open my $ifh, '<', $filename
  or die "Cannot open '$filename' for reading: $!";
local $/;
foreach my $chunk ( split /Separator\s+\d+/, scalar(<$ifh>) ) {
  # yay chunk!
}

##</code><code>##

# I might be way off-base here:
no warnings 'uninitialized';
my $pattern = qr{Separator\s\d+};
my $callback = sub { warn "Chunk: @_" };
binmode($ifh);
my $offset = 0;
my $buffer = '';
while( sysread($ifh, my $byte, 1, $offset++) ) {
  $buffer .= $byte;
  if( $buffer =~ $pattern ) {
    $callback->( $buffer );
    $buffer = '';
  }
}