London - Ashleigh Barty's bid to become the first woman since Serena Williams in 2015 to win the French Open and Wimbledon in the same year stayed on track with a 6-1, 6-3 second round victory over Belgium's Alison van Uytvanck on Thursday.
The 23-year-old Australian world number one will play British wild card Harriet Dart for a place in the last 16.
Barty said she would not be concerned by taking on a home hope in front of a partisan crowd.
"I wouldn't be playing a British crowd; I'm playing against Harriet," said Barty.
"Yes, she'll get more support being in Britain, as I would if we were in Australia. It's no different."
Barty, only the second Australian woman after Evonne Goolagong Cawley over 40 years ago to be number one in the world, said the most pleasure she has had in her new status is when she speaks to her niece back in Australia.
"Over and over she tells me you can go to infinity and beyond," sad Barty.
"She's an incredible little girl who gives me so much inspiration.
"It's been a very nice journey for myself, my team, my family, everyone. To be where we are now is really special."
Barty, who if she achieves the Roland Garros-Wimbledon double will be only the eighth woman to do so, said she would not be watching the blockbuster men's singles match between Rafael Nadal and her compatriot Nick Kyrgios later on Thursday.
"I think I'll be watching the cricket this afternoon," she said, referring to the second Ashes match between England's women and Australia.
Barty seized the initiative from the outset breaking Van Uytvanck, who had eliminated 2017 champion Garbine Muguruza in the second round of last year's tournament, twice in succession.
She repeated that in the second set and although the 25-year-old Belgian broke Barty when she served for the match, the Australian made no mistake when presented with a match point on her opponent's serve in the following game.
Also easing through was 2017 US Open champion Sloane Stephens who took the first eight games against her Chinese opponent Wang Yafan before winning 6-0, 6-2.
Stephens, seeded nine, will play either British 19th seed Johanna Konta or Katerina Siniakova of the Czech Republic in the next round.
They were merely the appetisers for the highly-charged men's singles second round match later on Thursday on Centre Court between two-time champion Nadal and the fiery but talented Kyrgios.
Kyrgios, who stunned the Spaniard when ranked 144th and aged 19 he beat him in 2014, and Nadal have exchanged words earlier this season with Nadal accusing the Australian of lacking respect.
Also on the programme is eight-time champion Roger Federer, looking for a more convincing display than his opening round four-setter, up against British wild card Jay Clarke.
It wll be asking a lot of Clarke to emulate Tim Henman, the only other Briton to beat the Swiss at Wimbledon back in 2001 in the quarter-finals.
Home fans appetites will be sated when former world number one Andy Murray plays in the men's doubles - months after 'life-changing hip surgery' - with French partner Pierre-Hugues Herbert against Marius Copil of Romania and Herbert's compatriot Ugo Humbert.
Murray's mixed doubles partner, seven-time champion Serena Williams will also be in action facing Slovenian qualifier Kaja Juvan.
Williams is chasing a record-equalling 24th major at the Wimbledon.