing composition of the growing foetuses was provided by specific growth rates calculated from the fitted equations. With minor exceptions, derived estimates of foetal concentrations of each constituent were found to agree quite well with most previously published estimates for ovine foetuses, but similar agreement on daily accretion rates was not to be expected in view of the sensitivity of such estimates to the choice of model for foetal growth. Rates of accretion in the gravid uterus increased up to about 5 weeks before parturition and tended to level off thereafter, but most of them still increased slightly over the last 2 weeks, even in ewes bearing triplets or quadruplets. Taking account of the changes in the maternal body of the ewes, it was concluded that although the prolific ewes incurred a substantial energy deficit, and could not have consumed sufficient of the diet to avoid this, their intakes in late pregnancy were nevertheless adequate to support the high rates of accretion of protein and of minerals in the gravid uterus.